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Sample records for nonlinear multigrid algorithm

  1. Discrete Fourier analysis of multigrid algorithms

    NARCIS (Netherlands)

    van der Vegt, Jacobus J.W.; Rhebergen, Sander

    2011-01-01

    The main topic of this report is a detailed discussion of the discrete Fourier multilevel analysis of multigrid algorithms. First, a brief overview of multigrid methods is given for discretizations of both linear and nonlinear partial differential equations. Special attention is given to the

  2. A survey of parallel multigrid algorithms

    Science.gov (United States)

    Chan, Tony F.; Tuminaro, Ray S.

    1987-01-01

    A typical multigrid algorithm applied to well-behaved linear-elliptic partial-differential equations (PDEs) is described. Criteria for designing and evaluating parallel algorithms are presented. Before evaluating the performance of some parallel multigrid algorithms, consideration is given to some theoretical complexity results for solving PDEs in parallel and for executing the multigrid algorithm. The effect of mapping and load imbalance on the partial efficiency of the algorithm is studied.

  3. Analysis of a parallel multigrid algorithm

    Science.gov (United States)

    Chan, Tony F.; Tuminaro, Ray S.

    1989-01-01

    The parallel multigrid algorithm of Frederickson and McBryan (1987) is considered. This algorithm uses multiple coarse-grid problems (instead of one problem) in the hope of accelerating convergence and is found to have a close relationship to traditional multigrid methods. Specifically, the parallel coarse-grid correction operator is identical to a traditional multigrid coarse-grid correction operator, except that the mixing of high and low frequencies caused by aliasing error is removed. Appropriate relaxation operators can be chosen to take advantage of this property. Comparisons between the standard multigrid and the new method are made.

  4. Some multigrid algorithms for SIMD machines

    Energy Technology Data Exchange (ETDEWEB)

    Dendy, J.E. Jr. [Los Alamos National Lab., NM (United States)

    1996-12-31

    Previously a semicoarsening multigrid algorithm suitable for use on SIMD architectures was investigated. Through the use of new software tools, the performance of this algorithm has been considerably improved. The method has also been extended to three space dimensions. The method performs well for strongly anisotropic problems and for problems with coefficients jumping by orders of magnitude across internal interfaces. The parallel efficiency of this method is analyzed, and its actual performance on the CM-5 is compared with its performance on the CRAY-YMP. A standard coarsening multigrid algorithm is also considered, and we compare its performance on these two platforms as well.

  5. Large-Scale Parallel Viscous Flow Computations using an Unstructured Multigrid Algorithm

    Science.gov (United States)

    Mavriplis, Dimitri J.

    1999-01-01

    The development and testing of a parallel unstructured agglomeration multigrid algorithm for steady-state aerodynamic flows is discussed. The agglomeration multigrid strategy uses a graph algorithm to construct the coarse multigrid levels from the given fine grid, similar to an algebraic multigrid approach, but operates directly on the non-linear system using the FAS (Full Approximation Scheme) approach. The scalability and convergence rate of the multigrid algorithm are examined on the SGI Origin 2000 and the Cray T3E. An argument is given which indicates that the asymptotic scalability of the multigrid algorithm should be similar to that of its underlying single grid smoothing scheme. For medium size problems involving several million grid points, near perfect scalability is obtained for the single grid algorithm, while only a slight drop-off in parallel efficiency is observed for the multigrid V- and W-cycles, using up to 128 processors on the SGI Origin 2000, and up to 512 processors on the Cray T3E. For a large problem using 25 million grid points, good scalability is observed for the multigrid algorithm using up to 1450 processors on a Cray T3E, even when the coarsest grid level contains fewer points than the total number of processors.

  6. Nonlinear Multigrid for Reservoir Simulation

    DEFF Research Database (Denmark)

    Christensen, Max la Cour; Eskildsen, Klaus Langgren; Engsig-Karup, Allan Peter

    2016-01-01

    efficiency for a black-oil model. Furthermore, the use of the FAS method enables a significant reduction in memory usage compared with conventional techniques, which suggests new possibilities for improved large-scale reservoir simulation and numerical efficiency. Last, nonlinear multilevel preconditioning...

  7. High Performance Parallel Multigrid Algorithms for Unstructured Grids

    Science.gov (United States)

    Frederickson, Paul O.

    1996-01-01

    We describe a high performance parallel multigrid algorithm for a rather general class of unstructured grid problems in two and three dimensions. The algorithm PUMG, for parallel unstructured multigrid, is related in structure to the parallel multigrid algorithm PSMG introduced by McBryan and Frederickson, for they both obtain a higher convergence rate through the use of multiple coarse grids. Another reason for the high convergence rate of PUMG is its smoother, an approximate inverse developed by Baumgardner and Frederickson.

  8. Mapping robust parallel multigrid algorithms to scalable memory architectures

    Science.gov (United States)

    Overman, Andrea; Vanrosendale, John

    1993-01-01

    The convergence rate of standard multigrid algorithms degenerates on problems with stretched grids or anisotropic operators. The usual cure for this is the use of line or plane relaxation. However, multigrid algorithms based on line and plane relaxation have limited and awkward parallelism and are quite difficult to map effectively to highly parallel architectures. Newer multigrid algorithms that overcome anisotropy through the use of multiple coarse grids rather than relaxation are better suited to massively parallel architectures because they require only simple point-relaxation smoothers. In this paper, we look at the parallel implementation of a V-cycle multiple semicoarsened grid (MSG) algorithm on distributed-memory architectures such as the Intel iPSC/860 and Paragon computers. The MSG algorithms provide two levels of parallelism: parallelism within the relaxation or interpolation on each grid and across the grids on each multigrid level. Both levels of parallelism must be exploited to map these algorithms effectively to parallel architectures. This paper describes a mapping of an MSG algorithm to distributed-memory architectures that demonstrates how both levels of parallelism can be exploited. The result is a robust and effective multigrid algorithm for distributed-memory machines.

  9. Multigrid

    CERN Document Server

    Trottenberg, Ulrich; Schuller, Anton

    2000-01-01

    Multigrid presents both an elementary introduction to multigrid methods for solving partial differential equations and a contemporary survey of advanced multigrid techniques and real-life applications.Multigrid methods are invaluable to researchers in scientific disciplines including physics, chemistry, meteorology, fluid and continuum mechanics, geology, biology, and all engineering disciplines. They are also becoming increasingly important in economics and financial mathematics.Readers are presented with an invaluable summary covering 25 years of practical experience acquired by the multigrid research group at the Germany National Research Center for Information Technology. The book presents both practical and theoretical points of view.* Covers the whole field of multigrid methods from its elements up to the most advanced applications* Style is essentially elementary but mathematically rigorous* No other book is so comprehensive and written for both practitioners and students

  10. Nonlinear Multigrid solver exploiting AMGe Coarse Spaces with Approximation Properties

    DEFF Research Database (Denmark)

    Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter

    The paper introduces a nonlinear multigrid solver for mixed finite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstructured problems is the guaranteed approximation property of the AMGe coarse...... properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on unstructured meshes has the ability to be as powerful/successful as FAS on geometrically refined meshes. For comparison, Newton’s method and Picard iterations with an inner state-of-the-art linear solver...... are compared to FAS on a nonlinear saddle point problem with applications to porous media flow. It is demonstrated that FAS is faster than Newton’s method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate...

  11. Multigrid Reduction in Time for Nonlinear Parabolic Problems

    Energy Technology Data Exchange (ETDEWEB)

    Falgout, R. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Manteuffel, T. A. [Univ. of Colorado, Boulder, CO (United States); O' Neill, B. [Univ. of Colorado, Boulder, CO (United States); Schroder, J. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2016-01-04

    The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.

  12. Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

    Science.gov (United States)

    Costiner, Sorin; Taasan, Shlomo

    1994-01-01

    This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

  13. HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. Part I. Multilevel Analysis

    NARCIS (Netherlands)

    van der Vegt, Jacobus J.W.; Rhebergen, Sander

    2011-01-01

    The hp-Multigrid as Smoother algorithm (hp-MGS) for the solution of higher order accurate space-(time) discontinuous Galerkin discretizations of advection dominated flows is presented. This algorithm combines p-multigrid with h-multigrid at all p-levels, where the h-multigrid acts as smoother in the

  14. NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES

    Energy Technology Data Exchange (ETDEWEB)

    Christensen, Max La Cour [Technical Univ. of Denmark, Lyngby (Denmark); Villa, Umberto E. [Univ. of Texas, Austin, TX (United States); Engsig-Karup, Allan P. [Technical Univ. of Denmark, Lyngby (Denmark); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2016-01-22

    The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.

  15. Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator

    International Nuclear Information System (INIS)

    Babich, R.; Brower, R. C.; Rebbi, C.; Brannick, J.; Clark, M. A.; Manteuffel, T. A.; McCormick, S. F.; Osborn, J. C.

    2010-01-01

    We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called γ 5 -Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume.

  16. Some nonlinear space decomposition algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Tai, Xue-Cheng; Espedal, M. [Univ. of Bergen (Norway)

    1996-12-31

    Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.

  17. Multigrid methods for partial differential equations - a short introduction

    International Nuclear Information System (INIS)

    Linden, J.; Stueben, K.

    1993-01-01

    These notes summarize the multigrid methods and emphasis is laid on the algorithmic concepts of multigrid for solving linear and non-linear partial differential equations. In this paper there is brief description of the basic structure of multigrid methods. Detailed introduction is also contained with applications to VLSI process simulation. (A.B.)

  18. Recent Development of Multigrid Algorithms for Mixed and Noncomforming Methods for Second Order Elliptical Problems

    Science.gov (United States)

    Chen, Zhangxin; Ewing, Richard E.

    1996-01-01

    Multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements are considered. The construction of several coarse-to-fine intergrid transfer operators for nonconforming multigrid algorithms is discussed. The equivalence between the nonconforming and mixed finite element methods with and without projection of the coefficient of the differential problems into finite element spaces is described.

  19. Nonlinear multigrid solvers exploiting AMGe coarse spaces with approximation properties

    DEFF Research Database (Denmark)

    Christensen, Max la Cour; Vassilevski, Panayot S.; Villa, Umberto

    2017-01-01

    discretizations on general unstructured grids for a large class of nonlinear partial differential equations, including saddle point problems. The approximation properties of the coarse spaces ensure that our FAS approach for general unstructured meshes leads to optimal mesh-independent convergence rates similar...... to those achieved by geometric FAS on a nested hierarchy of refined meshes. In the numerical results, Newton’s method and Picard iterations with state-of-the-art inner linear solvers are compared to our FAS algorithm for the solution of a nonlinear saddle point problem arising from porous media flow...

  20. A multigrid algorithm for the cell-centered finite difference scheme

    Science.gov (United States)

    Ewing, Richard E.; Shen, Jian

    1993-01-01

    In this article, we discuss a non-variational V-cycle multigrid algorithm based on the cell-centered finite difference scheme for solving a second-order elliptic problem with discontinuous coefficients. Due to the poor approximation property of piecewise constant spaces and the non-variational nature of our scheme, one step of symmetric linear smoothing in our V-cycle multigrid scheme may fail to be a contraction. Again, because of the simple structure of the piecewise constant spaces, prolongation and restriction are trivial; we save significant computation time with very promising computational results.

  1. A parallel version of a multigrid algorithm for isotropic transport equations

    International Nuclear Information System (INIS)

    Manteuffel, T.; McCormick, S.; Yang, G.; Morel, J.; Oliveira, S.

    1994-01-01

    The focus of this paper is on a parallel algorithm for solving the transport equations in a slab geometry using multigrid. The spatial discretization scheme used is a finite element method called the modified linear discontinuous (MLD) scheme. The MLD scheme represents a lumped version of the standard linear discontinuous (LD) scheme. The parallel algorithm was implemented on the Connection Machine 2 (CM2). Convergence rates and timings for this algorithm on the CM2 and Cray-YMP are shown

  2. Subroutine MLTGRD: a multigrid algorithm based on multiplicative correction and implicit non-stationary iteration

    International Nuclear Information System (INIS)

    Barry, J.M.; Pollard, J.P.

    1986-11-01

    A FORTRAN subroutine MLTGRD is provided to solve efficiently the large systems of linear equations arising from a five-point finite difference discretisation of some elliptic partial differential equations. MLTGRD is a multigrid algorithm which provides multiplicative correction to iterative solution estimates from successively reduced systems of linear equations. It uses the method of implicit non-stationary iteration for all grid levels

  3. Multigrid Algorithms for the Solution of Linear Complementarity Problems Arising from Free Boundary Problems.

    Science.gov (United States)

    1980-10-01

    solving (1.3); PFAS combines the concepts of multigrid algorithms with those of projected SOR. In Section 3, we discuss the implementation of PFAS, and...numerique de la torsion elasto- plastique d’une barre cylindrique. In Approximation et Methodes Iteratives de Resolution d’Inequations Variationelles et

  4. Simultaneous multigrid techniques for nonlinear eigenvalue problems: Solutions of the nonlinear Schrödinger-Poisson eigenvalue problem in two and three dimensions

    Science.gov (United States)

    Costiner, Sorin; Ta'asan, Shlomo

    1995-07-01

    Algorithms for nonlinear eigenvalue problems (EP's) often require solving self-consistently a large number of EP's. Convergence difficulties may occur if the solution is not sought in an appropriate region, if global constraints have to be satisfied, or if close or equal eigenvalues are present. Multigrid (MG) algorithms for nonlinear problems and for EP's obtained from discretizations of partial differential EP have often been shown to be more efficient than single level algorithms. This paper presents MG techniques and a MG algorithm for nonlinear Schrödinger Poisson EP's. The algorithm overcomes the above mentioned difficulties combining the following techniques: a MG simultaneous treatment of the eigenvectors and nonlinearity, and with the global constrains; MG stable subspace continuation techniques for the treatment of nonlinearity; and a MG projection coupled with backrotations for separation of solutions. These techniques keep the solutions in an appropriate region, where the algorithm converges fast, and reduce the large number of self-consistent iterations to only a few or one MG simultaneous iteration. The MG projection makes it possible to efficiently overcome difficulties related to clusters of close and equal eigenvalues. Computational examples for the nonlinear Schrödinger-Poisson EP in two and three dimensions, presenting special computational difficulties that are due to the nonlinearity and to the equal and closely clustered eigenvalues are demonstrated. For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N and for the corresponding eigenvalues. One MG simultaneous cycle per fine level was performed. The total computational cost is equivalent to only a few Gauss-Seidel relaxations per eigenvector. An asymptotic convergence rate of 0.15 per MG cycle is attained.

  5. Multidimensional radiative transfer with multilevel atoms. II. The non-linear multigrid method.

    Science.gov (United States)

    Fabiani Bendicho, P.; Trujillo Bueno, J.; Auer, L.

    1997-08-01

    A new iterative method for solving non-LTE multilevel radiative transfer (RT) problems in 1D, 2D or 3D geometries is presented. The scheme obtains the self-consistent solution of the kinetic and RT equations at the cost of only a few (iteration (Brandt, 1977, Math. Comp. 31, 333; Hackbush, 1985, Multi-Grid Methods and Applications, springer-Verlag, Berlin), an efficient multilevel RT scheme based on Gauss-Seidel iterations (cf. Trujillo Bueno & Fabiani Bendicho, 1995ApJ...455..646T), and accurate short-characteristics formal solution techniques. By combining a valid stopping criterion with a nested-grid strategy a converged solution with the desired true error is automatically guaranteed. Contrary to the current operator splitting methods the very high convergence speed of the new RT method does not deteriorate when the grid spatial resolution is increased. With this non-linear multigrid method non-LTE problems discretized on N grid points are solved in O(N) operations. The nested multigrid RT method presented here is, thus, particularly attractive in complicated multilevel transfer problems where small grid-sizes are required. The properties of the method are analyzed both analytically and with illustrative multilevel calculations for Ca II in 1D and 2D schematic model atmospheres.

  6. The development of an algebraic multigrid algorithm for symmetric positive definite linear systems

    Energy Technology Data Exchange (ETDEWEB)

    Vanek, P.; Mandel, J.; Brezina, M. [Univ. of Colorado, Denver, CO (United States)

    1996-12-31

    An algebraic multigrid algorithm for symmetric, positive definite linear systems is developed based on the concept of prolongation by smoothed aggregation. Coarse levels are generated automatically. We present a set of requirements motivated heuristically by a convergence theory. The algorithm then attempts to satisfy the requirements. Input to the method are the coefficient matrix and zero energy modes, which are determined from nodal coordinates and knowledge of the differential equation. Efficiency of the resulting algorithm is demonstrated by computational results on real world problems from solid elasticity, plate blending, and shells.

  7. Optimal multigrid algorithms for the massive Gaussian model and path integrals

    International Nuclear Information System (INIS)

    Brandt, A.; Galun, M.

    1996-01-01

    Multigrid algorithms are presented which, in addition to eliminating the critical slowing down, can also eliminate the open-quotes volume factorclose quotes. The elimination of the volume factor removes the need to produce many independent fine-grid configurations for averaging out their statistical deviations, by averaging over the many samples produced on coarse grids during the multigrid cycle. Thermodynamic limits of observables can be calculated to relative accuracy var-epsilon r in just O(var-epsilon r -2 ) computer operations, where var-epsilon r is the error relative to the standard deviation of the observable. In this paper, we describe in detail the calculation of the susceptibility in the one-dimensional massive Gaussian model, which is also a simple example of path integrals. Numerical experiments show that the susceptibility can be calculated to relative accuracy var-epsilon r in about 8 var-epsilon r -2 random number generations, independent of the mass size

  8. A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition

    KAUST Repository

    Bonito, Andrea; Pasciak, Joseph E.

    2013-01-01

    We discuss the preconditioning of systems coupling elliptic operators in Ω⊂Rd, d=2,3, with elliptic operators defined on hypersurfaces. These systems arise naturally when physical phenomena are affected by geometric boundary forces, such as the evolution of liquid drops subject to surface tension. The resulting operators are sums of interior and boundary terms weighted by parameters. We investigate the behavior of multigrid algorithms suited to this context and demonstrate numerical results which suggest uniform preconditioning bounds that are level and parameter independent.

  9. Convergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator

    KAUST Repository

    Bonito, Andrea

    2012-09-01

    We design and analyze variational and non-variational multigrid algorithms for the Laplace-Beltrami operator on a smooth and closed surface. In both cases, a uniform convergence for the V -cycle algorithm is obtained provided the surface geometry is captured well enough by the coarsest grid. The main argument hinges on a perturbation analysis from an auxiliary variational algorithm defined directly on the smooth surface. In addition, the vanishing mean value constraint is imposed on each level, thereby avoiding singular quadratic forms without adding additional computational cost. Numerical results supporting our analysis are reported. In particular, the algorithms perform well even when applied to surfaces with a large aspect ratio. © 2011 American Mathematical Society.

  10. Layer-oriented multigrid wavefront reconstruction algorithms for multi-conjugate adaptive optics

    Science.gov (United States)

    Gilles, Luc; Ellerbroek, Brent L.; Vogel, Curtis R.

    2003-02-01

    Multi-conjugate adaptive optics (MCAO) systems with 104-105 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of AO degrees of freedom. In this paper, we develop an iterative sparse matrix implementation of minimum variance wavefront reconstruction for telescope diameters up to 32m with more than 104 actuators. The basic approach is the preconditioned conjugate gradient method, using a multigrid preconditioner incorporating a layer-oriented (block) symmetric Gauss-Seidel iterative smoothing operator. We present open-loop numerical simulation results to illustrate algorithm convergence.

  11. HP-Multigrid as Smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. Part II: Optimization of the Runge-Kutta smoother

    NARCIS (Netherlands)

    van der Vegt, Jacobus J.W.; Rhebergen, Sander

    2012-01-01

    Using a detailed multilevel analysis of the complete hp-Multigrid as Smoother algorithm accurate predictions are obtained of the spectral radius and operator norms of the multigrid error transformation operator. This multilevel analysis is used to optimize the coefficients in the semi-implicit

  12. MAPCUMBA: A fast iterative multi-grid map-making algorithm for CMB experiments

    Science.gov (United States)

    Doré, O.; Teyssier, R.; Bouchet, F. R.; Vibert, D.; Prunet, S.

    2001-07-01

    The data analysis of current Cosmic Microwave Background (CMB) experiments like BOOMERanG or MAXIMA poses severe challenges which already stretch the limits of current (super-) computer capabilities, if brute force methods are used. In this paper we present a practical solution for the optimal map making problem which can be used directly for next generation CMB experiments like ARCHEOPS and TopHat, and can probably be extended relatively easily to the full PLANCK case. This solution is based on an iterative multi-grid Jacobi algorithm which is both fast and memory sparing. Indeed, if there are Ntod data points along the one dimensional timeline to analyse, the number of operations is of O (Ntod \\ln Ntod) and the memory requirement is O (Ntod). Timing and accuracy issues have been analysed on simulated ARCHEOPS and TopHat data, and we discuss as well the issue of the joint evaluation of the signal and noise statistical properties.

  13. An implicit multigrid algorithm for computing hypersonic, chemically reacting viscous flows

    International Nuclear Information System (INIS)

    Edwards, J.R.

    1996-01-01

    An implicit algorithm for computing viscous flows in chemical nonequilibrium is presented. Emphasis is placed on the numerical efficiency of the time integration scheme, both in terms of periteration workload and overall convergence rate. In this context, several techniques are introduced, including a stable, O(m 2 ) approximate factorization of the chemical source Jacobian and implementations of V-cycle and filtered multigrid acceleration methods. A five species-seventeen reaction air model is used to calculate hypersonic viscous flow over a cylinder at conditions corresponding to flight at 5 km/s, 60 km altitude and at 11.36 km/s, 76.42 km altitude. Inviscid calculations using an eleven-species reaction mechanism including ionization are presented for a case involving 11.37 km/s flow at an altitude of 84.6 km. Comparisons among various options for the implicit treatment of the chemical source terms and among different multilevel approaches for convergence acceleration are presented for all simulations

  14. A comparison between anisotropic analytical and multigrid superposition dose calculation algorithms in radiotherapy treatment planning

    International Nuclear Information System (INIS)

    Wu, Vincent W.C.; Tse, Teddy K.H.; Ho, Cola L.M.; Yeung, Eric C.Y.

    2013-01-01

    Monte Carlo (MC) simulation is currently the most accurate dose calculation algorithm in radiotherapy planning but requires relatively long processing time. Faster model-based algorithms such as the anisotropic analytical algorithm (AAA) by the Eclipse treatment planning system and multigrid superposition (MGS) by the XiO treatment planning system are 2 commonly used algorithms. This study compared AAA and MGS against MC, as the gold standard, on brain, nasopharynx, lung, and prostate cancer patients. Computed tomography of 6 patients of each cancer type was used. The same hypothetical treatment plan using the same machine and treatment prescription was computed for each case by each planning system using their respective dose calculation algorithm. The doses at reference points including (1) soft tissues only, (2) bones only, (3) air cavities only, (4) soft tissue-bone boundary (Soft/Bone), (5) soft tissue-air boundary (Soft/Air), and (6) bone-air boundary (Bone/Air), were measured and compared using the mean absolute percentage error (MAPE), which was a function of the percentage dose deviations from MC. Besides, the computation time of each treatment plan was recorded and compared. The MAPEs of MGS were significantly lower than AAA in all types of cancers (p<0.001). With regards to body density combinations, the MAPE of AAA ranged from 1.8% (soft tissue) to 4.9% (Bone/Air), whereas that of MGS from 1.6% (air cavities) to 2.9% (Soft/Bone). The MAPEs of MGS (2.6%±2.1) were significantly lower than that of AAA (3.7%±2.5) in all tissue density combinations (p<0.001). The mean computation time of AAA for all treatment plans was significantly lower than that of the MGS (p<0.001). Both AAA and MGS algorithms demonstrated dose deviations of less than 4.0% in most clinical cases and their performance was better in homogeneous tissues than at tissue boundaries. In general, MGS demonstrated relatively smaller dose deviations than AAA but required longer computation time

  15. Multigrid Methods for Fully Implicit Oil Reservoir Simulation

    Science.gov (United States)

    Molenaar, J.

    1996-01-01

    In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for

  16. Multigrid and multilevel domain decomposition for unstructured grids

    Energy Technology Data Exchange (ETDEWEB)

    Chan, T.; Smith, B.

    1994-12-31

    Multigrid has proven itself to be a very versatile method for the iterative solution of linear and nonlinear systems of equations arising from the discretization of PDES. In some applications, however, no natural multilevel structure of grids is available, and these must be generated as part of the solution procedure. In this presentation the authors will consider the problem of generating a multigrid algorithm when only a fine, unstructured grid is given. Their techniques generate a sequence of coarser grids by first forming an approximate maximal independent set of the vertices and then applying a Cavendish type algorithm to form the coarser triangulation. Numerical tests indicate that convergence using this approach can be as fast as standard multigrid on a structured mesh, at least in two dimensions.

  17. Algorithms For Integrating Nonlinear Differential Equations

    Science.gov (United States)

    Freed, A. D.; Walker, K. P.

    1994-01-01

    Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

  18. Electrical Resistivity Tomography using a finite element based BFGS algorithm with algebraic multigrid preconditioning

    Science.gov (United States)

    Codd, A. L.; Gross, L.

    2018-03-01

    We present a new inversion method for Electrical Resistivity Tomography which, in contrast to established approaches, minimizes the cost function prior to finite element discretization for the unknown electric conductivity and electric potential. Minimization is performed with the Broyden-Fletcher-Goldfarb-Shanno method (BFGS) in an appropriate function space. BFGS is self-preconditioning and avoids construction of the dense Hessian which is the major obstacle to solving large 3-D problems using parallel computers. In addition to the forward problem predicting the measurement from the injected current, the so-called adjoint problem also needs to be solved. For this problem a virtual current is injected through the measurement electrodes and an adjoint electric potential is obtained. The magnitude of the injected virtual current is equal to the misfit at the measurement electrodes. This new approach has the advantage that the solution process of the optimization problem remains independent to the meshes used for discretization and allows for mesh adaptation during inversion. Computation time is reduced by using superposition of pole loads for the forward and adjoint problems. A smoothed aggregation algebraic multigrid (AMG) preconditioned conjugate gradient is applied to construct the potentials for a given electric conductivity estimate and for constructing a first level BFGS preconditioner. Through the additional reuse of AMG operators and coarse grid solvers inversion time for large 3-D problems can be reduced further. We apply our new inversion method to synthetic survey data created by the resistivity profile representing the characteristics of subsurface fluid injection. We further test it on data obtained from a 2-D surface electrode survey on Heron Island, a small tropical island off the east coast of central Queensland, Australia.

  19. Combined algorithms in nonlinear problems of magnetostatics

    International Nuclear Information System (INIS)

    Gregus, M.; Khoromskij, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.

    1988-01-01

    To solve boundary problems of magnetostatics in unbounded two- and three-dimensional regions, we construct combined algorithms based on a combination of the method of boundary integral equations with the grid methods. We study the question of substantiation of the combined method of nonlinear magnetostatic problem without the preliminary discretization of equations and give some results on the convergence of iterative processes that arise in non-linear cases. We also discuss economical iterative processes and algorithms that solve boundary integral equations on certain surfaces. Finally, examples of numerical solutions of magnetostatic problems that arose when modelling the fields of electrophysical installations are given too. 14 refs.; 2 figs.; 1 tab

  20. Convergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator

    KAUST Repository

    Bonito, Andrea; Pasciak, Joseph E.

    2012-01-01

    is captured well enough by the coarsest grid. The main argument hinges on a perturbation analysis from an auxiliary variational algorithm defined directly on the smooth surface. In addition, the vanishing mean value constraint is imposed on each level, thereby

  1. Nonlinear model predictive control theory and algorithms

    CERN Document Server

    Grüne, Lars

    2017-01-01

    This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...

  2. Multigrid methods in structural mechanics

    Science.gov (United States)

    Raju, I. S.; Bigelow, C. A.; Taasan, S.; Hussaini, M. Y.

    1986-01-01

    Although the application of multigrid methods to the equations of elasticity has been suggested, few such applications have been reported in the literature. In the present work, multigrid techniques are applied to the finite element analysis of a simply supported Bernoulli-Euler beam, and various aspects of the multigrid algorithm are studied and explained in detail. In this study, six grid levels were used to model half the beam. With linear prolongation and sequential ordering, the multigrid algorithm yielded results which were of machine accuracy with work equivalent to 200 standard Gauss-Seidel iterations on the fine grid. Also with linear prolongation and sequential ordering, the V(1,n) cycle with n greater than 2 yielded better convergence rates than the V(n,1) cycle. The restriction and prolongation operators were derived based on energy principles. Conserving energy during the inter-grid transfers required that the prolongation operator be the transpose of the restriction operator, and led to improved convergence rates. With energy-conserving prolongation and sequential ordering, the multigrid algorithm yielded results of machine accuracy with a work equivalent to 45 Gauss-Seidel iterations on the fine grid. The red-black ordering of relaxations yielded solutions of machine accuracy in a single V(1,1) cycle, which required work equivalent to about 4 iterations on the finest grid level.

  3. A NetCDF version of the two-dimensional energy balance model based on the full multigrid algorithm

    Science.gov (United States)

    Zhuang, Kelin; North, Gerald R.; Stevens, Mark J.

    A NetCDF version of the two-dimensional energy balance model based on the full multigrid method in Fortran is introduced for both pedagogical and research purposes. Based on the land-sea-ice distribution, orbital elements, greenhouse gases concentration, and albedo, the code calculates the global seasonal surface temperature. A step-by-step guide with examples is provided for practice.

  4. On several aspects and applications of the multigrid method for solving partial differential equations

    Science.gov (United States)

    Dinar, N.

    1978-01-01

    Several aspects of multigrid methods are briefly described. The main subjects include the development of very efficient multigrid algorithms for systems of elliptic equations (Cauchy-Riemann, Stokes, Navier-Stokes), as well as the development of control and prediction tools (based on local mode Fourier analysis), used to analyze, check and improve these algorithms. Preliminary research on multigrid algorithms for time dependent parabolic equations is also described. Improvements in existing multigrid processes and algorithms for elliptic equations were studied.

  5. Self-correcting Multigrid Solver

    International Nuclear Information System (INIS)

    Lewandowski, Jerome L.V.

    2004-01-01

    A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It is shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard equivalent. When used in conjunction with a multigrid method, the resulting solver displays an improved convergence rate with no additional computational work

  6. A NetCDF version of the two-dimensional energy balance model based on the full multigrid algorithm

    Directory of Open Access Journals (Sweden)

    Kelin Zhuang

    2017-01-01

    Full Text Available A NetCDF version of the two-dimensional energy balance model based on the full multigrid method in Fortran is introduced for both pedagogical and research purposes. Based on the land–sea–ice distribution, orbital elements, greenhouse gases concentration, and albedo, the code calculates the global seasonal surface temperature. A step-by-step guide with examples is provided for practice.

  7. Semi-coarsening multigrid methods for parallel computing

    Energy Technology Data Exchange (ETDEWEB)

    Jones, J.E.

    1996-12-31

    Standard multigrid methods are not well suited for problems with anisotropic coefficients which can occur, for example, on grids that are stretched to resolve a boundary layer. There are several different modifications of the standard multigrid algorithm that yield efficient methods for anisotropic problems. In the paper, we investigate the parallel performance of these multigrid algorithms. Multigrid algorithms which work well for anisotropic problems are based on line relaxation and/or semi-coarsening. In semi-coarsening multigrid algorithms a grid is coarsened in only one of the coordinate directions unlike standard or full-coarsening multigrid algorithms where a grid is coarsened in each of the coordinate directions. When both semi-coarsening and line relaxation are used, the resulting multigrid algorithm is robust and automatic in that it requires no knowledge of the nature of the anisotropy. This is the basic multigrid algorithm whose parallel performance we investigate in the paper. The algorithm is currently being implemented on an IBM SP2 and its performance is being analyzed. In addition to looking at the parallel performance of the basic semi-coarsening algorithm, we present algorithmic modifications with potentially better parallel efficiency. One modification reduces the amount of computational work done in relaxation at the expense of using multiple coarse grids. This modification is also being implemented with the aim of comparing its performance to that of the basic semi-coarsening algorithm.

  8. An efficient control algorithm for nonlinear systems

    International Nuclear Information System (INIS)

    Sinha, S.

    1990-12-01

    We suggest a scheme to step up the efficiency of a recently proposed adaptive control algorithm, which is remarkably effective for regulating nonlinear systems. The technique involves monitoring of the ''stiffness of control'' to get maximum gain while maintaining a predetermined accuracy. The success of the procedure is demonstrated for the case of the logistic map, where we show that the improvement in performance is often factors of tens, and for small control stiffness, even factors of hundreds. (author). 4 refs, 1 fig., 1 tab

  9. Extending the applicability of multigrid methods

    International Nuclear Information System (INIS)

    Brannick, J; Brezina, M; Falgout, R; Manteuffel, T; McCormick, S; Ruge, J; Sheehan, B; Xu, J; Zikatanov, L

    2006-01-01

    Multigrid methods are ideal for solving the increasingly large-scale problems that arise in numerical simulations of physical phenomena because of their potential for computational costs and memory requirements that scale linearly with the degrees of freedom. Unfortunately, they have been historically limited by their applicability to elliptic-type problems and the need for special handling in their implementation. In this paper, we present an overview of several recent theoretical and algorithmic advances made by the TOPS multigrid partners and their collaborators in extending applicability of multigrid methods. specific examples that are presented include quantum chromodynamics, radiation transport, and electromagnetics

  10. Algorithms for adaptive nonlinear pattern recognition

    Science.gov (United States)

    Schmalz, Mark S.; Ritter, Gerhard X.; Hayden, Eric; Key, Gary

    2011-09-01

    In Bayesian pattern recognition research, static classifiers have featured prominently in the literature. A static classifier is essentially based on a static model of input statistics, thereby assuming input ergodicity that is not realistic in practice. Classical Bayesian approaches attempt to circumvent the limitations of static classifiers, which can include brittleness and narrow coverage, by training extensively on a data set that is assumed to cover more than the subtense of expected input. Such assumptions are not realistic for more complex pattern classification tasks, for example, object detection using pattern classification applied to the output of computer vision filters. In contrast, we have developed a two step process, that can render the majority of static classifiers adaptive, such that the tracking of input nonergodicities is supported. Firstly, we developed operations that dynamically insert (or resp. delete) training patterns into (resp. from) the classifier's pattern database, without requiring that the classifier's internal representation of its training database be completely recomputed. Secondly, we developed and applied a pattern replacement algorithm that uses the aforementioned pattern insertion/deletion operations. This algorithm is designed to optimize the pattern database for a given set of performance measures, thereby supporting closed-loop, performance-directed optimization. This paper presents theory and algorithmic approaches for the efficient computation of adaptive linear and nonlinear pattern recognition operators that use our pattern insertion/deletion technology - in particular, tabular nearest-neighbor encoding (TNE) and lattice associative memories (LAMs). Of particular interest is the classification of nonergodic datastreams that have noise corruption with time-varying statistics. The TNE and LAM based classifiers discussed herein have been successfully applied to the computation of object classification in hyperspectral

  11. Highly indefinite multigrid for eigenvalue problems

    Energy Technology Data Exchange (ETDEWEB)

    Borges, L.; Oliveira, S.

    1996-12-31

    Eigenvalue problems are extremely important in understanding dynamic processes such as vibrations and control systems. Large scale eigenvalue problems can be very difficult to solve, especially if a large number of eigenvalues and the corresponding eigenvectors need to be computed. For solving this problem a multigrid preconditioned algorithm is presented in {open_quotes}The Davidson Algorithm, preconditioning and misconvergence{close_quotes}. Another approach for solving eigenvalue problems is by developing efficient solutions for highly indefinite problems. In this paper we concentrate on the use of new highly indefinite multigrid algorithms for the eigenvalue problem.

  12. New preconditioned conjugate gradient algorithms for nonlinear unconstrained optimization problems

    International Nuclear Information System (INIS)

    Al-Bayati, A.; Al-Asadi, N.

    1997-01-01

    This paper presents two new predilection conjugate gradient algorithms for nonlinear unconstrained optimization problems and examines their computational performance. Computational experience shows that the new proposed algorithms generally imp lone the efficiency of Nazareth's [13] preconditioned conjugate gradient algorithm. (authors). 16 refs., 1 tab

  13. Multigrid for Staggered Lattice Fermions

    Energy Technology Data Exchange (ETDEWEB)

    Brower, Richard C. [Boston U.; Clark, M. A. [Unlisted, US; Strelchenko, Alexei [Fermilab; Weinberg, Evan [Boston U.

    2018-01-23

    Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.

  14. Unweighted least squares phase unwrapping by means of multigrid techniques

    Science.gov (United States)

    Pritt, Mark D.

    1995-11-01

    We present a multigrid algorithm for unweighted least squares phase unwrapping. This algorithm applies Gauss-Seidel relaxation schemes to solve the Poisson equation on smaller, coarser grids and transfers the intermediate results to the finer grids. This approach forms the basis of our multigrid algorithm for weighted least squares phase unwrapping, which is described in a separate paper. The key idea of our multigrid approach is to maintain the partial derivatives of the phase data in separate arrays and to correct these derivatives at the boundaries of the coarser grids. This maintains the boundary conditions necessary for rapid convergence to the correct solution. Although the multigrid algorithm is an iterative algorithm, we demonstrate that it is nearly as fast as the direct Fourier-based method. We also describe how to parallelize the algorithm for execution on a distributed-memory parallel processor computer or a network-cluster of workstations.

  15. Efficient multigrid computation of steady hypersonic flows

    NARCIS (Netherlands)

    Koren, B.; Hemker, P.W.; Murthy, T.K.S.

    1991-01-01

    In steady hypersonic flow computations, Newton iteration as a local relaxation procedure and nonlinear multigrid iteration as an acceleration procedure may both easily fail. In the present chapter, same remedies are presented for overcoming these problems. The equations considered are the steady,

  16. Algorithms for non-linear M-estimation

    DEFF Research Database (Denmark)

    Madsen, Kaj; Edlund, O; Ekblom, H

    1997-01-01

    In non-linear regression, the least squares method is most often used. Since this estimator is highly sensitive to outliers in the data, alternatives have became increasingly popular during the last decades. We present algorithms for non-linear M-estimation. A trust region approach is used, where...

  17. Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

    International Nuclear Information System (INIS)

    Adams, Mark F.; Samtaney, Ravi; Brandt, Achi

    2013-01-01

    Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations so-called textbook multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field, which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.

  18. Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

    KAUST Repository

    Adams, Mark F.; Samtaney, Ravi; Brandt, Achi

    2010-01-01

    Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations so-called "textbook" multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field, which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations. (C) 2010 Elsevier Inc. All rights reserved.

  19. Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

    KAUST Repository

    Adams, Mark F.

    2010-09-01

    Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations so-called "textbook" multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field, which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations. (C) 2010 Elsevier Inc. All rights reserved.

  20. Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

    International Nuclear Information System (INIS)

    Adams, Mark F.; Samtaney, Ravi; Brandt, Achi

    2010-01-01

    Multigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations - so-called 'textbook' multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field, which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations.

  1. Development of Multigrid Methods for diffusion, Advection, and the incompressible Navier-Stokes Equations

    Energy Technology Data Exchange (ETDEWEB)

    Gjesdal, Thor

    1997-12-31

    This thesis discusses the development and application of efficient numerical methods for the simulation of fluid flows, in particular the flow of incompressible fluids. The emphasis is on practical aspects of algorithm development and on application of the methods either to linear scalar model equations or to the non-linear incompressible Navier-Stokes equations. The first part deals with cell centred multigrid methods and linear correction scheme and presents papers on (1) generalization of the method to arbitrary sized grids for diffusion problems, (2) low order method for advection-diffusion problems, (3) attempt to extend the basic method to advection-diffusion problems, (4) Fourier smoothing analysis of multicolour relaxation schemes, and (5) analysis of high-order discretizations for advection terms. The second part discusses a multigrid based on pressure correction methods, non-linear full approximation scheme, and papers on (1) systematic comparison of the performance of different pressure correction smoothers and some other algorithmic variants, low to moderate Reynolds numbers, and (2) systematic study of implementation strategies for high order advection schemes, high-Re flow. An appendix contains Fortran 90 data structures for multigrid development. 160 refs., 26 figs., 22 tabs.

  2. A multigrid method for variational inequalities

    Energy Technology Data Exchange (ETDEWEB)

    Oliveira, S.; Stewart, D.E.; Wu, W.

    1996-12-31

    Multigrid methods have been used with great success for solving elliptic partial differential equations. Penalty methods have been successful in solving finite-dimensional quadratic programs. In this paper these two techniques are combined to give a fast method for solving obstacle problems. A nonlinear penalized problem is solved using Newton`s method for large values of a penalty parameter. Multigrid methods are used to solve the linear systems in Newton`s method. The overall numerical method developed is based on an exterior penalty function, and numerical results showing the performance of the method have been obtained.

  3. Improved algorithm for solving nonlinear parabolized stability equations

    Science.gov (United States)

    Zhao, Lei; Zhang, Cun-bo; Liu, Jian-xin; Luo, Ji-sheng

    2016-08-01

    Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. Project supported by the National Natural Science Foundation of China (Grant Nos. 11332007 and 11402167).

  4. Improved algorithm for solving nonlinear parabolized stability equations

    International Nuclear Information System (INIS)

    Zhao Lei; Zhang Cun-bo; Liu Jian-xin; Luo Ji-sheng

    2016-01-01

    Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. (paper)

  5. New multigrid solver advances in TOPS

    International Nuclear Information System (INIS)

    Falgout, R D; Brannick, J; Brezina, M; Manteuffel, T; McCormick, S

    2005-01-01

    In this paper, we highlight new multigrid solver advances in the Terascale Optimal PDE Simulations (TOPS) project in the Scientific Discovery Through Advanced Computing (SciDAC) program. We discuss two new algebraic multigrid (AMG) developments in TOPS: the adaptive smoothed aggregation method (αSA) and a coarse-grid selection algorithm based on compatible relaxation (CR). The αSA method is showing promising results in initial studies for Quantum Chromodynamics (QCD) applications. The CR method has the potential to greatly improve the applicability of AMG

  6. Segmental Refinement: A Multigrid Technique for Data Locality

    KAUST Repository

    Adams, Mark F.; Brown, Jed; Knepley, Matt; Samtaney, Ravi

    2016-01-01

    We investigate a domain decomposed multigrid technique, termed segmental refinement, for solving general nonlinear elliptic boundary value problems. We extend the method first proposed in 1994 by analytically and experimentally investigating its complexity. We confirm that communication of traditional parallel multigrid is eliminated on fine grids, with modest amounts of extra work and storage, while maintaining the asymptotic exactness of full multigrid. We observe an accuracy dependence on the segmental refinement subdomain size, which was not considered in the original analysis. We present a communication complexity analysis that quantifies the communication costs ameliorated by segmental refinement and report performance results with up to 64K cores on a Cray XC30.

  7. Segmental Refinement: A Multigrid Technique for Data Locality

    KAUST Repository

    Adams, Mark F.

    2016-08-04

    We investigate a domain decomposed multigrid technique, termed segmental refinement, for solving general nonlinear elliptic boundary value problems. We extend the method first proposed in 1994 by analytically and experimentally investigating its complexity. We confirm that communication of traditional parallel multigrid is eliminated on fine grids, with modest amounts of extra work and storage, while maintaining the asymptotic exactness of full multigrid. We observe an accuracy dependence on the segmental refinement subdomain size, which was not considered in the original analysis. We present a communication complexity analysis that quantifies the communication costs ameliorated by segmental refinement and report performance results with up to 64K cores on a Cray XC30.

  8. Multicloud: Multigrid convergence with a meshless operator

    International Nuclear Information System (INIS)

    Katz, Aaron; Jameson, Antony

    2009-01-01

    The primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud. Multicloud is well-founded in the mathematical basis of multigrid, but relies on a meshless operator on coarse levels. The meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes. The performance of multicloud is compared with established multigrid techniques for structured and unstructured meshes for the Euler equations on two-dimensional test cases. Results indicate comparable convergence rates per unit work for multicloud and multigrid. However, because of its mesh and scheme transparency, multicloud may be applied to a wide array of problems with no modification of fine level schemes as is often required with agglomeration techniques. The implication is that multicloud can be implemented in a completely modular fashion, allowing researchers to develop fine level algorithms independent of the convergence accelerator for complex three-dimensional problems.

  9. Applications and algorithms for mixed integer nonlinear programming

    International Nuclear Information System (INIS)

    Leyffer, Sven; Munson, Todd; Linderoth, Jeff; Luedtke, James; Miller, Andrew

    2009-01-01

    The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear constraint functions are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems faced by researchers and practitioners. In this paper, we describe relevant scientific applications that are naturally modeled as MINLPs, we provide an overview of available algorithms and software, and we describe ongoing methodological advances for solving MINLPs. These algorithmic advances are making increasingly larger instances of this important family of problems tractable.

  10. Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions

    Science.gov (United States)

    Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

    2018-04-01

    Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. We also show that the strategy is efficient and scales optimally with problem size.

  11. A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem

    Directory of Open Access Journals (Sweden)

    Mio Horai

    2016-01-01

    Full Text Available We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods.

  12. Multigrid methods III

    CERN Document Server

    Trottenberg, U; Third European Conference on Multigrid Methods

    1991-01-01

    These proceedings contain a selection of papers presented at the Third European Conference on Multigrid Methods which was held in Bonn on October 1-4, 1990. Following conferences in 1981 and 1985, a platform for the presentation of new Multigrid results was provided for a third time. Multigrid methods no longer have problems being accepted by numerical analysts and users of numerical methods; on the contrary, they have been further developed in such a successful way that they have penetrated a variety of new fields of application. The high number of 154 participants from 18 countries and 76 presented papers show the need to continue the series of the European Multigrid Conferences. The papers of this volume give a survey on the current Multigrid situation; in particular, they correspond to those fields where new developments can be observed. For example, se­ veral papers study the appropriate treatment of time dependent problems. Improvements can also be noticed in the Multigrid approach for semiconductor eq...

  13. On multigrid solution of the implicit equations of hydrodynamics. Experiments for the compressible Euler equations in general coordinates

    Science.gov (United States)

    Kifonidis, K.; Müller, E.

    2012-08-01

    Aims: We describe and study a family of new multigrid iterative solvers for the multidimensional, implicitly discretized equations of hydrodynamics. Schemes of this class are free of the Courant-Friedrichs-Lewy condition. They are intended for simulations in which widely differing wave propagation timescales are present. A preferred solver in this class is identified. Applications to some simple stiff test problems that are governed by the compressible Euler equations, are presented to evaluate the convergence behavior, and the stability properties of this solver. Algorithmic areas are determined where further work is required to make the method sufficiently efficient and robust for future application to difficult astrophysical flow problems. Methods: The basic equations are formulated and discretized on non-orthogonal, structured curvilinear meshes. Roe's approximate Riemann solver and a second-order accurate reconstruction scheme are used for spatial discretization. Implicit Runge-Kutta (ESDIRK) schemes are employed for temporal discretization. The resulting discrete equations are solved with a full-coarsening, non-linear multigrid method. Smoothing is performed with multistage-implicit smoothers. These are applied here to the time-dependent equations by means of dual time stepping. Results: For steady-state problems, our results show that the efficiency of the present approach is comparable to the best implicit solvers for conservative discretizations of the compressible Euler equations that can be found in the literature. The use of red-black as opposed to symmetric Gauss-Seidel iteration in the multistage-smoother is found to have only a minor impact on multigrid convergence. This should enable scalable parallelization without having to seriously compromise the method's algorithmic efficiency. For time-dependent test problems, our results reveal that the multigrid convergence rate degrades with increasing Courant numbers (i.e. time step sizes). Beyond a

  14. Impulse position control algorithms for nonlinear systems

    Energy Technology Data Exchange (ETDEWEB)

    Sesekin, A. N., E-mail: sesekin@list.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation); Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation); Nepp, A. N., E-mail: anepp@urfu.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation)

    2015-11-30

    The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.

  15. Impulse position control algorithms for nonlinear systems

    Science.gov (United States)

    Sesekin, A. N.; Nepp, A. N.

    2015-11-01

    The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.

  16. Multigrid methods for the computation of propagators in gauge fields

    International Nuclear Information System (INIS)

    Kalkreuter, T.

    1992-11-01

    In the present work generalizations of multigrid methods for propagators in gauge fields are investigated. We discuss proper averaging operations for bosons and for staggered fermions. An efficient algorithm for computing C numerically is presented. The averaging kernels C can be used not only in deterministic multigrid computations, but also in multigrid Monte Carlo simulations, and for the definition of block spins and blocked gauge fields in Monte Carlo renormalization group studies of gauge theories. Actual numerical computations of kernels and propagators are performed in compact four-dimensional SU(2) gauge fields. (orig./HSI)

  17. Progress with multigrid schemes for hypersonic flow problems

    International Nuclear Information System (INIS)

    Radespiel, R.; Swanson, R.C.

    1995-01-01

    Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm employs upwind spatial discretization with explicit multistage time stepping. Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high-aspect-ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 X 10 6 and Mach numbers up to 25. 32 refs., 31 figs., 1 tab

  18. Sparse Nonlinear Electromagnetic Imaging Accelerated With Projected Steepest Descent Algorithm

    KAUST Repository

    Desmal, Abdulla

    2017-04-03

    An efficient electromagnetic inversion scheme for imaging sparse 3-D domains is proposed. The scheme achieves its efficiency and accuracy by integrating two concepts. First, the nonlinear optimization problem is constrained using L₀ or L₁-norm of the solution as the penalty term to alleviate the ill-posedness of the inverse problem. The resulting Tikhonov minimization problem is solved using nonlinear Landweber iterations (NLW). Second, the efficiency of the NLW is significantly increased using a steepest descent algorithm. The algorithm uses a projection operator to enforce the sparsity constraint by thresholding the solution at every iteration. Thresholding level and iteration step are selected carefully to increase the efficiency without sacrificing the convergence of the algorithm. Numerical results demonstrate the efficiency and accuracy of the proposed imaging scheme in reconstructing sparse 3-D dielectric profiles.

  19. Ground-state projection multigrid for propagators in 4-dimensional SU(2) gauge fields

    International Nuclear Information System (INIS)

    Kalkreuter, T.

    1991-09-01

    The ground-state projection multigrid method is studied for computations of slowly decaying bosonic propagators in 4-dimensional SU(2) lattice gauge theory. The defining eigenvalue equation for the restriction operator is solved exactly. Although the critical exponent z is not reduced in nontrivial gauge fields, multigrid still yields considerable speedup compared with conventional relaxation. Multigrid is also able to outperform the conjugate gradient algorithm. (orig.)

  20. Concise quantum associative memories with nonlinear search algorithm

    International Nuclear Information System (INIS)

    Tchapet Njafa, J.P.; Nana Engo, S.G.

    2016-01-01

    The model of Quantum Associative Memories (QAM) we propose here consists in simplifying and generalizing that of Rigui Zhou et al. [1] which uses the quantum matrix with the binary decision diagram put forth by David Rosenbaum [2] and the Abrams and Lloyd's nonlinear search algorithm [3]. Our model gives the possibility to retrieve one of the sought states in multi-values retrieving scheme when a measurement is done on the first register in O(c-r) time complexity. It is better than Grover's algorithm and its modified form which need O(√((2 n )/(m))) steps when they are used as the retrieval algorithm. n is the number of qubits of the first register and m the number of x values for which f(x) = 1. As the nonlinearity makes the system highly susceptible to the noise, an analysis of the influence of the single qubit noise channels on the Nonlinear Search Algorithm of our model of QAM shows a fidelity of about 0.7 whatever the number of qubits existing in the first register, thus demonstrating the robustness of our model. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  1. Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

    Science.gov (United States)

    Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem

    2018-01-01

    In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

  2. Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

    Directory of Open Access Journals (Sweden)

    Azmat Ullah

    Full Text Available In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA with Interior Point Algorithm (IPA is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

  3. Iterative Nonlinear Tikhonov Algorithm with Constraints for Electromagnetic Tomography

    Science.gov (United States)

    Xu, Feng; Deshpande, Manohar

    2012-01-01

    Low frequency electromagnetic tomography such as the capacitance tomography (ECT) has been proposed for monitoring and mass-gauging of gas-liquid two-phase system under microgravity condition in NASA's future long-term space missions. Due to the ill-posed inverse problem of ECT, images reconstructed using conventional linear algorithms often suffer from limitations such as low resolution and blurred edges. Hence, new efficient high resolution nonlinear imaging algorithms are needed for accurate two-phase imaging. The proposed Iterative Nonlinear Tikhonov Regularized Algorithm with Constraints (INTAC) is based on an efficient finite element method (FEM) forward model of quasi-static electromagnetic problem. It iteratively minimizes the discrepancy between FEM simulated and actual measured capacitances by adjusting the reconstructed image using the Tikhonov regularized method. More importantly, it enforces the known permittivity of two phases to the unknown pixels which exceed the reasonable range of permittivity in each iteration. This strategy does not only stabilize the converging process, but also produces sharper images. Simulations show that resolution improvement of over 2 times can be achieved by INTAC with respect to conventional approaches. Strategies to further improve spatial imaging resolution are suggested, as well as techniques to accelerate nonlinear forward model and thus increase the temporal resolution.

  4. SINS/CNS Nonlinear Integrated Navigation Algorithm for Hypersonic Vehicle

    Directory of Open Access Journals (Sweden)

    Yong-jun Yu

    2015-01-01

    Full Text Available Celestial Navigation System (CNS has characteristics of accurate orientation and strong autonomy and has been widely used in Hypersonic Vehicle. Since the CNS location and orientation mainly depend upon the inertial reference that contains errors caused by gyro drifts and other error factors, traditional Strap-down Inertial Navigation System (SINS/CNS positioning algorithm setting the position error between SINS and CNS as measurement is not effective. The model of altitude azimuth, platform error angles, and horizontal position is designed, and the SINS/CNS tightly integrated algorithm is designed, in which CNS altitude azimuth is set as measurement information. GPF (Gaussian particle filter is introduced to solve the problem of nonlinear filtering. The results of simulation show that the precision of SINS/CNS algorithm which reaches 130 m using three stars is improved effectively.

  5. Multigrid treatment of implicit continuum diffusion

    Science.gov (United States)

    Francisquez, Manaure; Zhu, Ben; Rogers, Barrett

    2017-10-01

    Implicit treatment of diffusive terms of various differential orders common in continuum mechanics modeling, such as computational fluid dynamics, is investigated with spectral and multigrid algorithms in non-periodic 2D domains. In doubly periodic time dependent problems these terms can be efficiently and implicitly handled by spectral methods, but in non-periodic systems solved with distributed memory parallel computing and 2D domain decomposition, this efficiency is lost for large numbers of processors. We built and present here a multigrid algorithm for these types of problems which outperforms a spectral solution that employs the highly optimized FFTW library. This multigrid algorithm is not only suitable for high performance computing but may also be able to efficiently treat implicit diffusion of arbitrary order by introducing auxiliary equations of lower order. We test these solvers for fourth and sixth order diffusion with idealized harmonic test functions as well as a turbulent 2D magnetohydrodynamic simulation. It is also shown that an anisotropic operator without cross-terms can improve model accuracy and speed, and we examine the impact that the various diffusion operators have on the energy, the enstrophy, and the qualitative aspect of a simulation. This work was supported by DOE-SC-0010508. This research used resources of the National Energy Research Scientific Computing Center (NERSC).

  6. Preisach hysteresis model for non-linear 2D heat diffusion

    International Nuclear Information System (INIS)

    Jancskar, Ildiko; Ivanyi, Amalia

    2006-01-01

    This paper analyzes a non-linear heat diffusion process when the thermal diffusivity behaviour is a hysteretic function of the temperature. Modelling this temperature dependence, the discrete Preisach algorithm as general hysteresis model has been integrated into a non-linear multigrid solver. The hysteretic diffusion shows a heating-cooling asymmetry in character. The presented type of hysteresis speeds up the thermal processes in the modelled systems by a very interesting non-linear way

  7. Multigrid and defect correction for the steady Navier-Stokes equations : application to aerodynamics

    NARCIS (Netherlands)

    Koren, B.

    1991-01-01

    Theoretical and expcrimental convergence results are presented for nonlinear multigrid and iterative defect correction applied to finite volume discretizations of the full, steady, 2D, compressible NavierStokes equations. lterative defect correction is introduced for circumventing the difficulty in

  8. Multigrid and defect correction for the steady Navier-Stokes equations

    NARCIS (Netherlands)

    Koren, B.

    1990-01-01

    Theoretical and experimental convergence results are presented for nonlinear multigrid and iterative defect correction applied to finite volume discretizations of the full, steady, 2D, compressible Navier-Stokes equations. Iterative defect correction is introduced for circumventing the difficulty in

  9. Bonus algorithm for large scale stochastic nonlinear programming problems

    CERN Document Server

    Diwekar, Urmila

    2015-01-01

    This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these ...

  10. A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition

    OpenAIRE

    De Sterck, Hans

    2011-01-01

    A new algorithm is presented for computing a canonical rank-R tensor approximation that has minimal distance to a given tensor in the Frobenius norm, where the canonical rank-R tensor consists of the sum of R rank-one components. Each iteration of the method consists of three steps. In the first step, a tentative new iterate is generated by a stand-alone one-step process, for which we use alternating least squares (ALS). In the second step, an accelerated iterate is generated by a nonlinear g...

  11. Genetic algorithms applied to nonlinear and complex domains; TOPICAL

    International Nuclear Information System (INIS)

    Barash, D; Woodin, A E

    1999-01-01

    The dissertation, titled ''Genetic Algorithms Applied to Nonlinear and Complex Domains'', describes and then applies a new class of powerful search algorithms (GAS) to certain domains. GAS are capable of solving complex and nonlinear problems where many parameters interact to produce a ''final'' result such as the optimization of the laser pulse in the interaction of an atom with an intense laser field. GAS can very efficiently locate the global maximum by searching parameter space in problems which are unsuitable for a search using traditional methods. In particular, the dissertation contains new scientific findings in two areas. First, the dissertation examines the interaction of an ultra-intense short laser pulse with atoms. GAS are used to find the optimal frequency for stabilizing atoms in the ionization process. This leads to a new theoretical formulation, to explain what is happening during the ionization process and how the electron is responding to finite (real-life) laser pulse shapes. It is shown that the dynamics of the process can be very sensitive to the ramp of the pulse at high frequencies. The new theory which is formulated, also uses a novel concept (known as the (t,t') method) to numerically solve the time-dependent Schrodinger equation Second, the dissertation also examines the use of GAS in modeling decision making problems. It compares GAS with traditional techniques to solve a class of problems known as Markov Decision Processes. The conclusion of the dissertation should give a clear idea of where GAS are applicable, especially in the physical sciences, in problems which are nonlinear and complex, i.e. difficult to analyze by other means

  12. Genetic algorithms applied to nonlinear and complex domains

    International Nuclear Information System (INIS)

    Barash, D; Woodin, A E

    1999-01-01

    The dissertation, titled ''Genetic Algorithms Applied to Nonlinear and Complex Domains'', describes and then applies a new class of powerful search algorithms (GAS) to certain domains. GAS are capable of solving complex and nonlinear problems where many parameters interact to produce a ''final'' result such as the optimization of the laser pulse in the interaction of an atom with an intense laser field. GAS can very efficiently locate the global maximum by searching parameter space in problems which are unsuitable for a search using traditional methods. In particular, the dissertation contains new scientific findings in two areas. First, the dissertation examines the interaction of an ultra-intense short laser pulse with atoms. GAS are used to find the optimal frequency for stabilizing atoms in the ionization process. This leads to a new theoretical formulation, to explain what is happening during the ionization process and how the electron is responding to finite (real-life) laser pulse shapes. It is shown that the dynamics of the process can be very sensitive to the ramp of the pulse at high frequencies. The new theory which is formulated, also uses a novel concept (known as the (t,t') method) to numerically solve the time-dependent Schrodinger equation Second, the dissertation also examines the use of GAS in modeling decision making problems. It compares GAS with traditional techniques to solve a class of problems known as Markov Decision Processes. The conclusion of the dissertation should give a clear idea of where GAS are applicable, especially in the physical sciences, in problems which are nonlinear and complex, i.e. difficult to analyze by other means

  13. Final report on the Copper Mountain conference on multigrid methods

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1997-10-01

    The Copper Mountain Conference on Multigrid Methods was held on April 6-11, 1997. It took the same format used in the previous Copper Mountain Conferences on Multigrid Method conferences. Over 87 mathematicians from all over the world attended the meeting. 56 half-hour talks on current research topics were presented. Talks with similar content were organized into sessions. Session topics included: fluids; domain decomposition; iterative methods; basics; adaptive methods; non-linear filtering; CFD; applications; transport; algebraic solvers; supercomputing; and student paper winners.

  14. Data Reduction Algorithm Using Nonnegative Matrix Factorization with Nonlinear Constraints

    Science.gov (United States)

    Sembiring, Pasukat

    2017-12-01

    Processing ofdata with very large dimensions has been a hot topic in recent decades. Various techniques have been proposed in order to execute the desired information or structure. Non- Negative Matrix Factorization (NMF) based on non-negatives data has become one of the popular methods for shrinking dimensions. The main strength of this method is non-negative object, the object model by a combination of some basic non-negative parts, so as to provide a physical interpretation of the object construction. The NMF is a dimension reduction method thathasbeen used widely for numerous applications including computer vision,text mining, pattern recognitions,and bioinformatics. Mathematical formulation for NMF did not appear as a convex optimization problem and various types of algorithms have been proposed to solve the problem. The Framework of Alternative Nonnegative Least Square(ANLS) are the coordinates of the block formulation approaches that have been proven reliable theoretically and empirically efficient. This paper proposes a new algorithm to solve NMF problem based on the framework of ANLS.This algorithm inherits the convergenceproperty of the ANLS framework to nonlinear constraints NMF formulations.

  15. Investigations on application of multigrid method to MHD equilibrium analysis

    International Nuclear Information System (INIS)

    Ikuno, Soichiro

    2000-01-01

    The potentiality of application for Multi-grid method to MHD equilibrium analysis is investigated. The nonlinear eigenvalue problem often appears when the MHD equilibria are determined by solving the Grad-Shafranov equation numerically. After linearization of the equation, the problem is solved by use of the iterative method. Although the Red-Black SOR method or Gauss-Seidel method is often used for the solution of the linearized equation, it takes much CPU time to solve the problem. The Multi-grid method is compared with the SOR method for the Poisson Problem. The results of computations show that the CPU time required for the Multi-grid method is about 1000 times as small as that for the SOR method. (author)

  16. Multigrid Methods for EHL Problems

    Science.gov (United States)

    Nurgat, Elyas; Berzins, Martin

    1996-01-01

    In many bearings and contacts, forces are transmitted through thin continuous fluid films which separate two contacting elements. Objects in contact are normally subjected to friction and wear which can be reduced effectively by using lubricants. If the lubricant film is sufficiently thin to prevent the opposing solids from coming into contact and carries the entire load, then we have hydrodynamic lubrication, where the lubricant film is determined by the motion and geometry of the solids. However, for loaded contacts of low geometrical conformity, such as gears, rolling contact bearings and cams, this is not the case due to high pressures and this is referred to as Elasto-Hydrodynamic Lubrication (EHL) In EHL, elastic deformation of the contacting elements and the increase in fluid viscosity with pressure are very significant and cannot be ignored. Since the deformation results in changing the geometry of the lubricating film, which in turn determines the pressure distribution, an EHL mathematical model must simultaneously satisfy the complex elasticity (integral) and the Reynolds lubrication (differential) equations. The nonlinear and coupled nature of the two equations makes numerical calculations computationally intensive. This is especially true for highly loaded problems found in practice. One novel feature of these problems is that the solution may exhibit sharp pressure spikes in the outlet region. To this date both finite element and finite difference methods have been used to solve EHL problems with perhaps greater emphasis on the use of the finite difference approach. In both cases, a major computational difficulty is ensuring convergence of the nonlinear equations solver to a steady state solution. Two successful methods for achieving this are direct iteration and multigrid methods. Direct iteration methods (e.g Gauss Seidel) have long been used in conjunction with finite difference discretizations on regular meshes. Perhaps one of the best examples of

  17. An algorithm for nonlinear thermal analysis of fuel bearing pads

    International Nuclear Information System (INIS)

    Attia, M.H.; D'Silva, N.

    1983-01-01

    An algorithm has been developed for accurate prediction of the temperature field in a CANDU fuel bearing pad and the extent of the nucleate boiling in the crevice region. The methodology recognizes the nonlinear nature of the problem due to the fact that local boiling is both controlling and being controlled by the conditions of heat transfer at the boundaries. The finite difference model accounts for the volumetric effect of the thermal contact resistance at the bearing pad/pressure tube interface. It also allows the evaluation of the thermal barrier effect caused by applying an oxide film on the radiused surface of the bearing pad. Information pertaining to the distribution of the coefficient of heat transfer over water-cooled surfaces has been generated. Analysis of the results indicated the significance of considering the nonlinear behaviour of the system in determining its state of equilibrium. It also indicated that, depending on the thickness of the oxide layer and the position of the bearing pad along the core of the reactor, the nucleate boiling process can be prevented

  18. Parallel multigrid methods: implementation on message-passing computers and applications to fluid dynamics. A draft

    International Nuclear Information System (INIS)

    Solchenbach, K.; Thole, C.A.; Trottenberg, U.

    1987-01-01

    For a wide class of problems in scientific computing, in particular for partial differential equations, the multigrid principle has proved to yield highly efficient numerical methods. However, the principle has to be applied carefully: if the multigrid components are not chosen adequately with respect to the given problem, the efficiency may be much smaller than possible. This has been demonstrated for many practical problems. Unfortunately, the general theories on multigrid convergence do not give much help in constructing really efficient multigrid algorithms. Although some progress has been made in bridging the gap between theory and practice during the last few years, there are still several theoretical approaches which are misleading rather than helpful with respect to the objective of real efficiency. The research in finding highly efficient algorithms for non-model applications therefore is still a sophisticated mixture of theoretical considerations, a transfer of experiences from model to real life problems and systematical experimental work. The emphasis of the practical research activity today lies - among others - in the following fields: - finding efficient multigrid components for really complex problems, - combining the multigrid approach with advanced discretizative techniques: - constructing highly parallel multigrid algorithms. In this paper, we want to deal mainly with the last topic

  19. Parallel multigrid smoothing: polynomial versus Gauss-Seidel

    International Nuclear Information System (INIS)

    Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

    2003-01-01

    Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines

  20. Parallel multigrid smoothing: polynomial versus Gauss-Seidel

    Science.gov (United States)

    Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

    2003-07-01

    Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

  1. Diablo 2.0: A modern DNS/LES code for the incompressible NSE leveraging new time-stepping and multigrid algorithms

    Science.gov (United States)

    Cavaglieri, Daniele; Bewley, Thomas; Mashayek, Ali

    2015-11-01

    We present a new code, Diablo 2.0, for the simulation of the incompressible NSE in channel and duct flows with strong grid stretching near walls. The code leverages the fractional step approach with a few twists. New low-storage IMEX (implicit-explicit) Runge-Kutta time-marching schemes are tested which are superior to the traditional and widely-used CN/RKW3 (Crank-Nicolson/Runge-Kutta-Wray) approach; the new schemes tested are L-stable in their implicit component, and offer improved overall order of accuracy and stability with, remarkably, similar computational cost and storage requirements. For duct flow simulations, our new code also introduces a new smoother for the multigrid solver for the pressure Poisson equation. The classic approach, involving alternating-direction zebra relaxation, is replaced by a new scheme, dubbed tweed relaxation, which achieves the same convergence rate with roughly half the computational cost. The code is then tested on the simulation of a shear flow instability in a duct, a classic problem in fluid mechanics which has been the object of extensive numerical modelling for its role as a canonical pathway to energetic turbulence in several fields of science and engineering.

  2. Multigrid Methods for the Computation of Propagators in Gauge Fields

    Science.gov (United States)

    Kalkreuter, Thomas

    Multigrid methods were invented for the solution of discretized partial differential equations in order to overcome the slowness of traditional algorithms by updates on various length scales. In the present work generalizations of multigrid methods for propagators in gauge fields are investigated. Gauge fields are incorporated in algorithms in a covariant way. The kernel C of the restriction operator which averages from one grid to the next coarser grid is defined by projection on the ground-state of a local Hamiltonian. The idea behind this definition is that the appropriate notion of smoothness depends on the dynamics. The ground-state projection choice of C can be used in arbitrary dimension and for arbitrary gauge group. We discuss proper averaging operations for bosons and for staggered fermions. The kernels C can also be used in multigrid Monte Carlo simulations, and for the definition of block spins and blocked gauge fields in Monte Carlo renormalization group studies. Actual numerical computations are performed in four-dimensional SU(2) gauge fields. We prove that our proposals for block spins are “good”, using renormalization group arguments. A central result is that the multigrid method works in arbitrarily disordered gauge fields, in principle. It is proved that computations of propagators in gauge fields without critical slowing down are possible when one uses an ideal interpolation kernel. Unfortunately, the idealized algorithm is not practical, but it was important to answer questions of principle. Practical methods are able to outperform the conjugate gradient algorithm in case of bosons. The case of staggered fermions is harder. Multigrid methods give considerable speed-ups compared to conventional relaxation algorithms, but on lattices up to 184 conjugate gradient is superior.

  3. A Design of a Hybrid Non-Linear Control Algorithm

    Directory of Open Access Journals (Sweden)

    Farinaz Behrooz

    2017-11-01

    Full Text Available One of the high energy consuming devices in the buildings is the air-conditioning system. Designing a proper controller to consider the thermal comfort and simultaneously control the energy usage of the device will impact on the system energy efficiency and its performance. The aim of this study was to design a Multiple-Input and Multiple-Output (MIMO, non-linear, and intelligent controller on direct expansion air-conditioning system The control algorithm uses the Fuzzy Cognitive Map method as a main controller and the Generalized Predictive Control method is used for assigning the initial weights of the main controller. The results of the proposed controller shows that the controller was successfully designed and works in set point tracking and under disturbance rejection tests. The obtained results of the Generalized Predictive Control-Fuzzy Cognitive Map controller are compared with the previous MIMO Linear Quadratic Gaussian control design on the same direct expansion air-conditioning system under the same conditions. The comparative results indicate energy savings would be achieved with the proposed controller with long-term usage. Energy efficiency and thermal comfort conditions are achieved by the proposed controller.

  4. A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

    KAUST Repository

    Domí nguez, Luis F.; Pistikopoulos, Efstratios N.

    2012-01-01

    An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear

  5. Nonlinear dynamics optimization with particle swarm and genetic algorithms for SPEAR3 emittance upgrade

    International Nuclear Information System (INIS)

    Huang, Xiaobiao; Safranek, James

    2014-01-01

    Nonlinear dynamics optimization is carried out for a low emittance upgrade lattice of SPEAR3 in order to improve its dynamic aperture and Touschek lifetime. Two multi-objective optimization algorithms, a genetic algorithm and a particle swarm algorithm, are used for this study. The performance of the two algorithms are compared. The result shows that the particle swarm algorithm converges significantly faster to similar or better solutions than the genetic algorithm and it does not require seeding of good solutions in the initial population. These advantages of the particle swarm algorithm may make it more suitable for many accelerator optimization applications

  6. Nonlinear dynamics optimization with particle swarm and genetic algorithms for SPEAR3 emittance upgrade

    Energy Technology Data Exchange (ETDEWEB)

    Huang, Xiaobiao, E-mail: xiahuang@slac.stanford.edu; Safranek, James

    2014-09-01

    Nonlinear dynamics optimization is carried out for a low emittance upgrade lattice of SPEAR3 in order to improve its dynamic aperture and Touschek lifetime. Two multi-objective optimization algorithms, a genetic algorithm and a particle swarm algorithm, are used for this study. The performance of the two algorithms are compared. The result shows that the particle swarm algorithm converges significantly faster to similar or better solutions than the genetic algorithm and it does not require seeding of good solutions in the initial population. These advantages of the particle swarm algorithm may make it more suitable for many accelerator optimization applications.

  7. Copper Mountain conference on multigrid methods. Preliminary proceedings -- List of abstracts

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1995-12-31

    This report contains abstracts of the papers presented at the conference. Papers cover multigrid algorithms and applications of multigrid methods. Applications include the following: solution of elliptical problems; electric power grids; fluid mechanics; atmospheric data assimilation; thermocapillary effects on weld pool shape; boundary-value problems; prediction of hurricane tracks; modeling multi-dimensional combustion and detailed chemistry; black-oil reservoir simulation; image processing; and others.

  8. A multigrid Newton-Krylov method for flux-limited radiation diffusion

    International Nuclear Information System (INIS)

    Rider, W.J.; Knoll, D.A.; Olson, G.L.

    1998-01-01

    The authors focus on the integration of radiation diffusion including flux-limited diffusion coefficients. The nonlinear integration is accomplished with a Newton-Krylov method preconditioned with a multigrid Picard linearization of the governing equations. They investigate the efficiency of the linear and nonlinear iterative techniques

  9. A Model Predictive Algorithm for Active Control of Nonlinear Noise Processes

    Directory of Open Access Journals (Sweden)

    Qi-Zhi Zhang

    2005-01-01

    Full Text Available In this paper, an improved nonlinear Active Noise Control (ANC system is achieved by introducing an appropriate secondary source. For ANC system to be successfully implemented, the nonlinearity of the primary path and time delay of the secondary path must be overcome. A nonlinear Model Predictive Control (MPC strategy is introduced to deal with the time delay in the secondary path and the nonlinearity in the primary path of the ANC system. An overall online modeling technique is utilized for online secondary path and primary path estimation. The secondary path is estimated using an adaptive FIR filter, and the primary path is estimated using a Neural Network (NN. The two models are connected in parallel with the two paths. In this system, the mutual disturbances between the operation of the nonlinear ANC controller and modeling of the secondary can be greatly reduced. The coefficients of the adaptive FIR filter and weight vector of NN are adjusted online. Computer simulations are carried out to compare the proposed nonlinear MPC method with the nonlinear Filter-x Least Mean Square (FXLMS algorithm. The results showed that the convergence speed of the proposed nonlinear MPC algorithm is faster than that of nonlinear FXLMS algorithm. For testing the robust performance of the proposed nonlinear ANC system, the sudden changes in the secondary path and primary path of the ANC system are considered. Results indicated that the proposed nonlinear ANC system can rapidly track the sudden changes in the acoustic paths of the nonlinear ANC system, and ensure the adaptive algorithm stable when the nonlinear ANC system is time variable.

  10. Layout optimization with algebraic multigrid methods

    Science.gov (United States)

    Regler, Hans; Ruede, Ulrich

    1993-01-01

    Finding the optimal position for the individual cells (also called functional modules) on the chip surface is an important and difficult step in the design of integrated circuits. This paper deals with the problem of relative placement, that is the minimization of a quadratic functional with a large, sparse, positive definite system matrix. The basic optimization problem must be augmented by constraints to inhibit solutions where cells overlap. Besides classical iterative methods, based on conjugate gradients (CG), we show that algebraic multigrid methods (AMG) provide an interesting alternative. For moderately sized examples with about 10000 cells, AMG is already competitive with CG and is expected to be superior for larger problems. Besides the classical 'multiplicative' AMG algorithm where the levels are visited sequentially, we propose an 'additive' variant of AMG where levels may be treated in parallel and that is suitable as a preconditioner in the CG algorithm.

  11. Toward robust scalable algebraic multigrid solvers

    International Nuclear Information System (INIS)

    Waisman, Haim; Schroder, Jacob; Olson, Luke; Hiriyur, Badri; Gaidamour, Jeremie; Siefert, Christopher; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

    2010-01-01

    This talk highlights some multigrid challenges that arise from several application areas including structural dynamics, fluid flow, and electromagnetics. A general framework is presented to help introduce and understand algebraic multigrid methods based on energy minimization concepts. Connections between algebraic multigrid prolongators and finite element basis functions are made to explored. It is shown how the general algebraic multigrid framework allows one to adapt multigrid ideas to a number of different situations. Examples are given corresponding to linear elasticity and specifically in the solution of linear systems associated with extended finite elements for fracture problems.

  12. Sparse Nonlinear Electromagnetic Imaging Accelerated With Projected Steepest Descent Algorithm

    KAUST Repository

    Desmal, Abdulla; Bagci, Hakan

    2017-01-01

    steepest descent algorithm. The algorithm uses a projection operator to enforce the sparsity constraint by thresholding the solution at every iteration. Thresholding level and iteration step are selected carefully to increase the efficiency without

  13. Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems

    Science.gov (United States)

    Bramble, James H.; Kwak, Do Y.; Pasciak, Joseph E.

    1993-01-01

    In this paper, we present an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. We also study smoothers based entirely on the original operator. One is based on the normal form, that is, the product of the operator and its transpose. Other smoothers studied include point and line, Jacobi, and Gauss-Seidel. We show that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not depending on the number of multigrid levels).

  14. On a multigrid method for the coupled Stokes and porous media flow problem

    Science.gov (United States)

    Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

    2017-07-01

    The multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the coupled problem, which is discretized by finite volumes on staggered grids, giving rise to a saddle point linear system. Special treatment is required regarding the discretization at the interface. An Uzawa smoother is employed in multigrid, which is a decoupled procedure based on symmetric Gauss-Seidel smoothing for velocity components and a simple Richardson iteration for the pressure field. Since a relaxation parameter is part of a Richardson iteration, Local Fourier Analysis (LFA) is applied to determine the optimal parameters. Highly satisfactory multigrid convergence is reported, and, moreover, the algorithm performs well for small values of the hydraulic conductivity and fluid viscosity, that are relevant for applications.

  15. An evaluation of parallel multigrid as a solver and a preconditioner for singular perturbed problems

    Energy Technology Data Exchange (ETDEWEB)

    Oosterlee, C.W. [Inst. for Algorithms and Scientific Computing, Sankt Augustin (Germany); Washio, T. [C& C Research Lab., Sankt Augustin (Germany)

    1996-12-31

    In this paper we try to achieve h-independent convergence with preconditioned GMRES and BiCGSTAB for 2D singular perturbed equations. Three recently developed multigrid methods are adopted as a preconditioner. They are also used as solution methods in order to compare the performance of the methods as solvers and as preconditioners. Two of the multigrid methods differ only in the transfer operators. One uses standard matrix- dependent prolongation operators from. The second uses {open_quotes}upwind{close_quotes} prolongation operators, developed. Both employ the Galerkin coarse grid approximation and an alternating zebra line Gauss-Seidel smoother. The third method is based on the block LU decomposition of a matrix and on an approximate Schur complement. This multigrid variant is presented in. All three multigrid algorithms are algebraic methods.

  16. Aitken extrapolation and epsilon algorithm for an accelerated solution of weakly singular nonlinear Volterra integral equations

    International Nuclear Information System (INIS)

    Mesgarani, H; Parmour, P; Aghazadeh, N

    2010-01-01

    In this paper, we apply Aitken extrapolation and epsilon algorithm as acceleration technique for the solution of a weakly singular nonlinear Volterra integral equation of the second kind. In this paper, based on Tao and Yong (2006 J. Math. Anal. Appl. 324 225-37.) the integral equation is solved by Navot's quadrature formula. Also, Tao and Yong (2006) for the first time applied Richardson extrapolation to accelerating convergence for the weakly singular nonlinear Volterra integral equations of the second kind. To our knowledge, this paper may be the first attempt to apply Aitken extrapolation and epsilon algorithm for the weakly singular nonlinear Volterra integral equations of the second kind.

  17. The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems

    NARCIS (Netherlands)

    P.J. Collins (Pieter); A. Goldsztejn

    2008-01-01

    htmlabstractThis paper introduces a new algorithm dedicated to the rigorous reachability analysis of nonlinear dynamical systems. The algorithm is initially presented in the context of discrete time dynamical systems, and then extended to continuous time dynamical systems driven by ODEs. In

  18. Motion Cueing Algorithm Development: Human-Centered Linear and Nonlinear Approaches

    Science.gov (United States)

    Houck, Jacob A. (Technical Monitor); Telban, Robert J.; Cardullo, Frank M.

    2005-01-01

    While the performance of flight simulator motion system hardware has advanced substantially, the development of the motion cueing algorithm, the software that transforms simulated aircraft dynamics into realizable motion commands, has not kept pace. Prior research identified viable features from two algorithms: the nonlinear "adaptive algorithm", and the "optimal algorithm" that incorporates human vestibular models. A novel approach to motion cueing, the "nonlinear algorithm" is introduced that combines features from both approaches. This algorithm is formulated by optimal control, and incorporates a new integrated perception model that includes both visual and vestibular sensation and the interaction between the stimuli. Using a time-varying control law, the matrix Riccati equation is updated in real time by a neurocomputing approach. Preliminary pilot testing resulted in the optimal algorithm incorporating a new otolith model, producing improved motion cues. The nonlinear algorithm vertical mode produced a motion cue with a time-varying washout, sustaining small cues for longer durations and washing out large cues more quickly compared to the optimal algorithm. The inclusion of the integrated perception model improved the responses to longitudinal and lateral cues. False cues observed with the NASA adaptive algorithm were absent. The neurocomputing approach was crucial in that the number of presentations of an input vector could be reduced to meet the real time requirement without degrading the quality of the motion cues.

  19. Comparative efficiencies of three parallel algorithms for nonlinear ...

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    This algorithm is better suited for large size problems on coarse ... and reliable time integration algorithms for solving the second-order dynamic equilibrium equations that arise due ... Programming models required to take advantage of the parallel and distributed ..... In addition, MPI added the concept of a 'virtual topology'.

  20. Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library

    Energy Technology Data Exchange (ETDEWEB)

    2017-10-24

    ParELAG is a parallel C++ library for numerical upscaling of finite element discretizations and element-based algebraic multigrid solvers. It provides optimal complexity algorithms to build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equations (elliptic, hyperbolic, saddle point problems) on general unstructured meshes. Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.

  1. Parallel processors and nonlinear structural dynamics algorithms and software

    Science.gov (United States)

    Belytschko, Ted

    1989-01-01

    A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.

  2. Multigrid methods for fully implicit oil reservoir simulation

    Energy Technology Data Exchange (ETDEWEB)

    Molenaar, J.

    1995-12-31

    In this paper, the authors consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations the material balance or continuity equations, and the equation of motion (Darcy`s law). For the numerical solution of this system of nonlinear partial differential equations, there are two approaches: the fully implicit or simultaneous solution method, and the sequential solution method. In this paper, the authors consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations.

  3. NONLINEAR FILTER METHOD OF GPS DYNAMIC POSITIONING BASED ON BANCROFT ALGORITHM

    Institute of Scientific and Technical Information of China (English)

    ZHANGQin; TAOBen-zao; ZHAOChao-ying; WANGLi

    2005-01-01

    Because of the ignored items after linearization, the extended Kalman filter (EKF) becomes a form of suboptimal gradient descent algorithm. The emanative tendency exists in GPS solution when the filter equations are ill-posed. The deviation in the estimation cannot be avoided. Furthermore, the true solution may be lost in pseudorange positioning because the linearized pseudorange equations are partial solutions. To solve the above problems in GPS dynamic positioning by using EKF, a closed-form Kalman filter method called the two-stage algorithm is presented for the nonlinear algebraic solution of GPS dynamic positioning based on the global nonlinear least squares closed algorithm--Bancroft numerical algorithm of American. The method separates the spatial parts from temporal parts during processing the GPS filter problems, and solves the nonlinear GPS dynamic positioning, thus getting stable and reliable dynamic positioning solutions.

  4. Achieving Textbook Multigrid Efficiency for Hydrostatic Ice Sheet Flow

    KAUST Repository

    Brown, Jed

    2013-03-12

    The hydrostatic equations for ice sheet flow offer improved fidelity compared with the shallow ice approximation and shallow stream approximation popular in today\\'s ice sheet models. Nevertheless, they present a serious bottleneck because they require the solution of a three-dimensional (3D) nonlinear system, as opposed to the two-dimensional system present in the shallow stream approximation. This 3D system is posed on high-aspect domains with strong anisotropy and variation in coefficients, making it expensive to solve with current methods. This paper presents a Newton--Krylov multigrid solver for the hydrostatic equations that demonstrates textbook multigrid efficiency (an order of magnitude reduction in residual per iteration and solution of the fine-level system at a small multiple of the cost of a residual evaluation). Scalability on Blue Gene/P is demonstrated, and the method is compared to various algebraic methods that are in use or have been proposed as viable approaches.

  5. Achieving Textbook Multigrid Efficiency for Hydrostatic Ice Sheet Flow

    KAUST Repository

    Brown, Jed; Smith, Barry; Ahmadia, Aron

    2013-01-01

    The hydrostatic equations for ice sheet flow offer improved fidelity compared with the shallow ice approximation and shallow stream approximation popular in today's ice sheet models. Nevertheless, they present a serious bottleneck because they require the solution of a three-dimensional (3D) nonlinear system, as opposed to the two-dimensional system present in the shallow stream approximation. This 3D system is posed on high-aspect domains with strong anisotropy and variation in coefficients, making it expensive to solve with current methods. This paper presents a Newton--Krylov multigrid solver for the hydrostatic equations that demonstrates textbook multigrid efficiency (an order of magnitude reduction in residual per iteration and solution of the fine-level system at a small multiple of the cost of a residual evaluation). Scalability on Blue Gene/P is demonstrated, and the method is compared to various algebraic methods that are in use or have been proposed as viable approaches.

  6. Conjugate gradient coupled with multigrid for an indefinite problem

    Science.gov (United States)

    Gozani, J.; Nachshon, A.; Turkel, E.

    1984-01-01

    An iterative algorithm for the Helmholtz equation is presented. This scheme was based on the preconditioned conjugate gradient method for the normal equations. The preconditioning is one cycle of a multigrid method for the discrete Laplacian. The smoothing algorithm is red-black Gauss-Seidel and is constructed so it is a symmetric operator. The total number of iterations needed by the algorithm is independent of h. By varying the number of grids, the number of iterations depends only weakly on k when k(3)h(2) is constant. Comparisons with a SSOR preconditioner are presented.

  7. PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems

    Science.gov (United States)

    Liu, Haopeng; Zhu, Yunpeng; Luo, Zhong; Han, Qingkai

    2017-09-01

    In response to the identification problem concerning multi-degree of freedom (MDOF) nonlinear systems, this study presents the extended forward orthogonal regression (EFOR) based on predicted residual sums of squares (PRESS) to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs (NARX) model and aims to explicitly reveal the physical design parameters of the system. The PRESS-based EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio (AERR)-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5-DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.

  8. A quasi-Newton algorithm for large-scale nonlinear equations

    Directory of Open Access Journals (Sweden)

    Linghua Huang

    2017-02-01

    Full Text Available Abstract In this paper, the algorithm for large-scale nonlinear equations is designed by the following steps: (i a conjugate gradient (CG algorithm is designed as a sub-algorithm to obtain the initial points of the main algorithm, where the sub-algorithm’s initial point does not have any restrictions; (ii a quasi-Newton algorithm with the initial points given by sub-algorithm is defined as main algorithm, where a new nonmonotone line search technique is presented to get the step length α k $\\alpha_{k}$ . The given nonmonotone line search technique can avoid computing the Jacobian matrix. The global convergence and the 1 + q $1+q$ -order convergent rate of the main algorithm are established under suitable conditions. Numerical results show that the proposed method is competitive with a similar method for large-scale problems.

  9. Controller Parameter Optimization for Nonlinear Systems Using Enhanced Bacteria Foraging Algorithm

    Directory of Open Access Journals (Sweden)

    V. Rajinikanth

    2012-01-01

    Full Text Available An enhanced bacteria foraging optimization (EBFO algorithm-based Proportional + integral + derivative (PID controller tuning is proposed for a class of nonlinear process models. The EBFO algorithm is a modified form of standard BFO algorithm. A multiobjective performance index is considered to guide the EBFO algorithm for discovering the best possible value of controller parameters. The efficiency of the proposed scheme has been validated through a comparative study with classical BFO, adaptive BFO, PSO, and GA based controller tuning methods proposed in the literature. The proposed algorithm is tested in real time on a nonlinear spherical tank system. The real-time results show that, EBFO tuned PID controller gives a smooth response for setpoint tracking performance.

  10. New human-centered linear and nonlinear motion cueing algorithms for control of simulator motion systems

    Science.gov (United States)

    Telban, Robert J.

    While the performance of flight simulator motion system hardware has advanced substantially, the development of the motion cueing algorithm, the software that transforms simulated aircraft dynamics into realizable motion commands, has not kept pace. To address this, new human-centered motion cueing algorithms were developed. A revised "optimal algorithm" uses time-invariant filters developed by optimal control, incorporating human vestibular system models. The "nonlinear algorithm" is a novel approach that is also formulated by optimal control, but can also be updated in real time. It incorporates a new integrated visual-vestibular perception model that includes both visual and vestibular sensation and the interaction between the stimuli. A time-varying control law requires the matrix Riccati equation to be solved in real time by a neurocomputing approach. Preliminary pilot testing resulted in the optimal algorithm incorporating a new otolith model, producing improved motion cues. The nonlinear algorithm vertical mode produced a motion cue with a time-varying washout, sustaining small cues for longer durations and washing out large cues more quickly compared to the optimal algorithm. The inclusion of the integrated perception model improved the responses to longitudinal and lateral cues. False cues observed with the NASA adaptive algorithm were absent. As a result of unsatisfactory sensation, an augmented turbulence cue was added to the vertical mode for both the optimal and nonlinear algorithms. The relative effectiveness of the algorithms, in simulating aircraft maneuvers, was assessed with an eleven-subject piloted performance test conducted on the NASA Langley Visual Motion Simulator (VMS). Two methods, the quasi-objective NASA Task Load Index (TLX), and power spectral density analysis of pilot control, were used to assess pilot workload. TLX analysis reveals, in most cases, less workload and variation among pilots with the nonlinear algorithm. Control input

  11. Multigrid Computation of Stratified Flow over Two-Dimensional Obstacles

    Science.gov (United States)

    Paisley, M. F.

    1997-09-01

    A robust multigrid method for the incompressible Navier-Stokes equations is presented and applied to the computation of viscous flow over obstacles in a bounded domain under conditions of neutral stability and stable density stratification. Two obstacle shapes have been used, namely a vertical barrier, for which the grid is Cartesian, and a smooth cosine-shaped obstacle, for which a boundary-conforming transformation is incorporated. Results are given for laminar flows at low Reynolds numbers and turbulent flows at a high Reynolds number, when a simple mixing length turbulence model is included. The multigrid algorithm is used to compute steady flows for each obstacle at low and high Reynolds numbers in conditions of weak static stability, defined byK=ND/πU≤ 1, whereU,N, andDare the upstream velocity, bouyancy frequency, and domain height respectively. Results are also presented for the vertical barrier at low and high Reynolds number in conditions of strong static stability,K> 1, when lee wave motions ensure that the flow is unsteady, and the multigrid algorithm is used to compute the flow at each timestep.

  12. Nonlinear Algorithms for Channel Equalization and Map Symbol Detection.

    Science.gov (United States)

    Giridhar, K.

    The transfer of information through a communication medium invariably results in various kinds of distortion to the transmitted signal. In this dissertation, a feed -forward neural network-based equalizer, and a family of maximum a posteriori (MAP) symbol detectors are proposed for signal recovery in the presence of intersymbol interference (ISI) and additive white Gaussian noise. The proposed neural network-based equalizer employs a novel bit-mapping strategy to handle multilevel data signals in an equivalent bipolar representation. It uses a training procedure to learn the channel characteristics, and at the end of training, the multilevel symbols are recovered from the corresponding inverse bit-mapping. When the channel characteristics are unknown and no training sequences are available, blind estimation of the channel (or its inverse) and simultaneous data recovery is required. Convergence properties of several existing Bussgang-type blind equalization algorithms are studied through computer simulations, and a unique gain independent approach is used to obtain a fair comparison of their rates of convergence. Although simple to implement, the slow convergence of these Bussgang-type blind equalizers make them unsuitable for many high data-rate applications. Rapidly converging blind algorithms based on the principle of MAP symbol-by -symbol detection are proposed, which adaptively estimate the channel impulse response (CIR) and simultaneously decode the received data sequence. Assuming a linear and Gaussian measurement model, the near-optimal blind MAP symbol detector (MAPSD) consists of a parallel bank of conditional Kalman channel estimators, where the conditioning is done on each possible data subsequence that can convolve with the CIR. This algorithm is also extended to the recovery of convolutionally encoded waveforms in the presence of ISI. Since the complexity of the MAPSD algorithm increases exponentially with the length of the assumed CIR, a suboptimal

  13. Nonlinear PI Control with Adaptive Interaction Algorithm for Multivariable Wastewater Treatment Process

    Directory of Open Access Journals (Sweden)

    S. I. Samsudin

    2014-01-01

    Full Text Available The wastewater treatment plant (WWTP is highly known with the nonlinearity of the control parameters, thus it is difficult to be controlled. In this paper, the enhancement of nonlinear PI controller (ENon-PI to compensate the nonlinearity of the activated sludge WWTP is proposed. The ENon-PI controller is designed by cascading a sector-bounded nonlinear gain to linear PI controller. The rate variation of the nonlinear gain kn is automatically updated based on adaptive interaction algorithm. Initiative to simplify the ENon-PI control structure by adapting kn has been proved by significant improvement under various dynamic influents. More than 30% of integral square error and 14% of integral absolute error are reduced compared to benchmark PI for DO control and nitrate in nitrogen removal control. Better average effluent qualities, less number of effluent violations, and lower aeration energy consumption resulted.

  14. Medical Image Fusion Algorithm Based on Nonlinear Approximation of Contourlet Transform and Regional Features

    Directory of Open Access Journals (Sweden)

    Hui Huang

    2017-01-01

    Full Text Available According to the pros and cons of contourlet transform and multimodality medical imaging, here we propose a novel image fusion algorithm that combines nonlinear approximation of contourlet transform with image regional features. The most important coefficient bands of the contourlet sparse matrix are retained by nonlinear approximation. Low-frequency and high-frequency regional features are also elaborated to fuse medical images. The results strongly suggested that the proposed algorithm could improve the visual effects of medical image fusion and image quality, image denoising, and enhancement.

  15. Algorithms of estimation for nonlinear systems a differential and algebraic viewpoint

    CERN Document Server

    Martínez-Guerra, Rafael

    2017-01-01

    This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.

  16. A multigrid based 3D space-charge routine in the tracking code GPT

    NARCIS (Netherlands)

    Pöplau, G.; Rienen, van U.; Loos, de M.J.; Geer, van der S.B.; Berz, M.; Makino, K.

    2005-01-01

    Fast calculation of3D non-linear space-charge fields is essential for the simulation ofhigh-brightness charged particle beams. We report on our development of a new 3D spacecharge routine in the General Particle Tracer (GPT) code. The model is based on a nonequidistant multigrid Poisson solver that

  17. Generalized Nonlinear Chirp Scaling Algorithm for High-Resolution Highly Squint SAR Imaging.

    Science.gov (United States)

    Yi, Tianzhu; He, Zhihua; He, Feng; Dong, Zhen; Wu, Manqing

    2017-11-07

    This paper presents a modified approach for high-resolution, highly squint synthetic aperture radar (SAR) data processing. Several nonlinear chirp scaling (NLCS) algorithms have been proposed to solve the azimuth variance of the frequency modulation rates that are caused by the linear range walk correction (LRWC). However, the azimuth depth of focusing (ADOF) is not handled well by these algorithms. The generalized nonlinear chirp scaling (GNLCS) algorithm that is proposed in this paper uses the method of series reverse (MSR) to improve the ADOF and focusing precision. It also introduces a high order processing kernel to avoid the range block processing. Simulation results show that the GNLCS algorithm can enlarge the ADOF and focusing precision for high-resolution highly squint SAR data.

  18. Generalized Nonlinear Chirp Scaling Algorithm for High-Resolution Highly Squint SAR Imaging

    Directory of Open Access Journals (Sweden)

    Tianzhu Yi

    2017-11-01

    Full Text Available This paper presents a modified approach for high-resolution, highly squint synthetic aperture radar (SAR data processing. Several nonlinear chirp scaling (NLCS algorithms have been proposed to solve the azimuth variance of the frequency modulation rates that are caused by the linear range walk correction (LRWC. However, the azimuth depth of focusing (ADOF is not handled well by these algorithms. The generalized nonlinear chirp scaling (GNLCS algorithm that is proposed in this paper uses the method of series reverse (MSR to improve the ADOF and focusing precision. It also introduces a high order processing kernel to avoid the range block processing. Simulation results show that the GNLCS algorithm can enlarge the ADOF and focusing precision for high-resolution highly squint SAR data.

  19. Performance comparison of attitude determination, attitude estimation, and nonlinear observers algorithms

    Science.gov (United States)

    MOHAMMED, M. A. SI; BOUSSADIA, H.; BELLAR, A.; ADNANE, A.

    2017-01-01

    This paper presents a brief synthesis and useful performance analysis of different attitude filtering algorithms (attitude determination algorithms, attitude estimation algorithms, and nonlinear observers) applied to Low Earth Orbit Satellite in terms of accuracy, convergence time, amount of memory, and computation time. This latter is calculated in two ways, using a personal computer and also using On-board computer 750 (OBC 750) that is being used in many SSTL Earth observation missions. The use of this comparative study could be an aided design tool to the designer to choose from an attitude determination or attitude estimation or attitude observer algorithms. The simulation results clearly indicate that the nonlinear Observer is the more logical choice.

  20. Multi-Grid Lanczos

    Science.gov (United States)

    Clark, M. A.; Jung, Chulwoo; Lehner, Christoph

    2018-03-01

    We present a Lanczos algorithm utilizing multiple grids that reduces the memory requirements both on disk and in working memory by one order of magnitude for RBC/UKQCD's 48I and 64I ensembles at the physical pion mass. The precision of the resulting eigenvectors is on par with exact deflation.

  1. Multi-Grid Lanczos

    Directory of Open Access Journals (Sweden)

    Clark M. A.

    2018-01-01

    Full Text Available We present a Lanczos algorithm utilizing multiple grids that reduces the memory requirements both on disk and in working memory by one order of magnitude for RBC/UKQCD’s 48I and 64I ensembles at the physical pion mass. The precision of the resulting eigenvectors is on par with exact deflation.

  2. A Parallel Algebraic Multigrid Solver on Graphics Processing Units

    KAUST Repository

    Haase, Gundolf

    2010-01-01

    The paper presents a multi-GPU implementation of the preconditioned conjugate gradient algorithm with an algebraic multigrid preconditioner (PCG-AMG) for an elliptic model problem on a 3D unstructured grid. An efficient parallel sparse matrix-vector multiplication scheme underlying the PCG-AMG algorithm is presented for the many-core GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster and a multi-GPU configuration with eight GPUs is about 100 times faster than a typical server CPU core. © 2010 Springer-Verlag.

  3. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations

    Institute of Scientific and Technical Information of China (English)

    WANG; Shunjin; ZHANG; Hua

    2006-01-01

    The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system.The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,and a new algorithm-algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method.In the new algorithm,the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator.The exact analytical piece-like solution of the ordinary differential equations is expressd in terms of Taylor series with a local convergent radius,and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.

  4. Local multigrid mesh refinement in view of nuclear fuel 3D modelling in pressurised water reactors

    International Nuclear Information System (INIS)

    Barbie, L.

    2013-01-01

    The aim of this study is to improve the performances, in terms of memory space and computational time, of the current modelling of the Pellet-Cladding mechanical Interaction (PCI), complex phenomenon which may occurs during high power rises in pressurised water reactors. Among the mesh refinement methods - methods dedicated to efficiently treat local singularities - a local multi-grid approach was selected because it enables the use of a black-box solver while dealing few degrees of freedom at each level. The Local Defect Correction (LDC) method, well suited to a finite element discretization, was first analysed and checked in linear elasticity, on configurations resulting from the PCI, since its use in solid mechanics is little widespread. Various strategies concerning the implementation of the multilevel algorithm were also compared. Coupling the LDC method with the Zienkiewicz-Zhu a posteriori error estimator in order to automatically detect the zones to be refined, was then tested. Performances obtained on two-dimensional and three-dimensional cases are very satisfactory, since the algorithm proposed is more efficient than h-adaptive refinement methods. Lastly, the LDC algorithm was extended to nonlinear mechanics. Space/time refinement as well as transmission of the initial conditions during the re-meshing step were looked at. The first results obtained are encouraging and show the interest of using the LDC method for PCI modelling. (author) [fr

  5. Finite volume multigrid method of the planar contraction flow of a viscoelastic fluid

    Science.gov (United States)

    Moatssime, H. Al; Esselaoui, D.; Hakim, A.; Raghay, S.

    2001-08-01

    This paper reports on a numerical algorithm for the steady flow of viscoelastic fluid. The conservative and constitutive equations are solved using the finite volume method (FVM) with a hybrid scheme for the velocities and first-order upwind approximation for the viscoelastic stress. A non-uniform staggered grid system is used. The iterative SIMPLE algorithm is employed to relax the coupled momentum and continuity equations. The non-linear algebraic equations over the flow domain are solved iteratively by the symmetrical coupled Gauss-Seidel (SCGS) method. In both, the full approximation storage (FAS) multigrid algorithm is used. An Oldroyd-B fluid model was selected for the calculation. Results are reported for planar 4:1 abrupt contraction at various Weissenberg numbers. The solutions are found to be stable and smooth. The solutions show that at high Weissenberg number the domain must be long enough. The convergence of the method has been verified with grid refinement. All the calculations have been performed on a PC equipped with a Pentium III processor at 550 MHz. Copyright

  6. A conjugate gradients/trust regions algorithms for training multilayer perceptrons for nonlinear mapping

    Science.gov (United States)

    Madyastha, Raghavendra K.; Aazhang, Behnaam; Henson, Troy F.; Huxhold, Wendy L.

    1992-01-01

    This paper addresses the issue of applying a globally convergent optimization algorithm to the training of multilayer perceptrons, a class of Artificial Neural Networks. The multilayer perceptrons are trained towards the solution of two highly nonlinear problems: (1) signal detection in a multi-user communication network, and (2) solving the inverse kinematics for a robotic manipulator. The research is motivated by the fact that a multilayer perceptron is theoretically capable of approximating any nonlinear function to within a specified accuracy. The algorithm that has been employed in this study combines the merits of two well known optimization algorithms, the Conjugate Gradients and the Trust Regions Algorithms. The performance is compared to a widely used algorithm, the Backpropagation Algorithm, that is basically a gradient-based algorithm, and hence, slow in converging. The performances of the two algorithms are compared with the convergence rate. Furthermore, in the case of the signal detection problem, performances are also benchmarked by the decision boundaries drawn as well as the probability of error obtained in either case.

  7. Multi-grid Particle-in-cell Simulations of Plasma Microturbulence

    International Nuclear Information System (INIS)

    Lewandowski, J.L.V.

    2003-01-01

    A new scheme to accurately retain kinetic electron effects in particle-in-cell (PIC) simulations for the case of electrostatic drift waves is presented. The splitting scheme, which is based on exact separation between adiabatic and on adiabatic electron responses, is shown to yield more accurate linear growth rates than the standard df scheme. The linear and nonlinear elliptic problems that arise in the splitting scheme are solved using a multi-grid solver. The multi-grid particle-in-cell approach offers an attractive path, both from the physics and numerical points of view, to simulate kinetic electron dynamics in global toroidal plasmas

  8. Super-Relaxed ( -Proximal Point Algorithms, Relaxed ( -Proximal Point Algorithms, Linear Convergence Analysis, and Nonlinear Variational Inclusions

    Directory of Open Access Journals (Sweden)

    Agarwal RaviP

    2009-01-01

    Full Text Available We glance at recent advances to the general theory of maximal (set-valued monotone mappings and their role demonstrated to examine the convex programming and closely related field of nonlinear variational inequalities. We focus mostly on applications of the super-relaxed ( -proximal point algorithm to the context of solving a class of nonlinear variational inclusion problems, based on the notion of maximal ( -monotonicity. Investigations highlighted in this communication are greatly influenced by the celebrated work of Rockafellar (1976, while others have played a significant part as well in generalizing the proximal point algorithm considered by Rockafellar (1976 to the case of the relaxed proximal point algorithm by Eckstein and Bertsekas (1992. Even for the linear convergence analysis for the overrelaxed (or super-relaxed ( -proximal point algorithm, the fundamental model for Rockafellar's case does the job. Furthermore, we attempt to explore possibilities of generalizing the Yosida regularization/approximation in light of maximal ( -monotonicity, and then applying to first-order evolution equations/inclusions.

  9. Flaw characterization through nonlinear ultrasonics and wavelet cross-correlation algorithms

    Science.gov (United States)

    Bunget, Gheorghe; Yee, Andrew; Stewart, Dylan; Rogers, James; Henley, Stanley; Bugg, Chris; Cline, John; Webster, Matthew; Farinholt, Kevin; Friedersdorf, Fritz

    2018-04-01

    Ultrasonic measurements have become increasingly important non-destructive techniques to characterize flaws found within various in-service industrial components. The prediction of remaining useful life based on fracture analysis depends on the accurate estimation of flaw size and orientation. However, amplitude-based ultrasonic measurements are not able to estimate the plastic zones that exist ahead of crack tips. Estimating the size of the plastic zone is an advantage since some flaws may propagate faster than others. This paper presents a wavelet cross-correlation (WCC) algorithm that was applied to nonlinear analysis of ultrasonically guided waves (GW). By using this algorithm, harmonics present in the waveforms were extracted and nonlinearity parameters were used to indicate both the tip of the cracks and size of the plastic zone. B-scans performed with the quadratic nonlinearities were sensitive to micro-damage specific to plastic zones.

  10. An improved energy conserving implicit time integration algorithm for nonlinear dynamic structural analysis

    International Nuclear Information System (INIS)

    Haug, E.; Rouvray, A.L. de; Nguyen, Q.S.

    1977-01-01

    This study proposes a general nonlinear algorithm stability criterion; it introduces a nonlinear algorithm, easily implemented in existing incremental/iterative codes, and it applies the new scheme beneficially to problems of linear elastic dynamic snap buckling. Based on the concept of energy conservation, the paper outlines an algorithm which degenerates into the trapezoidal rule, if applied to linear systems. The new algorithm conserves energy in systems having elastic potentials up to the fourth order in the displacements. This is true in the important case of nonlinear total Lagrange formulations where linear elastic material properties are substituted. The scheme is easily implemented in existing incremental-iterative codes with provisions for stiffness reformation and containing the basic Newmark scheme. Numerical analyses of dynamic stability can be dramatically sensitive to amplitude errors, because damping algorithms may mask, and overestimating schemes may numerically trigger, the physical instability. The newly proposed scheme has been applied with larger time steps and less cost to the dynamic snap buckling of simple one and multi degree-of-freedom structures for various initial conditions

  11. An ensemble based nonlinear orthogonal matching pursuit algorithm for sparse history matching of reservoir models

    KAUST Repository

    Fsheikh, Ahmed H.

    2013-01-01

    A nonlinear orthogonal matching pursuit (NOMP) for sparse calibration of reservoir models is presented. Sparse calibration is a challenging problem as the unknowns are both the non-zero components of the solution and their associated weights. NOMP is a greedy algorithm that discovers at each iteration the most correlated components of the basis functions with the residual. The discovered basis (aka support) is augmented across the nonlinear iterations. Once the basis functions are selected from the dictionary, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on approximate gradient estimation using an iterative stochastic ensemble method (ISEM). ISEM utilizes an ensemble of directional derivatives to efficiently approximate gradients. In the current study, the search space is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm.

  12. A chaos-based evolutionary algorithm for general nonlinear programming problems

    International Nuclear Information System (INIS)

    El-Shorbagy, M.A.; Mousa, A.A.; Nasr, S.M.

    2016-01-01

    In this paper we present a chaos-based evolutionary algorithm (EA) for solving nonlinear programming problems named chaotic genetic algorithm (CGA). CGA integrates genetic algorithm (GA) and chaotic local search (CLS) strategy to accelerate the optimum seeking operation and to speed the convergence to the global solution. The integration of global search represented in genetic algorithm and CLS procedures should offer the advantages of both optimization methods while offsetting their disadvantages. By this way, it is intended to enhance the global convergence and to prevent to stick on a local solution. The inherent characteristics of chaos can enhance optimization algorithms by enabling it to escape from local solutions and increase the convergence to reach to the global solution. Twelve chaotic maps have been analyzed in the proposed approach. The simulation results using the set of CEC’2005 show that the application of chaotic mapping may be an effective strategy to improve the performances of EAs.

  13. A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems.

    Science.gov (United States)

    Kazemi, Mahdi; Arefi, Mohammad Mehdi

    2017-03-01

    In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  14. Multi-grid and ICCG for problems with interfaces

    International Nuclear Information System (INIS)

    Dendy, J.E.; Hyman, J.M.

    1980-01-01

    Computation times for the multi-grid (MG) algorithm, the incomplete Cholesky conjugate gradient (ICCG) algorithm [J. Comp. Phys. 26, 43-65 (1978); Math. Comp. 31, 148-162 (1977)], and the modified ICCG (MICCG) algorithm [BIT 18, 142-156 (1978)] to solve elliptic partial differential equations are compared. The MICCG and ICCG algorithms are more robust than the MG for general positive definite systems. A major advantage of the MG algorithm is that the structure of the problem can be exploited to reduce the solution time significantly. Five example problems are discussed. For problems with little structure and for one-shot calculations ICCG is recommended over MG, and MICCG, over ICCG. For problems that are done many times, it is worth investing the effort to study methods like MG. 1 table

  15. Advanced Emergency Braking Control Based on a Nonlinear Model Predictive Algorithm for Intelligent Vehicles

    Directory of Open Access Journals (Sweden)

    Ronghui Zhang

    2017-05-01

    Full Text Available Focusing on safety, comfort and with an overall aim of the comprehensive improvement of a vision-based intelligent vehicle, a novel Advanced Emergency Braking System (AEBS is proposed based on Nonlinear Model Predictive Algorithm. Considering the nonlinearities of vehicle dynamics, a vision-based longitudinal vehicle dynamics model is established. On account of the nonlinear coupling characteristics of the driver, surroundings, and vehicle itself, a hierarchical control structure is proposed to decouple and coordinate the system. To avoid or reduce the collision risk between the intelligent vehicle and collision objects, a coordinated cost function of tracking safety, comfort, and fuel economy is formulated. Based on the terminal constraints of stable tracking, a multi-objective optimization controller is proposed using the theory of non-linear model predictive control. To quickly and precisely track control target in a finite time, an electronic brake controller for AEBS is designed based on the Nonsingular Fast Terminal Sliding Mode (NFTSM control theory. To validate the performance and advantages of the proposed algorithm, simulations are implemented. According to the simulation results, the proposed algorithm has better integrated performance in reducing the collision risk and improving the driving comfort and fuel economy of the smart car compared with the existing single AEBS.

  16. The multigrid preconditioned conjugate gradient method

    Science.gov (United States)

    Tatebe, Osamu

    1993-01-01

    A multigrid preconditioned conjugate gradient method (MGCG method), which uses the multigrid method as a preconditioner of the PCG method, is proposed. The multigrid method has inherent high parallelism and improves convergence of long wavelength components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an efficient method with high parallelism and fast convergence is obtained. First, it is considered a necessary condition of the multigrid preconditioner in order to satisfy requirements of a preconditioner of the PCG method. Next numerical experiments show a behavior of the MGCG method and that the MGCG method is superior to both the ICCG method and the multigrid method in point of fast convergence and high parallelism. This fast convergence is understood in terms of the eigenvalue analysis of the preconditioned matrix. From this observation of the multigrid preconditioner, it is realized that the MGCG method converges in very few iterations and the multigrid preconditioner is a desirable preconditioner of the conjugate gradient method.

  17. An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics.

    Directory of Open Access Journals (Sweden)

    Jamshad Ahmad

    Full Text Available In this paper, a fractional complex transform (FCT is used to convert the given fractional partial differential equations (FPDEs into corresponding partial differential equations (PDEs and subsequently Reduced Differential Transform Method (RDTM is applied on the transformed system of linear and nonlinear time-fractional PDEs. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs and hence can be extended to other complex problems of diversified nonlinear nature.

  18. A frequency bin-wise nonlinear masking algorithm in convolutive mixtures for speech segregation.

    Science.gov (United States)

    Chi, Tai-Shih; Huang, Ching-Wen; Chou, Wen-Sheng

    2012-05-01

    A frequency bin-wise nonlinear masking algorithm is proposed in the spectrogram domain for speech segregation in convolutive mixtures. The contributive weight from each speech source to a time-frequency unit of the mixture spectrogram is estimated by a nonlinear function based on location cues. For each sound source, a non-binary mask is formed from the estimated weights and is multiplied to the mixture spectrogram to extract the sound. Head-related transfer functions (HRTFs) are used to simulate convolutive sound mixtures perceived by listeners. Simulation results show our proposed method outperforms convolutive independent component analysis and degenerate unmixing and estimation technique methods in almost all test conditions.

  19. A nonlinear filtering algorithm for denoising HR(S)TEM micrographs

    International Nuclear Information System (INIS)

    Du, Hongchu

    2015-01-01

    Noise reduction of micrographs is often an essential task in high resolution (scanning) transmission electron microscopy (HR(S)TEM) either for a higher visual quality or for a more accurate quantification. Since HR(S)TEM studies are often aimed at resolving periodic atomistic columns and their non-periodic deviation at defects, it is important to develop a noise reduction algorithm that can simultaneously handle both periodic and non-periodic features properly. In this work, a nonlinear filtering algorithm is developed based on widely used techniques of low-pass filter and Wiener filter, which can efficiently reduce noise without noticeable artifacts even in HR(S)TEM micrographs with contrast of variation of background and defects. The developed nonlinear filtering algorithm is particularly suitable for quantitative electron microscopy, and is also of great interest for beam sensitive samples, in situ analyses, and atomic resolution EFTEM. - Highlights: • A nonlinear filtering algorithm for denoising HR(S)TEM images is developed. • It can simultaneously handle both periodic and non-periodic features properly. • It is particularly suitable for quantitative electron microscopy. • It is of great interest for beam sensitive samples, in situ analyses, and atomic resolution EFTEM

  20. Multi-grid Beam and Warming scheme for the simulation of unsteady ...

    African Journals Online (AJOL)

    In this paper, a multi-grid algorithm is applied to a large-scale block matrix that is produced from a Beam and Warming scheme. The Beam and Warming scheme is used in the simulation of unsteady flow in an open channel. The Gauss-Seidel block-wise iteration method is used for a smoothing process with a few iterations.

  1. On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity

    Directory of Open Access Journals (Sweden)

    Koh Kim Jie

    2017-01-01

    Full Text Available Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution.

  2. Multigrid on unstructured grids using an auxiliary set of structured grids

    Energy Technology Data Exchange (ETDEWEB)

    Douglas, C.C.; Malhotra, S.; Schultz, M.H. [Yale Univ., New Haven, CT (United States)

    1996-12-31

    Unstructured grids do not have a convenient and natural multigrid framework for actually computing and maintaining a high floating point rate on standard computers. In fact, just the coarsening process is expensive for many applications. Since unstructured grids play a vital role in many scientific computing applications, many modifications have been proposed to solve this problem. One suggested solution is to map the original unstructured grid onto a structured grid. This can be used as a fine grid in a standard multigrid algorithm to precondition the original problem on the unstructured grid. We show that unless extreme care is taken, this mapping can lead to a system with a high condition number which eliminates the usefulness of the multigrid method. Theorems with lower and upper bounds are provided. Simple examples show that the upper bounds are sharp.

  3. Embedded algorithms within an FPGA-based system to process nonlinear time series data

    Science.gov (United States)

    Jones, Jonathan D.; Pei, Jin-Song; Tull, Monte P.

    2008-03-01

    This paper presents some preliminary results of an ongoing project. A pattern classification algorithm is being developed and embedded into a Field-Programmable Gate Array (FPGA) and microprocessor-based data processing core in this project. The goal is to enable and optimize the functionality of onboard data processing of nonlinear, nonstationary data for smart wireless sensing in structural health monitoring. Compared with traditional microprocessor-based systems, fast growing FPGA technology offers a more powerful, efficient, and flexible hardware platform including on-site (field-programmable) reconfiguration capability of hardware. An existing nonlinear identification algorithm is used as the baseline in this study. The implementation within a hardware-based system is presented in this paper, detailing the design requirements, validation, tradeoffs, optimization, and challenges in embedding this algorithm. An off-the-shelf high-level abstraction tool along with the Matlab/Simulink environment is utilized to program the FPGA, rather than coding the hardware description language (HDL) manually. The implementation is validated by comparing the simulation results with those from Matlab. In particular, the Hilbert Transform is embedded into the FPGA hardware and applied to the baseline algorithm as the centerpiece in processing nonlinear time histories and extracting instantaneous features of nonstationary dynamic data. The selection of proper numerical methods for the hardware execution of the selected identification algorithm and consideration of the fixed-point representation are elaborated. Other challenges include the issues of the timing in the hardware execution cycle of the design, resource consumption, approximation accuracy, and user flexibility of input data types limited by the simplicity of this preliminary design. Future work includes making an FPGA and microprocessor operate together to embed a further developed algorithm that yields better

  4. Multigrid solution of diffusion equations on distributed memory multiprocessor systems

    International Nuclear Information System (INIS)

    Finnemann, H.

    1988-01-01

    The subject is the solution of partial differential equations for simulation of the reactor core on high-performance computers. The parallelization and implementation of nodal multigrid diffusion algorithms on array and ring configurations of the DIRMU multiprocessor system is outlined. The particular iteration scheme employed in the nodal expansion method appears similarly efficient in serial and parallel environments. The combination of modern multi-level techniques with innovative hardware (vector-multiprocessor systems) provides powerful tools needed for real time simulation of physical systems. The parallel efficiencies range from 70 to 90%. The same performance is estimated for large problems on large multiprocessor systems being designed at present. (orig.) [de

  5. A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations

    Directory of Open Access Journals (Sweden)

    Er Gao

    2012-01-01

    Full Text Available We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q∈(1,2] based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the n-term approximation. At the same time, the n-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which shows that the new algorithm is efficient and accurate.

  6. Modified Hyperspheres Algorithm to Trace Homotopy Curves of Nonlinear Circuits Composed by Piecewise Linear Modelled Devices

    Directory of Open Access Journals (Sweden)

    H. Vazquez-Leal

    2014-01-01

    Full Text Available We present a homotopy continuation method (HCM for finding multiple operating points of nonlinear circuits composed of devices modelled by using piecewise linear (PWL representations. We propose an adaptation of the modified spheres path tracking algorithm to trace the homotopy trajectories of PWL circuits. In order to assess the benefits of this proposal, four nonlinear circuits composed of piecewise linear modelled devices are analysed to determine their multiple operating points. The results show that HCM can find multiple solutions within a single homotopy trajectory. Furthermore, we take advantage of the fact that homotopy trajectories are PWL curves meant to replace the multidimensional interpolation and fine tuning stages of the path tracking algorithm with a simple and highly accurate procedure based on the parametric straight line equation.

  7. Development of new multigrid schemes for the method of characteristics in neutron transport theory

    International Nuclear Information System (INIS)

    Grassi, G.

    2006-01-01

    This dissertation is based upon our doctoral research that dealt with the conception and development of new non-linear multigrid techniques for the Method of the Characteristics (MOC) within the TDT code. Here we focus upon a two-level scheme consisting of a fine level on which the neutron transport equation is iteratively solved using the MOC algorithm, and a coarse level defined by a more coarsely discretized phase space on which a low-order problem is considered. The solution of this problem is then used in order to correct the angular flux moments resulting from the previous transport iteration. A flux-volume homogenization procedure is employed to evaluate the coarse-level material properties after each transport iteration. This entails the non-linearity of the methods. According to the Generalised Equivalence Theory (GET), additional degrees of freedom are introduced for the low-order problem so that the convergence of the acceleration scheme can be ensured. We present two classes of non-linear methods: transport-like methods and discussion-like methods. Transport-like methods consider a homogenized low-order transport problem on the coarse level. This problem is iteratively solved using the same MOC algorithm as for the transport problem on the fine level. Discontinuity factors are then employed, per region or per surface, in order to reconstruct the currents evaluated by the low-order operator, which ensure the convergence of the acceleration scheme. On the other hand, discussion-like methods consider a low-order problem inspired by diffusion. We studied the non-linear Coarse Mesh Finite Difference (CMFD) method, already present in literature, in the perspective of integrating it into TDT code. Then, we developed a new non-linear method on the model of CMFD. From the latter, we borrowed the idea to establish a simple relation between currents and fluxes in order to obtain a problem involving only coarse fluxes. Finally, those non-linear methods have been

  8. Parallel supercomputing: Advanced methods, algorithms, and software for large-scale linear and nonlinear problems

    Energy Technology Data Exchange (ETDEWEB)

    Carey, G.F.; Young, D.M.

    1993-12-31

    The program outlined here is directed to research on methods, algorithms, and software for distributed parallel supercomputers. Of particular interest are finite element methods and finite difference methods together with sparse iterative solution schemes for scientific and engineering computations of very large-scale systems. Both linear and nonlinear problems will be investigated. In the nonlinear case, applications with bifurcation to multiple solutions will be considered using continuation strategies. The parallelizable numerical methods of particular interest are a family of partitioning schemes embracing domain decomposition, element-by-element strategies, and multi-level techniques. The methods will be further developed incorporating parallel iterative solution algorithms with associated preconditioners in parallel computer software. The schemes will be implemented on distributed memory parallel architectures such as the CRAY MPP, Intel Paragon, the NCUBE3, and the Connection Machine. We will also consider other new architectures such as the Kendall-Square (KSQ) and proposed machines such as the TERA. The applications will focus on large-scale three-dimensional nonlinear flow and reservoir problems with strong convective transport contributions. These are legitimate grand challenge class computational fluid dynamics (CFD) problems of significant practical interest to DOE. The methods developed and algorithms will, however, be of wider interest.

  9. Summary Report: Multigrid for Systems of Elliptic PDEs

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Barry [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2016-11-17

    We are interested in determining if multigrid can be effectively applied to the system. The conclusion that I seem to be drawn to is that it is impossible to develop a blackbox multigrid solver for these general systems. Analysis of the system of PDEs must be conducted first to determine pre-processing procedures on the continuous problem before applying a multigrid method. Determining this pre-processing is currently not incorporated in black-box multigrid strategies. Nevertheless, we characterize some system features that will make the system more amenable to multigrid approaches, techniques that may lead to more amenable systems, and multigrid procedures that are generally more appropriate for these systems.

  10. Analysis and development of stochastic multigrid methods in lattice field theory

    International Nuclear Information System (INIS)

    Grabenstein, M.

    1994-01-01

    We study the relation between the dynamical critical behavior and the kinematics of stochastic multigrid algorithms. The scale dependence of acceptance rates for nonlocal Metropolis updates is analyzed with the help of an approximation formula. A quantitative study of the kinematics of multigrid algorithms in several interacting models is performed. We find that for a critical model with Hamiltonian H(Φ) absence of critical slowing down can only be expected if the expansion of (H(Φ+ψ)) in terms of the shift ψ contains no relevant term (mass term). The predictions of this rule was verified in a multigrid Monte Carlo simulation of the Sine Gordon model in two dimensions. Our analysis can serve as a guideline for the development of new algorithms: We propose a new multigrid method for nonabelian lattice gauge theory, the time slice blocking. For SU(2) gauge fields in two dimensions, critical slowing down is almost completely eliminated by this method, in accordance with the theoretical prediction. The generalization of the time slice blocking to SU(2) in four dimensions is investigated analytically and by numerical simulations. Compared to two dimensions, the local disorder in the four dimensional gauge field leads to kinematical problems. (orig.)

  11. An integer optimization algorithm for robust identification of non-linear gene regulatory networks

    Directory of Open Access Journals (Sweden)

    Chemmangattuvalappil Nishanth

    2012-09-01

    Full Text Available Abstract Background Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. Results We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters

  12. A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

    Science.gov (United States)

    White, J. A.; Morrison, J. H.

    1999-01-01

    A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

  13. Fast noise level estimation algorithm based on principal component analysis transform and nonlinear rectification

    Science.gov (United States)

    Xu, Shaoping; Zeng, Xiaoxia; Jiang, Yinnan; Tang, Yiling

    2018-01-01

    We proposed a noniterative principal component analysis (PCA)-based noise level estimation (NLE) algorithm that addresses the problem of estimating the noise level with a two-step scheme. First, we randomly extracted a number of raw patches from a given noisy image and took the smallest eigenvalue of the covariance matrix of the raw patches as the preliminary estimation of the noise level. Next, the final estimation was directly obtained with a nonlinear mapping (rectification) function that was trained on some representative noisy images corrupted with different known noise levels. Compared with the state-of-art NLE algorithms, the experiment results show that the proposed NLE algorithm can reliably infer the noise level and has robust performance over a wide range of image contents and noise levels, showing a good compromise between speed and accuracy in general.

  14. New recursive-least-squares algorithms for nonlinear active control of sound and vibration using neural networks.

    Science.gov (United States)

    Bouchard, M

    2001-01-01

    In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.

  15. Algorithm Design and Validation for Adaptive Nonlinear Control Enhancement (ADVANCE) Technology Development for Resilient Flight Control, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — SSCI proposes to develop and test a framework referred to as the ADVANCE (Algorithm Design and Validation for Adaptive Nonlinear Control Enhancement), within which...

  16. Energy demand forecasting in Iranian metal industry using linear and nonlinear models based on evolutionary algorithms

    International Nuclear Information System (INIS)

    Piltan, Mehdi; Shiri, Hiva; Ghaderi, S.F.

    2012-01-01

    Highlights: ► Investigating different fitness functions for evolutionary algorithms in energy forecasting. ► Energy forecasting of Iranian metal industry by value added, energy prices, investment and employees. ► Using real-coded instead of binary-coded genetic algorithm decreases energy forecasting error. - Abstract: Developing energy-forecasting models is known as one of the most important steps in long-term planning. In order to achieve sustainable energy supply toward economic development and social welfare, it is required to apply precise forecasting model. Applying artificial intelligent models for estimation complex economic and social functions is growing up considerably in many researches recently. In this paper, energy consumption in industrial sector as one of the critical sectors in the consumption of energy has been investigated. Two linear and three nonlinear functions have been used in order to forecast and analyze energy in the Iranian metal industry, Particle Swarm Optimization (PSO) and Genetic Algorithms (GAs) are applied to attain parameters of the models. The Real-Coded Genetic Algorithm (RCGA) has been developed based on real numbers, which is introduced as a new approach in the field of energy forecasting. In the proposed model, electricity consumption has been considered as a function of different variables such as electricity tariff, manufacturing value added, prevailing fuel prices, the number of employees, the investment in equipment and consumption in the previous years. Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Absolute Deviation (MAD) and Mean Absolute Percent Error (MAPE) are the four functions which have been used as the fitness function in the evolutionary algorithms. The results show that the logarithmic nonlinear model using PSO algorithm with 1.91 error percentage has the best answer. Furthermore, the prediction of electricity consumption in industrial sector of Turkey and also Turkish industrial sector

  17. Memetic Algorithms to Solve a Global Nonlinear Optimization Problem. A Review

    Directory of Open Access Journals (Sweden)

    M. K. Sakharov

    2015-01-01

    Full Text Available In recent decades, evolutionary algorithms have proven themselves as the powerful optimization techniques of search engine. Their popularity is due to the fact that they are easy to implement and can be used in all areas, since they are based on the idea of universal evolution. For example, in the problems of a large number of local optima, the traditional optimization methods, usually, fail in finding the global optimum. To solve such problems using a variety of stochastic methods, in particular, the so-called population-based algorithms, which are a kind of evolutionary methods. The main disadvantage of this class of methods is their slow convergence to the exact solution in the neighborhood of the global optimum, as these methods incapable to use the local information about the landscape of the function. This often limits their use in largescale real-world problems where the computation time is a critical factor.One of the promising directions in the field of modern evolutionary computation are memetic algorithms, which can be regarded as a combination of population search of the global optimum and local procedures for verifying solutions, which gives a synergistic effect. In the context of memetic algorithms, the meme is an implementation of the local optimization method to refine solution in the search.The concept of memetic algorithms provides ample opportunities for the development of various modifications of these algorithms, which can vary the frequency of the local search, the conditions of its end, and so on. The practically significant memetic algorithm modifications involve the simultaneous use of different memes. Such algorithms are called multi-memetic.The paper gives statement of the global problem of nonlinear unconstrained optimization, describes the most promising areas of AI modifications, including hybridization and metaoptimization. The main content of the work is the classification and review of existing varieties of

  18. Nonlinear Filtering with IMM Algorithm for Ultra-Tight GPS/INS Integration

    Directory of Open Access Journals (Sweden)

    Dah-Jing Jwo

    2013-05-01

    Full Text Available Abstract This paper conducts a performance evaluation for the ultra-tight integration of a Global positioning system (GPS and an inertial navigation system (INS, using nonlinear filtering approaches with an interacting multiple model (IMM algorithm. An ultra-tight GPS/INS architecture involves the integration of in-phase and quadrature components from the correlator of a GPS receiver with INS data. An unscented Kalman filter (UKF, which employs a set of sigma points by deterministic sampling, avoids the error caused by linearization as in an extended Kalman filter (EKF. Based on the filter structural adaptation for describing various dynamic behaviours, the IMM nonlinear filtering provides an alternative for designing the adaptive filter in the ultra-tight GPS/INS integration. The use of IMM enables tuning of an appropriate value for the process of noise covariance so as to maintain good estimation accuracy and tracking capability. Two examples are provided to illustrate the effectiveness of the design and demonstrate the effective improvement in navigation estimation accuracy. A performance comparison among various filtering methods for ultra-tight integration of GPS and INS is also presented. The IMM based nonlinear filtering approach demonstrates the effectiveness of the algorithm for improved positioning performance.

  19. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

  20. A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrödinger system

    International Nuclear Information System (INIS)

    Cai Jia-Xiang; Wang Yu-Shun

    2013-01-01

    We derive a new method for a coupled nonlinear Schrödinger system by using the square of first-order Fourier spectral differentiation matrix D 1 instead of traditional second-order Fourier spectral differentiation matrix D 2 to approximate the second derivative. We prove the proposed method preserves the charge and energy conservation laws exactly. In numerical tests, we display the accuracy of numerical solution and the role of the nonlinear coupling parameter in cases of soliton collisions. Numerical experiments also exhibit the excellent performance of the method in preserving the charge and energy conservation laws. These numerical results verify that the proposed method is both a charge-preserving and an energy-preserving algorithm

  1. A Multigrid NLS-4DVar Data Assimilation Scheme with Advanced Research WRF (ARW)

    Science.gov (United States)

    Zhang, H.; Tian, X.

    2017-12-01

    The motions of the atmosphere have multiscale properties in space and/or time, and the background error covariance matrix (Β) should thus contain error information at different correlation scales. To obtain an optimal analysis, the multigrid three-dimensional variational data assimilation scheme is used widely when sequentially correcting errors from large to small scales. However, introduction of the multigrid technique into four-dimensional variational data assimilation is not easy, due to its strong dependence on the adjoint model, which has extremely high computational costs in data coding, maintenance, and updating. In this study, the multigrid technique was introduced into the nonlinear least-squares four-dimensional variational assimilation (NLS-4DVar) method, which is an advanced four-dimensional ensemble-variational method that can be applied without invoking the adjoint models. The multigrid NLS-4DVar (MG-NLS-4DVar) scheme uses the number of grid points to control the scale, with doubling of this number when moving from a coarse to a finer grid. Furthermore, the MG-NLS-4DVar scheme not only retains the advantages of NLS-4DVar, but also sufficiently corrects multiscale errors to achieve a highly accurate analysis. The effectiveness and efficiency of the proposed MG-NLS-4DVar scheme were evaluated by several groups of observing system simulation experiments using the Advanced Research Weather Research and Forecasting Model. MG-NLS-4DVar outperformed NLS-4DVar, with a lower computational cost.

  2. A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations

    OpenAIRE

    Gao, Er; Song, Songhe; Zhang, Xinjian

    2012-01-01

    We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q∈(1,2] based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the n-term approximation. At the same time, the n-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which sh...

  3. The genetic algorithm for the nonlinear programming of water pollution control system

    Energy Technology Data Exchange (ETDEWEB)

    Wei, J.; Zhang, J. [China University of Geosciences (China)

    1999-08-01

    In the programming of water pollution control system the combined method of optimization with simulation is used generally. It is not only laborious in calculation, but also the global optimum of the obtained solution is guaranteed difficult. In this paper, the genetic algorithm (GA) used in the nonlinear programming of water pollution control system is given, by which the preferred conception for the programming of waste water system is found in once-through operation. It is more succinct than the conventional method and the global optimum of the obtained solution could be ensured. 6 refs., 4 figs., 3 tabs.

  4. Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem

    DEFF Research Database (Denmark)

    Delbary, Fabrice; Knudsen, Kim

    2014-01-01

    to the generalized Laplace equation. The 3D problem was solved in theory in late 1980s using complex geometrical optics solutions and a scattering transform. Several approximations to the reconstruction method have been suggested and implemented numerically in the literature, but here, for the first time, a complete...... computer implementation of the full nonlinear algorithm is given. First a boundary integral equation is solved by a Nystrom method for the traces of the complex geometrical optics solutions, second the scattering transform is computed and inverted using fast Fourier transform, and finally a boundary value...

  5. A Nonmonotone Line Search Filter Algorithm for the System of Nonlinear Equations

    Directory of Open Access Journals (Sweden)

    Zhong Jin

    2012-01-01

    Full Text Available We present a new iterative method based on the line search filter method with the nonmonotone strategy to solve the system of nonlinear equations. The equations are divided into two groups; some equations are treated as constraints and the others act as the objective function, and the two groups are just updated at the iterations where it is needed indeed. We employ the nonmonotone idea to the sufficient reduction conditions and filter technique which leads to a flexibility and acceptance behavior comparable to monotone methods. The new algorithm is shown to be globally convergent and numerical experiments demonstrate its effectiveness.

  6. Stack emission monitoring using non-dispersive infrared spectroscopy with an optimized nonlinear absorption cross interference correction algorithm

    Directory of Open Access Journals (Sweden)

    Y. W. Sun

    2013-08-01

    Full Text Available In this paper, we present an optimized analysis algorithm for non-dispersive infrared (NDIR to in situ monitor stack emissions. The proposed algorithm simultaneously compensates for nonlinear absorption and cross interference among different gases. We present a mathematical derivation for the measurement error caused by variations in interference coefficients when nonlinear absorption occurs. The proposed algorithm is derived from a classical one and uses interference functions to quantify cross interference. The interference functions vary proportionally with the nonlinear absorption. Thus, interference coefficients among different gases can be modeled by the interference functions whether gases are characterized by linear or nonlinear absorption. In this study, the simultaneous analysis of two components (CO2 and CO serves as an example for the validation of the proposed algorithm. The interference functions in this case can be obtained by least-squares fitting with third-order polynomials. Experiments show that the results of cross interference correction are improved significantly by utilizing the fitted interference functions when nonlinear absorptions occur. The dynamic measurement ranges of CO2 and CO are improved by about a factor of 1.8 and 3.5, respectively. A commercial analyzer with high accuracy was used to validate the CO and CO2 measurements derived from the NDIR analyzer prototype in which the new algorithm was embedded. The comparison of the two analyzers show that the prototype works well both within the linear and nonlinear ranges.

  7. Model-independent nonlinear control algorithm with application to a liquid bridge experiment

    International Nuclear Information System (INIS)

    Petrov, V.; Haaning, A.; Muehlner, K.A.; Van Hook, S.J.; Swinney, H.L.

    1998-01-01

    We present a control method for high-dimensional nonlinear dynamical systems that can target remote unstable states without a priori knowledge of the underlying dynamical equations. The algorithm constructs a high-dimensional look-up table based on the system's responses to a sequence of random perturbations. The method is demonstrated by stabilizing unstable flow of a liquid bridge surface-tension-driven convection experiment that models the float zone refining process. Control of the dynamics is achieved by heating or cooling two thermoelectric Peltier devices placed in the vicinity of the liquid bridge surface. The algorithm routines along with several example programs written in the MATLAB language can be found at ftp://ftp.mathworks.com/pub/contrib/v5/control/nlcontrol. copyright 1998 The American Physical Society

  8. An algorithm for robust non-linear analysis of radioimmunoassays and other bioassays

    International Nuclear Information System (INIS)

    Normolle, D.P.

    1993-01-01

    The four-parameter logistic function is an appropriate model for many types of bioassays that have continuous response variables, such as radioimmunoassays. By modelling the variance of replicates in an assay, one can modify the usual parameter estimation techniques (for example, Gauss-Newton or Marquardt-Levenberg) to produce parameter estimates for the standard curve that are robust against outlying observations. This article describes the computation of robust (M-) estimates for the parameters of the four-parameter logistic function. It describes techniques for modelling the variance structure of the replicates, modifications to the usual iterative algorithms for parameter estimation in non-linear models, and a formula for inverse confidence intervals. To demonstrate the algorithm, the article presents examples where the robustly estimated four-parameter logistic model is compared with the logit-log and four-parameter logistic models with least-squares estimates. (author)

  9. Aplicação do pré-condicionador Multigrid Algébrico baseado em Wavelet no cálculo de campos magnéticos não lineares

    Directory of Open Access Journals (Sweden)

    Fabio Henrique Pereira

    2009-01-01

    Full Text Available In this work the performance of ¿-cycle wavelet-based algebraic multigrid preconditioner for iterative methods is investigated. The method is applied as a preconditioner for the classical iterative methods Bi-Conjugate Gradient Stabilized (BiCGStab, Generalized Minimum Residual (GMRes and Conjugate Gradient (CG to the solution of non-linear system of algebraic equations from the analysis of a switched reluctance motor with ferromagnetic material the steel S45C and nonlinear magnetization curve, associated with the Newton-Raphson algorithm. Particular attention has been focused in both V- and W-cycle convergence factors, as well as the CPU time. Numerical results show the efficiency of the proposed techniques when compared with classical preconditioner, such as Incomplete Cholesky and Incomplete LU decomposition.

  10. An efficient identification approach for stable and unstable nonlinear systems using Colliding Bodies Optimization algorithm.

    Science.gov (United States)

    Pal, Partha S; Kar, R; Mandal, D; Ghoshal, S P

    2015-11-01

    This paper presents an efficient approach to identify different stable and practically useful Hammerstein models as well as unstable nonlinear process along with its stable closed loop counterpart with the help of an evolutionary algorithm as Colliding Bodies Optimization (CBO) optimization algorithm. The performance measures of the CBO based optimization approach such as precision, accuracy are justified with the minimum output mean square value (MSE) which signifies that the amount of bias and variance in the output domain are also the least. It is also observed that the optimization of output MSE in the presence of outliers has resulted in a very close estimation of the output parameters consistently, which also justifies the effective general applicability of the CBO algorithm towards the system identification problem and also establishes the practical usefulness of the applied approach. Optimum values of the MSEs, computational times and statistical information of the MSEs are all found to be the superior as compared with those of the other existing similar types of stochastic algorithms based approaches reported in different recent literature, which establish the robustness and efficiency of the applied CBO based identification scheme. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  11. Multilayer perceptron for robust nonlinear interval regression analysis using genetic algorithms.

    Science.gov (United States)

    Hu, Yi-Chung

    2014-01-01

    On the basis of fuzzy regression, computational models in intelligence such as neural networks have the capability to be applied to nonlinear interval regression analysis for dealing with uncertain and imprecise data. When training data are not contaminated by outliers, computational models perform well by including almost all given training data in the data interval. Nevertheless, since training data are often corrupted by outliers, robust learning algorithms employed to resist outliers for interval regression analysis have been an interesting area of research. Several approaches involving computational intelligence are effective for resisting outliers, but the required parameters for these approaches are related to whether the collected data contain outliers or not. Since it seems difficult to prespecify the degree of contamination beforehand, this paper uses multilayer perceptron to construct the robust nonlinear interval regression model using the genetic algorithm. Outliers beyond or beneath the data interval will impose slight effect on the determination of data interval. Simulation results demonstrate that the proposed method performs well for contaminated datasets.

  12. A measurement fusion method for nonlinear system identification using a cooperative learning algorithm.

    Science.gov (United States)

    Xia, Youshen; Kamel, Mohamed S

    2007-06-01

    Identification of a general nonlinear noisy system viewed as an estimation of a predictor function is studied in this article. A measurement fusion method for the predictor function estimate is proposed. In the proposed scheme, observed data are first fused by using an optimal fusion technique, and then the optimal fused data are incorporated in a nonlinear function estimator based on a robust least squares support vector machine (LS-SVM). A cooperative learning algorithm is proposed to implement the proposed measurement fusion method. Compared with related identification methods, the proposed method can minimize both the approximation error and the noise error. The performance analysis shows that the proposed optimal measurement fusion function estimate has a smaller mean square error than the LS-SVM function estimate. Moreover, the proposed cooperative learning algorithm can converge globally to the optimal measurement fusion function estimate. Finally, the proposed measurement fusion method is applied to ARMA signal and spatial temporal signal modeling. Experimental results show that the proposed measurement fusion method can provide a more accurate model.

  13. Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm

    Science.gov (United States)

    Chen, C.; Xia, J.; Liu, J.; Feng, G.

    2006-01-01

    Using a genetic algorithm to solve an inverse problem of complex nonlinear geophysical equations is advantageous because it does not require computer gradients of models or "good" initial models. The multi-point search of a genetic algorithm makes it easier to find the globally optimal solution while avoiding falling into a local extremum. As is the case in other optimization approaches, the search efficiency for a genetic algorithm is vital in finding desired solutions successfully in a multi-dimensional model space. A binary-encoding genetic algorithm is hardly ever used to resolve an optimization problem such as a simple geophysical inversion with only three unknowns. The encoding mechanism, genetic operators, and population size of the genetic algorithm greatly affect search processes in the evolution. It is clear that improved operators and proper population size promote the convergence. Nevertheless, not all genetic operations perform perfectly while searching under either a uniform binary or a decimal encoding system. With the binary encoding mechanism, the crossover scheme may produce more new individuals than with the decimal encoding. On the other hand, the mutation scheme in a decimal encoding system will create new genes larger in scope than those in the binary encoding. This paper discusses approaches of exploiting the search potential of genetic operations in the two encoding systems and presents an approach with a hybrid-encoding mechanism, multi-point crossover, and dynamic population size for geophysical inversion. We present a method that is based on the routine in which the mutation operation is conducted in the decimal code and multi-point crossover operation in the binary code. The mix-encoding algorithm is called the hybrid-encoding genetic algorithm (HEGA). HEGA provides better genes with a higher probability by a mutation operator and improves genetic algorithms in resolving complicated geophysical inverse problems. Another significant

  14. Experiences using multigrid for geothermal simulation

    Energy Technology Data Exchange (ETDEWEB)

    Bullivant, D.P.; O`Sullivan, M.J. [Univ. of Auckland (New Zealand); Yang, Z. [Univ. of New South Wales (Australia)

    1995-03-01

    Experiences of applying multigrid to the calculation of natural states for geothermal simulations are discussed. The modelling of natural states was chosen for this study because they can take a long time to compute and the computation is often dominated by the development of phase change boundaries that take up a small region in the simulation. For the first part of this work a modified version of TOUGH was used for 2-D vertical problems. A {open_quotes}test-bed{close_quotes} program is now being used to investigate some of the problems encountered with implementing multigrid. This is ongoing work. To date, there have been some encouraging but not startling results.

  15. An Algorithmic Comparison of the Hyper-Reduction and the Discrete Empirical Interpolation Method for a Nonlinear Thermal Problem

    Directory of Open Access Journals (Sweden)

    Felix Fritzen

    2018-02-01

    Full Text Available A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems is presented. First, the Galerkin reduced basis (RB formulation is presented, which fails at providing significant gains with respect to the computational efficiency for nonlinear problems. Renowned methods for the reduction of the computing time of nonlinear reduced order models are the Hyper-Reduction and the (Discrete Empirical Interpolation Method (EIM, DEIM. An algorithmic description and a methodological comparison of both methods are provided. The accuracy of the predictions of the hyper-reduced model and the (DEIM in comparison to the Galerkin RB is investigated. All three approaches are applied to a simple uncertainty quantification of a planar nonlinear thermal conduction problem. The results are compared to computationally intense finite element simulations.

  16. Nonlinear Rayleigh wave inversion based on the shuffled frog-leaping algorithm

    Science.gov (United States)

    Sun, Cheng-Yu; Wang, Yan-Yan; Wu, Dun-Shi; Qin, Xiao-Jun

    2017-12-01

    At present, near-surface shear wave velocities are mainly calculated through Rayleigh wave dispersion-curve inversions in engineering surface investigations, but the required calculations pose a highly nonlinear global optimization problem. In order to alleviate the risk of falling into a local optimal solution, this paper introduces a new global optimization method, the shuffle frog-leaping algorithm (SFLA), into the Rayleigh wave dispersion-curve inversion process. SFLA is a swarm-intelligence-based algorithm that simulates a group of frogs searching for food. It uses a few parameters, achieves rapid convergence, and is capability of effective global searching. In order to test the reliability and calculation performance of SFLA, noise-free and noisy synthetic datasets were inverted. We conducted a comparative analysis with other established algorithms using the noise-free dataset, and then tested the ability of SFLA to cope with data noise. Finally, we inverted a real-world example to examine the applicability of SFLA. Results from both synthetic and field data demonstrated the effectiveness of SFLA in the interpretation of Rayleigh wave dispersion curves. We found that SFLA is superior to the established methods in terms of both reliability and computational efficiency, so it offers great potential to improve our ability to solve geophysical inversion problems.

  17. Enhanced spatial resolution in fluorescence molecular tomography using restarted L1-regularized nonlinear conjugate gradient algorithm.

    Science.gov (United States)

    Shi, Junwei; Liu, Fei; Zhang, Guanglei; Luo, Jianwen; Bai, Jing

    2014-04-01

    Owing to the high degree of scattering of light through tissues, the ill-posedness of fluorescence molecular tomography (FMT) inverse problem causes relatively low spatial resolution in the reconstruction results. Unlike L2 regularization, L1 regularization can preserve the details and reduce the noise effectively. Reconstruction is obtained through a restarted L1 regularization-based nonlinear conjugate gradient (re-L1-NCG) algorithm, which has been proven to be able to increase the computational speed with low memory consumption. The algorithm consists of inner and outer iterations. In the inner iteration, L1-NCG is used to obtain the L1-regularized results. In the outer iteration, the restarted strategy is used to increase the convergence speed of L1-NCG. To demonstrate the performance of re-L1-NCG in terms of spatial resolution, simulation and physical phantom studies with fluorescent targets located with different edge-to-edge distances were carried out. The reconstruction results show that the re-L1-NCG algorithm has the ability to resolve targets with an edge-to-edge distance of 0.1 cm at a depth of 1.5 cm, which is a significant improvement for FMT.

  18. Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

    Science.gov (United States)

    Lavery, N.; Taylor, C.

    1999-07-01

    Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright

  19. An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems

    Science.gov (United States)

    Deng, Qingping

    1996-01-01

    A multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.

  20. On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics

    NARCIS (Netherlands)

    F.J. Gaspar Lorenz (Franscisco); C. Rodrigo (Carmen)

    2017-01-01

    textabstractThe fixed-stress split method has been widely used as solution method in the coupling of flow and geomechanics. In this work, we analyze the behavior of an inexact version of this algorithm as smoother within a geometric multigrid method, in order to obtain an efficient monolithic solver

  1. The multigrid method for reactor calculations

    International Nuclear Information System (INIS)

    Douglas, S.R.

    1991-07-01

    Iterative solutions to linear systems of equations are discussed. The emphasis is on the concepts that affect convergence rates of these solution methods. The multigrid method is described, including the smoothing property, restriction, and prolongation. A simple example is used to illustrate the ideas

  2. A nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations

    Science.gov (United States)

    Edwards, Jack R.; Mcrae, D. S.

    1992-01-01

    A highly efficient implicit method for the computation of steady, two-dimensional compressible Navier-Stokes flowfields is presented. The discretization of the governing equations is hybrid in nature, with flux-vector splitting utilized in the streamwise direction and central differences with flux-limited artificial dissipation used for the transverse fluxes. Line Jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line Gauss-Seidel sweeps. The applicability of quasi-Newton methods as convergence accelerators for this and other line relaxation algorithms is discussed, and efficient implementations of such techniques are presented. Convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high-speed compression corner interactions. Results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies, particularly for flowfields containing large pockets of streamwise subsonic flow.

  3. An inertia-free filter line-search algorithm for large-scale nonlinear programming

    Energy Technology Data Exchange (ETDEWEB)

    Chiang, Nai-Yuan; Zavala, Victor M.

    2016-02-15

    We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to tackle large-scale problems on modern computing architectures. The proposed approach performs curvature tests along the search step to detect negative curvature and to trigger convexification. We prove that the approach is globally convergent and we implement the approach within a parallel interior-point framework to solve large-scale and highly nonlinear problems. Our numerical tests demonstrate that the inertia-free approach is as efficient as inertia detection via symmetric indefinite factorizations. We also demonstrate that the inertia-free approach can lead to reductions in solution time because it reduces the amount of convexification needed.

  4. Identification of time-varying nonlinear systems using differential evolution algorithm

    DEFF Research Database (Denmark)

    Perisic, Nevena; Green, Peter L; Worden, Keith

    2013-01-01

    (DE) algorithm for the identification of time-varying systems. DE is an evolutionary optimisation method developed to perform direct search in a continuous space without requiring any derivative estimation. DE is modified so that the objective function changes with time to account for the continuing......, thus identification of time-varying systems with nonlinearities can be a very challenging task. In order to avoid conventional least squares and gradient identification methods which require uni-modal and double differentiable objective functions, this work proposes a modified differential evolution...... inclusion of new data within an error metric. This paper presents results of identification of a time-varying SDOF system with Coulomb friction using simulated noise-free and noisy data for the case of time-varying friction coefficient, stiffness and damping. The obtained results are promising and the focus...

  5. Nonlinear Bayesian Algorithms for Gas Plume Detection and Estimation from Hyper-spectral Thermal Image Data

    Energy Technology Data Exchange (ETDEWEB)

    Heasler, Patrick G.; Posse, Christian; Hylden, Jeff L.; Anderson, Kevin K.

    2007-06-13

    This paper presents a nonlinear Bayesian regression algorithm for the purpose of detecting and estimating gas plume content from hyper-spectral data. Remote sensing data, by its very nature, is collected under less controlled conditions than laboratory data. As a result, the physics-based model that is used to describe the relationship between the observed remotesensing spectra, and the terrestrial (or atmospheric) parameters that we desire to estimate, is typically littered with many unknown "nuisance" parameters (parameters that we are not interested in estimating, but also appear in the model). Bayesian methods are well-suited for this context as they automatically incorporate the uncertainties associated with all nuisance parameters into the error estimates of the parameters of interest. The nonlinear Bayesian regression methodology is illustrated on realistic simulated data from a three-layer model for longwave infrared (LWIR) measurements from a passive instrument. This shows that this approach should permit more accurate estimation as well as a more reasonable description of estimate uncertainty.

  6. Comparative Study of Evolutionary Multi-objective Optimization Algorithms for a Non-linear Greenhouse Climate Control Problem

    DEFF Research Database (Denmark)

    Ghoreishi, Newsha; Sørensen, Jan Corfixen; Jørgensen, Bo Nørregaard

    2015-01-01

    Non-trivial real world decision-making processes usually involve multiple parties having potentially conflicting interests over a set of issues. State-of-the-art multi-objective evolutionary algorithms (MOEA) are well known to solve this class of complex real-world problems. In this paper, we...... compare the performance of state-of-the-art multi-objective evolutionary algorithms to solve a non-linear multi-objective multi-issue optimisation problem found in Greenhouse climate control. The chosen algorithms in the study includes NSGAII, eNSGAII, eMOEA, PAES, PESAII and SPEAII. The performance...... of all aforementioned algorithms is assessed and compared using performance indicators to evaluate proximity, diversity and consistency. Our insights to this comparative study enhanced our understanding of MOEAs performance in order to solve a non-linear complex climate control problem. The empirical...

  7. On structure-exploiting trust-region regularized nonlinear least squares algorithms for neural-network learning.

    Science.gov (United States)

    Mizutani, Eiji; Demmel, James W

    2003-01-01

    This paper briefly introduces our numerical linear algebra approaches for solving structured nonlinear least squares problems arising from 'multiple-output' neural-network (NN) models. Our algorithms feature trust-region regularization, and exploit sparsity of either the 'block-angular' residual Jacobian matrix or the 'block-arrow' Gauss-Newton Hessian (or Fisher information matrix in statistical sense) depending on problem scale so as to render a large class of NN-learning algorithms 'efficient' in both memory and operation costs. Using a relatively large real-world nonlinear regression application, we shall explain algorithmic strengths and weaknesses, analyzing simulation results obtained by both direct and iterative trust-region algorithms with two distinct NN models: 'multilayer perceptrons' (MLP) and 'complementary mixtures of MLP-experts' (or neuro-fuzzy modular networks).

  8. An evolutionary firefly algorithm for the estimation of nonlinear biological model parameters.

    Directory of Open Access Journals (Sweden)

    Afnizanfaizal Abdullah

    Full Text Available The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.

  9. Genetic Algorithm for Mixed Integer Nonlinear Bilevel Programming and Applications in Product Family Design

    Directory of Open Access Journals (Sweden)

    Chenlu Miao

    2016-01-01

    Full Text Available Many leader-follower relationships exist in product family design engineering problems. We use bilevel programming (BLP to reflect the leader-follower relationship and describe such problems. Product family design problems have unique characteristics; thus, mixed integer nonlinear BLP (MINLBLP, which has both continuous and discrete variables and multiple independent lower-level problems, is widely used in product family optimization. However, BLP is difficult in theory and is an NP-hard problem. Consequently, using traditional methods to solve such problems is difficult. Genetic algorithms (GAs have great value in solving BLP problems, and many studies have designed GAs to solve BLP problems; however, such GAs are typically designed for special cases that do not involve MINLBLP with one or multiple followers. Therefore, we propose a bilevel GA to solve these particular MINLBLP problems, which are widely used in product family problems. We give numerical examples to demonstrate the effectiveness of the proposed algorithm. In addition, a reducer family case study is examined to demonstrate practical applications of the proposed BLGA.

  10. An evolutionary firefly algorithm for the estimation of nonlinear biological model parameters.

    Science.gov (United States)

    Abdullah, Afnizanfaizal; Deris, Safaai; Anwar, Sohail; Arjunan, Satya N V

    2013-01-01

    The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.

  11. Nested sampling algorithm for subsurface flow model selection, uncertainty quantification, and nonlinear calibration

    KAUST Repository

    Elsheikh, A. H.

    2013-12-01

    Calibration of subsurface flow models is an essential step for managing ground water aquifers, designing of contaminant remediation plans, and maximizing recovery from hydrocarbon reservoirs. We investigate an efficient sampling algorithm known as nested sampling (NS), which can simultaneously sample the posterior distribution for uncertainty quantification, and estimate the Bayesian evidence for model selection. Model selection statistics, such as the Bayesian evidence, are needed to choose or assign different weights to different models of different levels of complexities. In this work, we report the first successful application of nested sampling for calibration of several nonlinear subsurface flow problems. The estimated Bayesian evidence by the NS algorithm is used to weight different parameterizations of the subsurface flow models (prior model selection). The results of the numerical evaluation implicitly enforced Occam\\'s razor where simpler models with fewer number of parameters are favored over complex models. The proper level of model complexity was automatically determined based on the information content of the calibration data and the data mismatch of the calibrated model.

  12. Multigrid preconditioning of the generator two-phase mixture balance equations in the Genepi software

    International Nuclear Information System (INIS)

    Belliard, M.; Grandotto, M.

    2003-01-01

    In the framework of the two-phase fluid simulations of the steam generators of pressurized water nuclear reactors, we present in this paper a geometric version of a pseudo-Full MultiGrid (pseudo- FMG) Full Approximation Storage (FAS) preconditioning of balance equations in the GENEPI code. In our application, the 3D steady state flow is reached by a transient computation using a semi-implicit fractional step algorithm for the averaged two-phase mixture balance equations (mass, momentum and energy for the secondary flow). Our application, running on workstation clusters, is based on a CEA code-linker and the PVM package. The difficulties to apply the geometric FAS multigrid method to the momentum and mass balance equations are addressed. The use of a sequential pseudo-FMG FAS twogrid method for both energy and mass/momentum balance equations, using dynamic multigrid cycles, leads to perceptibly improvements in the computation convergences. An original parallel red-black pseudo-FMG FAS three-grid algorithm is presented too. The numerical tests (steam generator mockup simulations) underline the sizable increase in speed of convergence of the computations, essentially for the ones involving a large number of freedom degrees (about 100 thousand cells). The two-phase mixture balance equation residuals are quickly reduced: the reached speed-up stands between 2 and 3 following the number of grids. The effects on the convergence behavior of the numerical parameters are investigated

  13. A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems

    KAUST Repository

    Domínguez, Luis F.

    2012-06-25

    An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear programming subproblem and a mixed-integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp-QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed-integer outer approximation (mp-MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers (AIChE).

  14. The Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces

    KAUST Repository

    Chen, Yujia

    2015-01-01

    © 2015 Society for Industrial and Applied Mathematics. Elliptic partial differential equations are important from both application and analysis points of view. In this paper we apply the closest point method to solve elliptic equations on general curved surfaces. Based on the closest point representation of the underlying surface, we formulate an embedding equation for the surface elliptic problem, then discretize it using standard finite differences and interpolation schemes on banded but uniform Cartesian grids. We prove the convergence of the difference scheme for the Poisson\\'s equation on a smooth closed curve. In order to solve the resulting large sparse linear systems, we propose a specific geometric multigrid method in the setting of the closest point method. Convergence studies in both the accuracy of the difference scheme and the speed of the multigrid algorithm show that our approaches are effective.

  15. Multigrid Finite Element Method in Calculation of 3D Homogeneous and Composite Solids

    Directory of Open Access Journals (Sweden)

    A.D. Matveev

    2016-12-01

    Full Text Available In the present paper, a method of multigrid finite elements to calculate elastic three-dimensional homogeneous and composite solids under static loading has been suggested. The method has been developed based on the finite element method algorithms using homogeneous and composite three-dimensional multigrid finite elements (MFE. The procedures for construction of MFE of both rectangular parallelepiped and complex shapes have been shown. The advantages of MFE are that they take into account, following the rules of the microapproach, heterogeneous and microhomogeneous structures of the bodies, describe the three-dimensional stress-strain state (without any simplifying hypotheses in homogeneous and composite solids, as well as generate small dimensional discrete models and numerical solutions with a high accuracy.

  16. An Improved Global Harmony Search Algorithm for the Identification of Nonlinear Discrete-Time Systems Based on Volterra Filter Modeling

    Directory of Open Access Journals (Sweden)

    Zongyan Li

    2016-01-01

    Full Text Available This paper describes an improved global harmony search (IGHS algorithm for identifying the nonlinear discrete-time systems based on second-order Volterra model. The IGHS is an improved version of the novel global harmony search (NGHS algorithm, and it makes two significant improvements on the NGHS. First, the genetic mutation operation is modified by combining normal distribution and Cauchy distribution, which enables the IGHS to fully explore and exploit the solution space. Second, an opposition-based learning (OBL is introduced and modified to improve the quality of harmony vectors. The IGHS algorithm is implemented on two numerical examples, and they are nonlinear discrete-time rational system and the real heat exchanger, respectively. The results of the IGHS are compared with those of the other three methods, and it has been verified to be more effective than the other three methods on solving the above two problems with different input signals and system memory sizes.

  17. Nonlinear and parallel algorithms for finite element discretizations of the incompressible Navier-Stokes equations

    Science.gov (United States)

    Arteaga, Santiago Egido

    1998-12-01

    linearization strategies considered and whose computational cost is negligible. The algebraic properties of these systems depend on both the discretization and nonlinear method used. We study in detail the positive definiteness and skewsymmetry of the advection submatrices (essentially, convection-diffusion problems). We propose a discretization based on a new trilinear form for Newton's method. We solve the linear systems using three Krylov subspace methods, GMRES, QMR and TFQMR, and compare the advantages of each. Our emphasis is on parallel algorithms, and so we consider preconditioners suitable for parallel computers such as line variants of the Jacobi and Gauss- Seidel methods, alternating direction implicit methods, and Chebyshev and least squares polynomial preconditioners. These work well for moderate viscosities (moderate Reynolds number). For small viscosities we show that effective parallel solution of the advection subproblem is a critical factor to improve performance. Implementation details on a CM-5 are presented.

  18. Calibration of Mine Ventilation Network Models Using the Non-Linear Optimization Algorithm

    Directory of Open Access Journals (Sweden)

    Guang Xu

    2017-12-01

    Full Text Available Effective ventilation planning is vital to underground mining. To ensure stable operation of the ventilation system and to avoid airflow disorder, mine ventilation network (MVN models have been widely used in simulating and optimizing the mine ventilation system. However, one of the challenges for MVN model simulation is that the simulated airflow distribution results do not match the measured data. To solve this problem, a simple and effective calibration method is proposed based on the non-linear optimization algorithm. The calibrated model not only makes simulated airflow distribution results in accordance with the on-site measured data, but also controls the errors of other parameters within a minimum range. The proposed method was then applied to calibrate an MVN model in a real case, which is built based on ventilation survey results and Ventsim software. Finally, airflow simulation experiments are carried out respectively using data before and after calibration, whose results were compared and analyzed. This showed that the simulated airflows in the calibrated model agreed much better to the ventilation survey data, which verifies the effectiveness of calibrating method.

  19. Nonlinear inversion of resistivity sounding data for 1-D earth models using the Neighbourhood Algorithm

    Science.gov (United States)

    Ojo, A. O.; Xie, Jun; Olorunfemi, M. O.

    2018-01-01

    To reduce ambiguity related to nonlinearities in the resistivity model-data relationships, an efficient direct-search scheme employing the Neighbourhood Algorithm (NA) was implemented to solve the 1-D resistivity problem. In addition to finding a range of best-fit models which are more likely to be global minimums, this method investigates the entire multi-dimensional model space and provides additional information about the posterior model covariance matrix, marginal probability density function and an ensemble of acceptable models. This provides new insights into how well the model parameters are constrained and make assessing trade-offs between them possible, thus avoiding some common interpretation pitfalls. The efficacy of the newly developed program is tested by inverting both synthetic (noisy and noise-free) data and field data from other authors employing different inversion methods so as to provide a good base for comparative performance. In all cases, the inverted model parameters were in good agreement with the true and recovered model parameters from other methods and remarkably correlate with the available borehole litho-log and known geology for the field dataset. The NA method has proven to be useful whilst a good starting model is not available and the reduced number of unknowns in the 1-D resistivity inverse problem makes it an attractive alternative to the linearized methods. Hence, it is concluded that the newly developed program offers an excellent complementary tool for the global inversion of the layered resistivity structure.

  20. Prediction of Flood Warning in Taiwan Using Nonlinear SVM with Simulated Annealing Algorithm

    Science.gov (United States)

    Lee, C.

    2013-12-01

    The issue of the floods is important in Taiwan. It is because the narrow and high topography of the island make lots of rivers steep in Taiwan. The tropical depression likes typhoon always causes rivers to flood. Prediction of river flow under the extreme rainfall circumstances is important for government to announce the warning of flood. Every time typhoon passed through Taiwan, there were always floods along some rivers. The warning is classified to three levels according to the warning water levels in Taiwan. The propose of this study is to predict the level of floods warning from the information of precipitation, rainfall duration and slope of riverbed. To classify the level of floods warning by the above-mentioned information and modeling the problems, a machine learning model, nonlinear Support vector machine (SVM), is formulated to classify the level of floods warning. In addition, simulated annealing (SA), a probabilistic heuristic algorithm, is used to determine the optimal parameter of the SVM model. A case study of flooding-trend rivers of different gradients in Taiwan is conducted. The contribution of this SVM model with simulated annealing is capable of making efficient announcement for flood warning and keeping the danger of flood from residents along the rivers.

  1. Ship nonlinear-feedback course keeping algorithm based on MMG model driven by bipolar sigmoid function for berthing

    Directory of Open Access Journals (Sweden)

    Qiang Zhang

    2017-09-01

    Full Text Available Course keeping is hard to implement under the condition of the propeller stopping or reversing at slow speed for berthing due to the ship's dynamic motion becoming highly nonlinear. To solve this problem, a practical Maneuvering Modeling Group (MMG ship mathematic model with propeller reversing transverse forces and low speed correction is first discussed to be applied for the right-handed single-screw ship. Secondly, a novel PID-based nonlinear feedback algorithm driven by bipolar sigmoid function is proposed. The PID parameters are determined by a closed-loop gain shaping algorithm directly, while the closed-loop gain shaping theory was employed for effects analysis of this algorithm. Finally, simulation experiments were carried out on an LPG ship. It is shown that the energy consumption and the smoothness performance of the nonlinear feedback control are reduced by 4.2% and 14.6% with satisfactory control effects; the proposed algorithm has the advantages of robustness, energy saving and safety in berthing practice.

  2. Analysis of multigrid methods on massively parallel computers: Architectural implications

    Science.gov (United States)

    Matheson, Lesley R.; Tarjan, Robert E.

    1993-01-01

    We study the potential performance of multigrid algorithms running on massively parallel computers with the intent of discovering whether presently envisioned machines will provide an efficient platform for such algorithms. We consider the domain parallel version of the standard V cycle algorithm on model problems, discretized using finite difference techniques in two and three dimensions on block structured grids of size 10(exp 6) and 10(exp 9), respectively. Our models of parallel computation were developed to reflect the computing characteristics of the current generation of massively parallel multicomputers. These models are based on an interconnection network of 256 to 16,384 message passing, 'workstation size' processors executing in an SPMD mode. The first model accomplishes interprocessor communications through a multistage permutation network. The communication cost is a logarithmic function which is similar to the costs in a variety of different topologies. The second model allows single stage communication costs only. Both models were designed with information provided by machine developers and utilize implementation derived parameters. With the medium grain parallelism of the current generation and the high fixed cost of an interprocessor communication, our analysis suggests an efficient implementation requires the machine to support the efficient transmission of long messages, (up to 1000 words) or the high initiation cost of a communication must be significantly reduced through an alternative optimization technique. Furthermore, with variable length message capability, our analysis suggests the low diameter multistage networks provide little or no advantage over a simple single stage communications network.

  3. Fractional Fourier domain optical image hiding using phase retrieval algorithm based on iterative nonlinear double random phase encoding.

    Science.gov (United States)

    Wang, Xiaogang; Chen, Wen; Chen, Xudong

    2014-09-22

    We present a novel image hiding method based on phase retrieval algorithm under the framework of nonlinear double random phase encoding in fractional Fourier domain. Two phase-only masks (POMs) are efficiently determined by using the phase retrieval algorithm, in which two cascaded phase-truncated fractional Fourier transforms (FrFTs) are involved. No undesired information disclosure, post-processing of the POMs or digital inverse computation appears in our proposed method. In order to achieve the reduction in key transmission, a modified image hiding method based on the modified phase retrieval algorithm and logistic map is further proposed in this paper, in which the fractional orders and the parameters with respect to the logistic map are regarded as encryption keys. Numerical results have demonstrated the feasibility and effectiveness of the proposed algorithms.

  4. Estimating model error covariances in nonlinear state-space models using Kalman smoothing and the expectation-maximisation algorithm

    KAUST Repository

    Dreano, Denis

    2017-04-05

    Specification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation-maximisation (EM) algorithm to estimate the model error covariances using classical extended and ensemble versions of the Kalman smoother. We show that, for additive model errors, the estimate of the error covariance converges. We also investigate other forms of model error, such as parametric or multiplicative errors. We show that additive Gaussian model error is able to compensate for non additive sources of error in the algorithms we propose. We also demonstrate the limitations of the extended version of the algorithm and recommend the use of the more robust and flexible ensemble version. This article is a proof of concept of the methodology with the Lorenz-63 attractor. We developed an open-source Python library to enable future users to apply the algorithm to their own nonlinear dynamical models.

  5. Quantum associative memory with linear and non-linear algorithms for the diagnosis of some tropical diseases.

    Science.gov (United States)

    Tchapet Njafa, J-P; Nana Engo, S G

    2018-01-01

    This paper presents the QAMDiagnos, a model of Quantum Associative Memory (QAM) that can be a helpful tool for medical staff without experience or laboratory facilities, for the diagnosis of four tropical diseases (malaria, typhoid fever, yellow fever and dengue) which have several similar signs and symptoms. The memory can distinguish a single infection from a polyinfection. Our model is a combination of the improved versions of the original linear quantum retrieving algorithm proposed by Ventura and the non-linear quantum search algorithm of Abrams and Lloyd. From the given simulation results, it appears that the efficiency of recognition is good when particular signs and symptoms of a disease are inserted given that the linear algorithm is the main algorithm. The non-linear algorithm helps confirm or correct the diagnosis or give some advice to the medical staff for the treatment. So, our QAMDiagnos that has a friendly graphical user interface for desktop and smart-phone is a sensitive and a low-cost diagnostic tool that enables rapid and accurate diagnosis of four tropical diseases. Copyright © 2017 Elsevier Ltd. All rights reserved.

  6. An Error-Entropy Minimization Algorithm for Tracking Control of Nonlinear Stochastic Systems with Non-Gaussian Variables

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Yunlong; Wang, Aiping; Guo, Lei; Wang, Hong

    2017-07-09

    This paper presents an error-entropy minimization tracking control algorithm for a class of dynamic stochastic system. The system is represented by a set of time-varying discrete nonlinear equations with non-Gaussian stochastic input, where the statistical properties of stochastic input are unknown. By using Parzen windowing with Gaussian kernel to estimate the probability densities of errors, recursive algorithms are then proposed to design the controller such that the tracking error can be minimized. The performance of the error-entropy minimization criterion is compared with the mean-square-error minimization in the simulation results.

  7. 33rd International School of Mathematics "G Stampacchia ": High Performance Algorithms and Software for Nonlinear Optics "Ettore Majorana"

    CERN Document Server

    Murli, Almerico; High Performance Algorithms and Software for Nonlinear Optics

    2003-01-01

    This volume contains the edited texts of the lectures presented at the Workshop on High Performance Algorithms and Software for Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 30 - July 8, 2001. In the first year of the new century, the aim of the Workshop was to assess the past and to discuss the future of Nonlinear Optimization, and to highlight recent achieve­ ments and promising research trends in this field. An emphasis was requested on algorithmic and high performance software developments and on new computational experiences, as well as on theoretical advances. We believe that such goal was basically achieved. The Workshop was attended by 71 people from 22 countries. Although not all topics were covered, the presentations gave indeed a wide overview of the field, from different and complementary stand­ points. Besides the lectures, several formal and informal discussions took place. We wish ...

  8. Is the Multigrid Method Fault Tolerant? The Two-Grid Case

    Energy Technology Data Exchange (ETDEWEB)

    Ainsworth, Mark [Brown Univ., Providence, RI (United States). Division of Applied Mathematics; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division; Glusa, Christian [Brown Univ., Providence, RI (United States). Division of Applied Mathematics

    2016-06-30

    The predicted reduced resiliency of next-generation high performance computers means that it will become necessary to take into account the effects of randomly occurring faults on numerical methods. Further, in the event of a hard fault occurring, a decision has to be made as to what remedial action should be taken in order to resume the execution of the algorithm. The action that is chosen can have a dramatic effect on the performance and characteristics of the scheme. Ideally, the resulting algorithm should be subjected to the same kind of mathematical analysis that was applied to the original, deterministic variant. The purpose of this work is to provide an analysis of the behaviour of the multigrid algorithm in the presence of faults. Multigrid is arguably the method of choice for the solution of large-scale linear algebra problems arising from discretization of partial differential equations and it is of considerable importance to anticipate its behaviour on an exascale machine. The analysis of resilience of algorithms is in its infancy and the current work is perhaps the first to provide a mathematical model for faults and analyse the behaviour of a state-of-the-art algorithm under the model. It is shown that the Two Grid Method fails to be resilient to faults. Attention is then turned to identifying the minimal necessary remedial action required to restore the rate of convergence to that enjoyed by the ideal fault-free method.

  9. Integrated Navigation System Design for Micro Planetary Rovers: Comparison of Absolute Heading Estimation Algorithms and Nonlinear Filtering

    Science.gov (United States)

    Ilyas, Muhammad; Hong, Beomjin; Cho, Kuk; Baeg, Seung-Ho; Park, Sangdeok

    2016-01-01

    This paper provides algorithms to fuse relative and absolute microelectromechanical systems (MEMS) navigation sensors, suitable for micro planetary rovers, to provide a more accurate estimation of navigation information, specifically, attitude and position. Planetary rovers have extremely slow speed (~1 cm/s) and lack conventional navigation sensors/systems, hence the general methods of terrestrial navigation may not be applicable to these applications. While relative attitude and position can be tracked in a way similar to those for ground robots, absolute navigation information is hard to achieve on a remote celestial body, like Moon or Mars, in contrast to terrestrial applications. In this study, two absolute attitude estimation algorithms were developed and compared for accuracy and robustness. The estimated absolute attitude was fused with the relative attitude sensors in a framework of nonlinear filters. The nonlinear Extended Kalman filter (EKF) and Unscented Kalman filter (UKF) were compared in pursuit of better accuracy and reliability in this nonlinear estimation problem, using only on-board low cost MEMS sensors. Experimental results confirmed the viability of the proposed algorithms and the sensor suite, for low cost and low weight micro planetary rovers. It is demonstrated that integrating the relative and absolute navigation MEMS sensors reduces the navigation errors to the desired level. PMID:27223293

  10. Totally parallel multilevel algorithms

    Science.gov (United States)

    Frederickson, Paul O.

    1988-01-01

    Four totally parallel algorithms for the solution of a sparse linear system have common characteristics which become quite apparent when they are implemented on a highly parallel hypercube such as the CM2. These four algorithms are Parallel Superconvergent Multigrid (PSMG) of Frederickson and McBryan, Robust Multigrid (RMG) of Hackbusch, the FFT based Spectral Algorithm, and Parallel Cyclic Reduction. In fact, all four can be formulated as particular cases of the same totally parallel multilevel algorithm, which are referred to as TPMA. In certain cases the spectral radius of TPMA is zero, and it is recognized to be a direct algorithm. In many other cases the spectral radius, although not zero, is small enough that a single iteration per timestep keeps the local error within the required tolerance.

  11. Hybrid Projected Gradient-Evolutionary Search Algorithm for Mixed Integer Nonlinear Optimization Problems

    National Research Council Canada - National Science Library

    Homaifar, Abdollah; Esterline, Albert; Kimiaghalam, Bahram

    2005-01-01

    The Hybrid Projected Gradient-Evolutionary Search Algorithm (HPGES) algorithm uses a specially designed evolutionary-based global search strategy to efficiently create candidate solutions in the solution space...

  12. Nonlinear fitness-space-structure adaptation and principal component analysis in genetic algorithms: an application to x-ray reflectivity analysis

    International Nuclear Information System (INIS)

    Tiilikainen, J; Tilli, J-M; Bosund, V; Mattila, M; Hakkarainen, T; Airaksinen, V-M; Lipsanen, H

    2007-01-01

    Two novel genetic algorithms implementing principal component analysis and an adaptive nonlinear fitness-space-structure technique are presented and compared with conventional algorithms in x-ray reflectivity analysis. Principal component analysis based on Hessian or interparameter covariance matrices is used to rotate a coordinate frame. The nonlinear adaptation applies nonlinear estimates to reshape the probability distribution of the trial parameters. The simulated x-ray reflectivity of a realistic model of a periodic nanolaminate structure was used as a test case for the fitting algorithms. The novel methods had significantly faster convergence and less stagnation than conventional non-adaptive genetic algorithms. The covariance approach needs no additional curve calculations compared with conventional methods, and it had better convergence properties than the computationally expensive Hessian approach. These new algorithms can also be applied to other fitting problems where tight interparameter dependence is present

  13. Higher-order ice-sheet modelling accelerated by multigrid on graphics cards

    Science.gov (United States)

    Brædstrup, Christian; Egholm, David

    2013-04-01

    Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.

  14. From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM

    Directory of Open Access Journals (Sweden)

    Akemi Gálvez

    2013-01-01

    Full Text Available Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor’s method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.

  15. Comparative Study of FDTD-Adopted Numerical Algorithms for Kerr Nonlinearities

    DEFF Research Database (Denmark)

    Maksymov, Ivan S.; Sukhorukov, Andrey A.; Lavrinenko, Andrei

    2011-01-01

    Accurate finite-difference time-domain (FDTD) modeling of optical pulse propagation in nonlinear media usually implies the use of auxiliary differential equation (ADE) techniques. The updating of electric field in full-vectorial 3-D ADE FDTD modeling of the optical Kerr effect and two-photon abso...... approaches. Such schemes can significantly reduce the CPU time for nonlinear computations, especially in 3-D models....

  16. An Artificial Neural Network-Based Algorithm for Evaluation of Fatigue Crack Propagation Considering Nonlinear Damage Accumulation.

    Science.gov (United States)

    Zhang, Wei; Bao, Zhangmin; Jiang, Shan; He, Jingjing

    2016-06-17

    In the aerospace and aviation sectors, the damage tolerance concept has been applied widely so that the modeling analysis of fatigue crack growth has become more and more significant. Since the process of crack propagation is highly nonlinear and determined by many factors, such as applied stress, plastic zone in the crack tip, length of the crack, etc. , it is difficult to build up a general and flexible explicit function to accurately quantify this complicated relationship. Fortunately, the artificial neural network (ANN) is considered a powerful tool for establishing the nonlinear multivariate projection which shows potential in handling the fatigue crack problem. In this paper, a novel fatigue crack calculation algorithm based on a radial basis function (RBF)-ANN is proposed to study this relationship from the experimental data. In addition, a parameter called the equivalent stress intensity factor is also employed as training data to account for loading interaction effects. The testing data is then placed under constant amplitude loading with different stress ratios or overloads used for model validation. Moreover, the Forman and Wheeler equations are also adopted to compare with our proposed algorithm. The current investigation shows that the ANN-based approach can deliver a better agreement with the experimental data than the other two models, which supports that the RBF-ANN has nontrivial advantages in handling the fatigue crack growth problem. Furthermore, it implies that the proposed algorithm is possibly a sophisticated and promising method to compute fatigue crack growth in terms of loading interaction effects.

  17. An Interval Type-2 Fuzzy System with a Species-Based Hybrid Algorithm for Nonlinear System Control Design

    Directory of Open Access Journals (Sweden)

    Chung-Ta Li

    2014-01-01

    Full Text Available We propose a species-based hybrid of the electromagnetism-like mechanism (EM and back-propagation algorithms (SEMBP for an interval type-2 fuzzy neural system with asymmetric membership functions (AIT2FNS design. The interval type-2 asymmetric fuzzy membership functions (IT2 AFMFs and the TSK-type consequent part are adopted to implement the network structure in AIT2FNS. In addition, the type reduction procedure is integrated into an adaptive network structure to reduce computational complexity. Hence, the AIT2FNS can enhance the approximation accuracy effectively by using less fuzzy rules. The AIT2FNS is trained by the SEMBP algorithm, which contains the steps of uniform initialization, species determination, local search, total force calculation, movement, and evaluation. It combines the advantages of EM and back-propagation (BP algorithms to attain a faster convergence and a lower computational complexity. The proposed SEMBP algorithm adopts the uniform method (which evenly scatters solution agents over the feasible solution region and the species technique to improve the algorithm’s ability to find the global optimum. Finally, two illustrative examples of nonlinear systems control are presented to demonstrate the performance and the effectiveness of the proposed AIT2FNS with the SEMBP algorithm.

  18. Segmental Refinement: A Multigrid Technique for Data Locality

    Energy Technology Data Exchange (ETDEWEB)

    Adams, Mark [Columbia Univ., New York, NY (United States). Applied Physics and Applied Mathematics Dept.; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

    2014-10-27

    We investigate a technique - segmental refinement (SR) - proposed by Brandt in the 1970s as a low memory multigrid method. The technique is attractive for modern computer architectures because it provides high data locality, minimizes network communication, is amenable to loop fusion, and is naturally highly parallel and asynchronous. The network communication minimization property was recognized by Brandt and Diskin in 1994; we continue this work by developing a segmental refinement method for a finite volume discretization of the 3D Laplacian on massively parallel computers. An understanding of the asymptotic complexities, required to maintain textbook multigrid efficiency, are explored experimentally with a simple SR method. A two-level memory model is developed to compare the asymptotic communication complexity of a proposed SR method with traditional parallel multigrid. Performance and scalability are evaluated with a Cray XC30 with up to 64K cores. We achieve modest improvement in scalability from traditional parallel multigrid with a simple SR implementation.

  19. Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation

    KAUST Repository

    Chen, Meng-Huo; Sun, Shuyu; Salama, Amgad

    2015-01-01

    and issues will be addressed and the corresponding remedies will be studied. As the multigrid methods are used as the linear solver, the simulator can be parallelized (although not trivial) and the high-resolution simulation become feasible, the ultimately

  20. Multigrid methods for S/sub N/ problems

    International Nuclear Information System (INIS)

    Nowak, P.F.; Larsen, E.W.; Martin, W.R.

    1987-01-01

    It has long been known that the standard source iteration (SI) method for obtaining iterative solutions of S/sub N/ problems is very slowly converging in optically thick regions with low absorption. The rebalance and diffusion synthetic acceleration (DSA) methods are generalizations of SI that have been developed to accelerate convergence, but neither of these methods has been completely successful. In particular, the rebalance method tends to become unstable in problems where it is needed most (problems with high scattering ratios c = 1), while the DSA method, to be implemented in a stable fashion, requires the solution of a particular system of acceleration equations, and this has been done efficiently in two-dimensional geometries only for the diamond difference S/sub N/ equations. This paper discusses another extension of the SI method, namely, SI combined with the spatial multigrid algorithm (SIMG). This appears to be a viable way to accelerate many S/sub N/ problems in multidimensional geometries, provided the finest mesh consists of cells that are not optically thick

  1. Novel probabilistic and distributed algorithms for guidance, control, and nonlinear estimation of large-scale multi-agent systems

    Science.gov (United States)

    Bandyopadhyay, Saptarshi

    guidance algorithms using results from numerical simulations and closed-loop hardware experiments on multiple quadrotors. In the second part of this dissertation, we present two novel discrete-time algorithms for distributed estimation, which track a single target using a network of heterogeneous sensing agents. The Distributed Bayesian Filtering (DBF) algorithm, the sensing agents combine their normalized likelihood functions using the logarithmic opinion pool and the discrete-time dynamic average consensus algorithm. Each agent's estimated likelihood function converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. Using a new proof technique, the convergence, stability, and robustness properties of the DBF algorithm are rigorously characterized. The explicit bounds on the time step of the robust DBF algorithm are shown to depend on the time-scale of the target dynamics. Furthermore, the DBF algorithm for linear-Gaussian models can be cast into a modified form of the Kalman information filter. In the Bayesian Consensus Filtering (BCF) algorithm, the agents combine their estimated posterior pdfs multiple times within each time step using the logarithmic opinion pool scheme. Thus, each agent's consensual pdf minimizes the sum of Kullback-Leibler divergences with the local posterior pdfs. The performance and robust properties of these algorithms are validated using numerical simulations. In the third part of this dissertation, we present an attitude control strategy and a new nonlinear tracking controller for a spacecraft carrying a large object, such as an asteroid or a boulder. If the captured object is larger or comparable in size to the spacecraft and has significant modeling uncertainties, conventional nonlinear control laws that use exact feed-forward cancellation are not suitable because they exhibit a large resultant disturbance torque. The proposed nonlinear tracking control law guarantees

  2. Neural multigrid for gauge theories and other disordered systems

    International Nuclear Information System (INIS)

    Baeker, M.; Kalkreuter, T.; Mack, G.; Speh, M.

    1992-09-01

    We present evidence that multigrid works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder, but one needs to introduce a 'neural computations' point of view into large scale simulations: First, the system must learn how to do the simulations efficiently, then do the simulation (fast). The method can also be used to provide smooth interpolation kernels which are needed in multigrid Monte Carlo updates. (orig.)

  3. Matrix-dependent multigrid-homogenization for diffusion problems

    Energy Technology Data Exchange (ETDEWEB)

    Knapek, S. [Institut fuer Informatik tu Muenchen (Germany)

    1996-12-31

    We present a method to approximately determine the effective diffusion coefficient on the coarse scale level of problems with strongly varying or discontinuous diffusion coefficients. It is based on techniques used also in multigrid, like Dendy`s matrix-dependent prolongations and the construction of coarse grid operators by means of the Galerkin approximation. In numerical experiments, we compare our multigrid-homogenization method with homogenization, renormalization and averaging approaches.

  4. A Critical Study of Agglomerated Multigrid Methods for Diffusion

    Science.gov (United States)

    Nishikawa, Hiroaki; Diskin, Boris; Thomas, James L.

    2011-01-01

    Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that multigrid with an inconsistent coarse-grid scheme using only the edge terms (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods but its convergence deteriorates on finer grids. Multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also grid-dependent. In contrast, grid-independent convergence rates are demonstrated for multigrid with consistent coarse-grid discretizations. Convergence rates of multigrid cycles are verified with quantitative analysis methods in which parts of the two-grid cycle are replaced by their idealized counterparts.

  5. The Mixed Finite Element Multigrid Method for Stokes Equations

    Science.gov (United States)

    Muzhinji, K.; Shateyi, S.; Motsa, S. S.

    2015-01-01

    The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q 2-Q 1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361

  6. A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations

    International Nuclear Information System (INIS)

    Yan Zhenya

    2005-01-01

    A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gordon equation, the Magma equation and the generalized Pochhammer-Chree (PC) equation to illustrate the method. As a result, many types of new doubly periodic solutions are obtained. Moreover when using the method to these special nonlinear differential equations, some transformations are firstly needed. The method can be also extended to other nonlinear differential equations

  7. Algorithms

    Indian Academy of Sciences (India)

    polynomial) division have been found in Vedic Mathematics which are dated much before Euclid's algorithm. A programming language Is used to describe an algorithm for execution on a computer. An algorithm expressed using a programming.

  8. Local pursuit strategy-inspired cooperative trajectory planning algorithm for a class of nonlinear constrained dynamical systems

    Science.gov (United States)

    Xu, Yunjun; Remeikas, Charles; Pham, Khanh

    2014-03-01

    Cooperative trajectory planning is crucial for networked vehicles to respond rapidly in cluttered environments and has a significant impact on many applications such as air traffic or border security monitoring and assessment. One of the challenges in cooperative planning is to find a computationally efficient algorithm that can accommodate both the complexity of the environment and real hardware and configuration constraints of vehicles in the formation. Inspired by a local pursuit strategy observed in foraging ants, feasible and optimal trajectory planning algorithms are proposed in this paper for a class of nonlinear constrained cooperative vehicles in environments with densely populated obstacles. In an iterative hierarchical approach, the local behaviours, such as the formation stability, obstacle avoidance, and individual vehicle's constraints, are considered in each vehicle's (i.e. follower's) decentralised optimisation. The cooperative-level behaviours, such as the inter-vehicle collision avoidance, are considered in the virtual leader's centralised optimisation. Early termination conditions are derived to reduce the computational cost by not wasting time in the local-level optimisation if the virtual leader trajectory does not satisfy those conditions. The expected advantages of the proposed algorithms are (1) the formation can be globally asymptotically maintained in a decentralised manner; (2) each vehicle decides its local trajectory using only the virtual leader and its own information; (3) the formation convergence speed is controlled by one single parameter, which makes it attractive for many practical applications; (4) nonlinear dynamics and many realistic constraints, such as the speed limitation and obstacle avoidance, can be easily considered; (5) inter-vehicle collision avoidance can be guaranteed in both the formation transient stage and the formation steady stage; and (6) the computational cost in finding both the feasible and optimal

  9. A Modified LQG Algorithm (MLQG for Robust Control of Nonlinear Multivariable Systems

    Directory of Open Access Journals (Sweden)

    Jens G. Balchen

    1993-07-01

    Full Text Available The original LQG algorithm is often characterized for its lack of robustness. This is because in the design of the estimator (Kalman filter the process disturbance is assumed to be white noise. If the estimator is to give good estimates, the Kalman gain is increased which means that the estimator fails to become robust. A solution to this problem is to replace the proportional Kalman gain matrix by a dynamic PI algorithm and the proportional LQ feedback gain matrix by a PI algorithm. A tuning method is developed which facilitates the tuning of a modified LQG control system (MLQG by only two tuning parameters.

  10. Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H∞ control.

    Science.gov (United States)

    Wu, Huai-Ning; Luo, Biao

    2012-12-01

    It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

  11. Application of the largest Lyapunov exponent and non-linear fractal extrapolation algorithm to short-term load forecasting

    International Nuclear Information System (INIS)

    Wang Jianzhou; Jia Ruiling; Zhao Weigang; Wu Jie; Dong Yao

    2012-01-01

    Highlights: ► The maximal predictive step size is determined by the largest Lyapunov exponent. ► A proper forecasting step size is applied to load demand forecasting. ► The improved approach is validated by the actual load demand data. ► Non-linear fractal extrapolation method is compared with three forecasting models. ► Performance of the models is evaluated by three different error measures. - Abstract: Precise short-term load forecasting (STLF) plays a key role in unit commitment, maintenance and economic dispatch problems. Employing a subjective and arbitrary predictive step size is one of the most important factors causing the low forecasting accuracy. To solve this problem, the largest Lyapunov exponent is adopted to estimate the maximal predictive step size so that the step size in the forecasting is no more than this maximal one. In addition, in this paper a seldom used forecasting model, which is based on the non-linear fractal extrapolation (NLFE) algorithm, is considered to develop the accuracy of predictions. The suitability and superiority of the two solutions are illustrated through an application to real load forecasting using New South Wales electricity load data from the Australian National Electricity Market. Meanwhile, three forecasting models: the gray model, the seasonal autoregressive integrated moving average approach and the support vector machine method, which received high approval in STLF, are selected to compare with the NLFE algorithm. Comparison results also show that the NLFE model is outstanding, effective, practical and feasible.

  12. An ensemble based nonlinear orthogonal matching pursuit algorithm for sparse history matching of reservoir models

    KAUST Repository

    Fsheikh, Ahmed H.; Wheeler, Mary Fanett; Hoteit, Ibrahim

    2013-01-01

    the dictionary, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on approximate gradient estimation using an iterative stochastic ensemble method (ISEM). ISEM utilizes an ensemble of directional derivatives

  13. Performance evaluation of firefly algorithm with variation in sorting for non-linear benchmark problems

    Science.gov (United States)

    Umbarkar, A. J.; Balande, U. T.; Seth, P. D.

    2017-06-01

    The field of nature inspired computing and optimization techniques have evolved to solve difficult optimization problems in diverse fields of engineering, science and technology. The firefly attraction process is mimicked in the algorithm for solving optimization problems. In Firefly Algorithm (FA) sorting of fireflies is done by using sorting algorithm. The original FA is proposed with bubble sort for ranking the fireflies. In this paper, the quick sort replaces bubble sort to decrease the time complexity of FA. The dataset used is unconstrained benchmark functions from CEC 2005 [22]. The comparison of FA using bubble sort and FA using quick sort is performed with respect to best, worst, mean, standard deviation, number of comparisons and execution time. The experimental result shows that FA using quick sort requires less number of comparisons but requires more execution time. The increased number of fireflies helps to converge into optimal solution whereas by varying dimension for algorithm performed better at a lower dimension than higher dimension.

  14. Nested sampling algorithm for subsurface flow model selection, uncertainty quantification, and nonlinear calibration

    KAUST Repository

    Elsheikh, A. H.; Wheeler, M. F.; Hoteit, Ibrahim

    2013-01-01

    Calibration of subsurface flow models is an essential step for managing ground water aquifers, designing of contaminant remediation plans, and maximizing recovery from hydrocarbon reservoirs. We investigate an efficient sampling algorithm known

  15. A unified framework of descent algorithms for nonlinear programs and variational inequalities

    International Nuclear Information System (INIS)

    Patriksson, M.

    1993-01-01

    We present a framework of algorithms for the solution of continuous optimization and variational inequality problems. In the general algorithm, a search direction finding auxiliary problems is obtained by replacing the original cost function with an approximating monotone cost function. The proposed framework encompasses algorithm classes presented earlier by Cohen, Dafermos, Migdalas, and Tseng, and includes numerous descent and successive approximation type methods, such as Newton methods, Jacobi and Gauss-Siedel type decomposition methods for problems defined over Cartesian product sets, and proximal point methods, among others. The auxiliary problem of the general algorithm also induces equivalent optimization reformulation and descent methods for asymmetric variational inequalities. We study the convergence properties of the general algorithm when applied to unconstrained optimization, nondifferentiable optimization, constrained differentiable optimization, and variational inequalities; the emphasis of the convergence analyses is placed on basic convergence results, convergence using different line search strategies and truncated subproblem solutions, and convergence rate results. This analysis offer a unification of known results; moreover, it provides strengthenings of convergence results for many existing algorithms, and indicates possible improvements of their realizations. 482 refs

  16. Three-dimensional forward modeling of DC resistivity using the aggregation-based algebraic multigrid method

    Science.gov (United States)

    Chen, Hui; Deng, Ju-Zhi; Yin, Min; Yin, Chang-Chun; Tang, Wen-Wu

    2017-03-01

    To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.

  17. Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems.

    Science.gov (United States)

    Miró, Anton; Pozo, Carlos; Guillén-Gosálbez, Gonzalo; Egea, Jose A; Jiménez, Laureano

    2012-05-10

    The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by BARON.

  18. OKVAR-Boost: a novel boosting algorithm to infer nonlinear dynamics and interactions in gene regulatory networks.

    Science.gov (United States)

    Lim, Néhémy; Senbabaoglu, Yasin; Michailidis, George; d'Alché-Buc, Florence

    2013-06-01

    Reverse engineering of gene regulatory networks remains a central challenge in computational systems biology, despite recent advances facilitated by benchmark in silico challenges that have aided in calibrating their performance. A number of approaches using either perturbation (knock-out) or wild-type time-series data have appeared in the literature addressing this problem, with the latter using linear temporal models. Nonlinear dynamical models are particularly appropriate for this inference task, given the generation mechanism of the time-series data. In this study, we introduce a novel nonlinear autoregressive model based on operator-valued kernels that simultaneously learns the model parameters, as well as the network structure. A flexible boosting algorithm (OKVAR-Boost) that shares features from L2-boosting and randomization-based algorithms is developed to perform the tasks of parameter learning and network inference for the proposed model. Specifically, at each boosting iteration, a regularized Operator-valued Kernel-based Vector AutoRegressive model (OKVAR) is trained on a random subnetwork. The final model consists of an ensemble of such models. The empirical estimation of the ensemble model's Jacobian matrix provides an estimation of the network structure. The performance of the proposed algorithm is first evaluated on a number of benchmark datasets from the DREAM3 challenge and then on real datasets related to the In vivo Reverse-Engineering and Modeling Assessment (IRMA) and T-cell networks. The high-quality results obtained strongly indicate that it outperforms existing approaches. The OKVAR-Boost Matlab code is available as the archive: http://amis-group.fr/sourcecode-okvar-boost/OKVARBoost-v1.0.zip. Supplementary data are available at Bioinformatics online.

  19. Genetic Algorithm for Mixed Integer Nonlinear Bilevel Programming and Applications in Product Family Design

    OpenAIRE

    Chenlu Miao; Gang Du; Yi Xia; Danping Wang

    2016-01-01

    Many leader-follower relationships exist in product family design engineering problems. We use bilevel programming (BLP) to reflect the leader-follower relationship and describe such problems. Product family design problems have unique characteristics; thus, mixed integer nonlinear BLP (MINLBLP), which has both continuous and discrete variables and multiple independent lower-level problems, is widely used in product family optimization. However, BLP is difficult in theory and is an NP-hard pr...

  20. Conservative multigrid methods for Cahn-Hilliard fluids

    International Nuclear Information System (INIS)

    Kim, Junseok; Kang, Kyungkeun; Lowengrub, John

    2004-01-01

    We develop a conservative, second-order accurate fully implicit discretization of the Navier-Stokes (NS) and Cahn-Hilliard (CH) system that has an associated discrete energy functional. This system provides a diffuse-interface description of binary fluid flows with compressible or incompressible flow components [R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 454 (1998) 2617]. In this work, we focus on the case of flows containing two immiscible, incompressible and density-matched components. The scheme, however, has a straightforward extension to multi-component systems. To efficiently solve the discrete system at the implicit time-level, we develop a nonlinear multigrid method to solve the CH equation which is then coupled to a projection method that is used to solve the NS equation. We demonstrate convergence of our scheme numerically in both the presence and absence of flow and perform simulations of phase separation via spinodal decomposition. We examine the separate effects of surface tension and external flow on the decomposition. We find surface tension driven flow alone increases coalescence rates through the retraction of interfaces. When there is an applied external shear, the evolution of the flow is nontrivial and the flow morphology repeats itself in time as multiple pinchoff and reconnection events occur. Eventually, the periodic motion ceases and the system relaxes to a global equilibrium. The equilibria we observe appears has a similar structure in all cases although the dynamics of the evolution is quite different. We view the work presented in this paper as preparatory for a detailed investigation of liquid-liquid interfaces with surface tension where the interfaces separate two immiscible fluids [On the pinchoff of liquid-liquid jets with surface tension, in preparation]. To this end, we also include a simulation of the pinchoff of a liquid thread under the Rayleigh instability at finite Reynolds number

  1. h-multigrid agglomeration based solution strategies for discontinuous Galerkin discretizations of incompressible flow problems

    Science.gov (United States)

    Botti, L.; Colombo, A.; Bassi, F.

    2017-10-01

    In this work we exploit agglomeration based h-multigrid preconditioners to speed-up the iterative solution of discontinuous Galerkin discretizations of the Stokes and Navier-Stokes equations. As a distinctive feature h-coarsened mesh sequences are generated by recursive agglomeration of a fine grid, admitting arbitrarily unstructured grids of complex domains, and agglomeration based discontinuous Galerkin discretizations are employed to deal with agglomerated elements of coarse levels. Both the expense of building coarse grid operators and the performance of the resulting multigrid iteration are investigated. For the sake of efficiency coarse grid operators are inherited through element-by-element L2 projections, avoiding the cost of numerical integration over agglomerated elements. Specific care is devoted to the projection of viscous terms discretized by means of the BR2 dG method. We demonstrate that enforcing the correct amount of stabilization on coarse grids levels is mandatory for achieving uniform convergence with respect to the number of levels. The numerical solution of steady and unsteady, linear and non-linear problems is considered tackling challenging 2D test cases and 3D real life computations on parallel architectures. Significant execution time gains are documented.

  2. Least-squares wave-front reconstruction of Shack-Hartmann sensors and shearing interferometers using multigrid techniques

    International Nuclear Information System (INIS)

    Baker, K.L.

    2005-01-01

    This article details a multigrid algorithm that is suitable for least-squares wave-front reconstruction of Shack-Hartmann and shearing interferometer wave-front sensors. The algorithm detailed in this article is shown to scale with the number of subapertures in the same fashion as fast Fourier transform techniques, making it suitable for use in applications requiring a large number of subapertures and high Strehl ratio systems such as for high spatial frequency characterization of high-density plasmas, optics metrology, and multiconjugate and extreme adaptive optics systems

  3. Level-Dependent Nonlinear Hearing Protector Model in the Auditory Hazard Assessment Algorithm for Humans

    Science.gov (United States)

    2015-04-01

    HPD model. In an article on measuring HPD attenuation, Berger (1986) points out that Real Ear Attenuation at Threshold (REAT) tests are...men. Audiology . 1991;30:345–356. Fedele P, Binseel M, Kalb J, Price GR. Using the auditory hazard assessment algorithm for humans (AHAAH) with

  4. A non-linear algorithm for current signal filtering and peak detection in SiPM

    International Nuclear Information System (INIS)

    Putignano, M; Intermite, A; Welsch, C P

    2012-01-01

    Read-out of Silicon Photomultipliers is commonly achieved by means of charge integration, a method particularly susceptible to after-pulsing noise and not efficient for low level light signals. Current signal monitoring, characterized by easier electronic implementation and intrinsically faster than charge integration, is also more suitable for low level light signals and can potentially result in much decreased after-pulsing noise effects. However, its use is to date limited by the need of developing a suitable read-out algorithm for signal analysis and filtering able to achieve current peak detection and measurement with the needed precision and accuracy. In this paper we present an original algorithm, based on a piecewise linear-fitting approach, to filter the noise of the current signal and hence efficiently identifying and measuring current peaks. The proposed algorithm is then compared with the optimal linear filtering algorithm for time-encoded peak detection, based on a moving average routine, and assessed in terms of accuracy, precision, and peak detection efficiency, demonstrating improvements of 1÷2 orders of magnitude in all these quality factors.

  5. A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

    Science.gov (United States)

    Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

    2016-01-01

    This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

  6. Algorithms

    Indian Academy of Sciences (India)

    to as 'divide-and-conquer'. Although there has been a large effort in realizing efficient algorithms, there are not many universally accepted algorithm design paradigms. In this article, we illustrate algorithm design techniques such as balancing, greedy strategy, dynamic programming strategy, and backtracking or traversal of ...

  7. Optimal Performance of a Nonlinear Gantry Crane System via Priority-based Fitness Scheme in Binary PSO Algorithm

    International Nuclear Information System (INIS)

    Jaafar, Hazriq Izzuan; Ali, Nursabillilah Mohd; Selamat, Nur Asmiza; Kassim, Anuar Mohamed; Mohamed, Z; Abidin, Amar Faiz Zainal; Jamian, J J

    2013-01-01

    This paper presents development of an optimal PID and PD controllers for controlling the nonlinear gantry crane system. The proposed Binary Particle Swarm Optimization (BPSO) algorithm that uses Priority-based Fitness Scheme is adopted in obtaining five optimal controller gains. The optimal gains are tested on a control structure that combines PID and PD controllers to examine system responses including trolley displacement and payload oscillation. The dynamic model of gantry crane system is derived using Lagrange equation. Simulation is conducted within Matlab environment to verify the performance of system in terms of settling time (Ts), steady state error (SSE) and overshoot (OS). This proposed technique demonstrates that implementation of Priority-based Fitness Scheme in BPSO is effective and able to move the trolley as fast as possible to the various desired position

  8. An Ensemble Nonlinear Model Predictive Control Algorithm in an Artificial Pancreas for People with Type 1 Diabetes

    DEFF Research Database (Denmark)

    Boiroux, Dimitri; Hagdrup, Morten; Mahmoudi, Zeinab

    2016-01-01

    patients with different physiological parameters and a time-varying insulin sensitivity using the Medtronic Virtual Patient (MVP) model. We augment the MVP model with stochastic diffusion terms, time-varying insulin sensitivity and noise-corrupted CGM measurements. We consider meal challenges where......This paper presents a novel ensemble nonlinear model predictive control (NMPC) algorithm for glucose regulation in type 1 diabetes. In this approach, we consider a number of scenarios describing different uncertainties, for instance meals or metabolic variations. We simulate a population of 9...... the uncertainty in meal size is ±50%. Numerical results show that the ensemble NMPC reduces the risk of hypoglycemia compared to standard NMPC in the case where the meal size is overestimated or correctly estimated at the expense of a slightly increased number of hyperglycemia. Therefore, ensemble MPC...

  9. Non-linear algorithms solved with the help of the GIBIANE macro-language

    International Nuclear Information System (INIS)

    Ebersolt, L.; Combescure, A.; Millard, A.; Verpeaux, P.

    1987-01-01

    Non linear finite element problems are often solved with the help of iteratives procedures. In the finite element program CASTEM 2000, the syntax of the dataset permits the user to derive his own algorithm and tune it to his problem. These basic ideas, simple to imagine, needed a proper frame to be materialized in a general purpose finite element program, and three concepts emerged: Operators, the Gibiane macro-language. In the two first paragraphs, we will detail these concepts, in the third paragraph, we will describe the different possibilities of the program, in the fourth paragraph, we will show, by combining operators in a proper order, how to obtain the desired algorithm. (orig./GL)

  10. Development of a multi-grid FDTD code for three-dimensional simulation of large microwave sintering experiments

    Energy Technology Data Exchange (ETDEWEB)

    White, M.J.; Iskander, M.F. [Univ. of Utah, Salt Lake City, UT (United States). Electrical Engineering Dept.; Kimrey, H.D. [Oak Ridge National Lab., TN (United States)

    1996-12-31

    The Finite-Difference Time-Domain (FDTD) code available at the University of Utah has been used to simulate sintering of ceramics in single and multimode cavities, and many useful results have been reported in literature. More detailed and accurate results, specifically around and including the ceramic sample, are often desired to help evaluate the adequacy of the heating procedure. In electrically large multimode cavities, however, computer memory requirements limit the number of the mathematical cells, and the desired resolution is impractical to achieve due to limited computer resources. Therefore, an FDTD algorithm which incorporates multiple-grid regions with variable-grid sizes is required to adequately perform the desired simulations. In this paper the authors describe the development of a three-dimensional multi-grid FDTD code to help focus a large number of cells around the desired region. Test geometries were solved using a uniform-grid and the developed multi-grid code to help validate the results from the developed code. Results from these comparisons, as well as the results of comparisons between the developed FDTD code and other available variable-grid codes are presented. In addition, results from the simulation of realistic microwave sintering experiments showed improved resolution in critical sites inside the three-dimensional sintering cavity. With the validation of the FDTD code, simulations were performed for electrically large, multimode, microwave sintering cavities to fully demonstrate the advantages of the developed multi-grid FDTD code.

  11. Accelerating Lattice QCD Multigrid on GPUs Using Fine-Grained Parallelization

    Energy Technology Data Exchange (ETDEWEB)

    Clark, M. A. [NVIDIA Corp., Santa Clara; Joó, Bálint [Jefferson Lab; Strelchenko, Alexei [Fermilab; Cheng, Michael [Boston U., Ctr. Comp. Sci.; Gambhir, Arjun [William-Mary Coll.; Brower, Richard [Boston U.

    2016-12-22

    The past decade has witnessed a dramatic acceleration of lattice quantum chromodynamics calculations in nuclear and particle physics. This has been due to both significant progress in accelerating the iterative linear solvers using multi-grid algorithms, and due to the throughput improvements brought by GPUs. Deploying hierarchical algorithms optimally on GPUs is non-trivial owing to the lack of parallelism on the coarse grids, and as such, these advances have not proved multiplicative. Using the QUDA library, we demonstrate that by exposing all sources of parallelism that the underlying stencil problem possesses, and through appropriate mapping of this parallelism to the GPU architecture, we can achieve high efficiency even for the coarsest of grids. Results are presented for the Wilson-Clover discretization, where we demonstrate up to 10x speedup over present state-of-the-art GPU-accelerated methods on Titan. Finally, we look to the future, and consider the software implications of our findings.

  12. On Algorithms for Nonlinear Minimax and Min-Max-Min Problems and Their Efficiency

    Science.gov (United States)

    2011-03-01

    dissertation is complete, I can finally stay home after dinner to play Wii with you. LET’S GO Mario and Yellow Mushroom... xv THIS PAGE INTENTIONALLY... balance the accuracy of the approximation with problem ill-conditioning. The sim- plest smoothing algorithm creates an accurate smooth approximating...sizing in electronic circuit boards (Chen & Fan, 1998), obstacle avoidance for robots (Kirjner- Neto & Polak, 1998), optimal design centering

  13. A Tutorial on Nonlinear Time-Series Data Mining in Engineering Asset Health and Reliability Prediction: Concepts, Models, and Algorithms

    Directory of Open Access Journals (Sweden)

    Ming Dong

    2010-01-01

    Full Text Available The primary objective of engineering asset management is to optimize assets service delivery potential and to minimize the related risks and costs over their entire life through the development and application of asset health and usage management in which the health and reliability prediction plays an important role. In real-life situations where an engineering asset operates under dynamic operational and environmental conditions, the lifetime of an engineering asset is generally described as monitored nonlinear time-series data and subject to high levels of uncertainty and unpredictability. It has been proved that application of data mining techniques is very useful for extracting relevant features which can be used as parameters for assets diagnosis and prognosis. In this paper, a tutorial on nonlinear time-series data mining in engineering asset health and reliability prediction is given. Besides that an overview on health and reliability prediction techniques for engineering assets is covered, this tutorial will focus on concepts, models, algorithms, and applications of hidden Markov models (HMMs and hidden semi-Markov models (HSMMs in engineering asset health prognosis, which are representatives of recent engineering asset health prediction techniques.

  14. Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation

    KAUST Repository

    Chen, Meng-Huo

    2015-09-13

    In this research we are particularly interested in extending the robustness of multigrid solvers to encounter complex systems related to subsurface reservoir applications for flow problems in porous media. In many cases, the step for solving the pressure filed in subsurface flow simulation becomes a bottleneck for the performance of the simulator. For solving large sparse linear system arising from MPFA discretization, we choose multigrid methods as the linear solver. The possible difficulties and issues will be addressed and the corresponding remedies will be studied. As the multigrid methods are used as the linear solver, the simulator can be parallelized (although not trivial) and the high-resolution simulation become feasible, the ultimately goal which we desire to achieve.

  15. A multigrid solution method for mixed hybrid finite elements

    Energy Technology Data Exchange (ETDEWEB)

    Schmid, W. [Universitaet Augsburg (Germany)

    1996-12-31

    We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.

  16. Final Report for 'Implimentation and Evaluation of Multigrid Linear Solvers into Extended Magnetohydrodynamic Codes for Petascale Computing'

    International Nuclear Information System (INIS)

    Vadlamani, Srinath; Kruger, Scott; Austin, Travis

    2008-01-01

    Extended magnetohydrodynamic (MHD) codes are used to model the large, slow-growing instabilities that are projected to limit the performance of International Thermonuclear Experimental Reactor (ITER). The multiscale nature of the extended MHD equations requires an implicit approach. The current linear solvers needed for the implicit algorithm scale poorly because the resultant matrices are so ill-conditioned. A new solver is needed, especially one that scales to the petascale. The most successful scalable parallel processor solvers to date are multigrid solvers. Applying multigrid techniques to a set of equations whose fundamental modes are dispersive waves is a promising solution to CEMM problems. For the Phase 1, we implemented multigrid preconditioners from the HYPRE project of the Center for Applied Scientific Computing at LLNL via PETSc of the DOE SciDAC TOPS for the real matrix systems of the extended MHD code NIMROD which is a one of the primary modeling codes of the OFES-funded Center for Extended Magnetohydrodynamic Modeling (CEMM) SciDAC. We implemented the multigrid solvers on the fusion test problem that allows for real matrix systems with success, and in the process learned about the details of NIMROD data structures and the difficulties of inverting NIMROD operators. The further success of this project will allow for efficient usage of future petascale computers at the National Leadership Facilities: Oak Ridge National Laboratory, Argonne National Laboratory, and National Energy Research Scientific Computing Center. The project will be a collaborative effort between computational plasma physicists and applied mathematicians at Tech-X Corporation, applied mathematicians Front Range Scientific Computations, Inc. (who are collaborators on the HYPRE project), and other computational plasma physicists involved with the CEMM project.

  17. A scalable geometric multigrid solver for nonsymmetric elliptic systems with application to variable-density flows

    Science.gov (United States)

    Esmaily, M.; Jofre, L.; Mani, A.; Iaccarino, G.

    2018-03-01

    A geometric multigrid algorithm is introduced for solving nonsymmetric linear systems resulting from the discretization of the variable density Navier-Stokes equations on nonuniform structured rectilinear grids and high-Reynolds number flows. The restriction operation is defined such that the resulting system on the coarser grids is symmetric, thereby allowing for the use of efficient smoother algorithms. To achieve an optimal rate of convergence, the sequence of interpolation and restriction operations are determined through a dynamic procedure. A parallel partitioning strategy is introduced to minimize communication while maintaining the load balance between all processors. To test the proposed algorithm, we consider two cases: 1) homogeneous isotropic turbulence discretized on uniform grids and 2) turbulent duct flow discretized on stretched grids. Testing the algorithm on systems with up to a billion unknowns shows that the cost varies linearly with the number of unknowns. This O (N) behavior confirms the robustness of the proposed multigrid method regarding ill-conditioning of large systems characteristic of multiscale high-Reynolds number turbulent flows. The robustness of our method to density variations is established by considering cases where density varies sharply in space by a factor of up to 104, showing its applicability to two-phase flow problems. Strong and weak scalability studies are carried out, employing up to 30,000 processors, to examine the parallel performance of our implementation. Excellent scalability of our solver is shown for a granularity as low as 104 to 105 unknowns per processor. At its tested peak throughput, it solves approximately 4 billion unknowns per second employing over 16,000 processors with a parallel efficiency higher than 50%.

  18. Scalable smoothing strategies for a geometric multigrid method for the immersed boundary equations

    Energy Technology Data Exchange (ETDEWEB)

    Bhalla, Amneet Pal Singh [Univ. of North Carolina, Chapel Hill, NC (United States); Knepley, Matthew G. [Rice Univ., Houston, TX (United States); Adams, Mark F. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Guy, Robert D. [Univ. of California, Davis, CA (United States); Griffith, Boyce E. [Univ. of North Carolina, Chapel Hill, NC (United States)

    2016-12-20

    The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular because of their simplicity and generality. In prior work (Guy et al., Adv Comput Math, 2015), some of us developed a geometric multigrid preconditioner for a stable semi-implicit IB method under Stokes flow conditions; however, this solver methodology used a Vanka-type smoother that presented limited opportunities for parallelization. This work extends this Stokes-IB solver methodology by developing smoothing techniques that are suitable for parallel implementation. Specifically, we demonstrate that an additive version of the Vanka smoother can yield an effective multigrid preconditioner for the Stokes-IB equations, and we introduce an efficient Schur complement-based smoother that is also shown to be effective for the Stokes-IB equations. We investigate the performance of these solvers for a broad range of material stiffnesses, both for Stokes flows and flows at nonzero Reynolds numbers, and for thick and thin structural models. We show here that linear solver performance degrades with increasing Reynolds number and material stiffness, especially for thin interface cases. Nonetheless, the proposed approaches promise to yield effective solution algorithms, especially at lower Reynolds numbers and at modest-to-high elastic stiffnesses.

  19. Design Considerations for a Flexible Multigrid Preconditioning Library

    Directory of Open Access Journals (Sweden)

    Jérémie Gaidamour

    2012-01-01

    Full Text Available MueLu is a library within the Trilinos software project [An overview of Trilinos, Technical Report SAND2003-2927, Sandia National Laboratories, 2003] and provides a framework for parallel multigrid preconditioning methods for large sparse linear systems. While providing efficient implementations of modern multigrid methods based on smoothed aggregation and energy minimization concepts, MueLu is designed to be customized and extended. This article gives an overview of design considerations for the MueLu package: user interfaces, internal design, data management, usage of modern software constructs, leveraging Trilinos capabilities, linear algebra operations and advanced application.

  20. Estimating the kinetic parameters of activated sludge storage using weighted non-linear least-squares and accelerating genetic algorithm.

    Science.gov (United States)

    Fang, Fang; Ni, Bing-Jie; Yu, Han-Qing

    2009-06-01

    In this study, weighted non-linear least-squares analysis and accelerating genetic algorithm are integrated to estimate the kinetic parameters of substrate consumption and storage product formation of activated sludge. A storage product formation equation is developed and used to construct the objective function for the determination of its production kinetics. The weighted least-squares analysis is employed to calculate the differences in the storage product concentration between the model predictions and the experimental data as the sum of squared weighted errors. The kinetic parameters for the substrate consumption and the storage product formation are estimated to be the maximum heterotrophic growth rate of 0.121/h, the yield coefficient of 0.44 mg CODX/mg CODS (COD, chemical oxygen demand) and the substrate half saturation constant of 16.9 mg/L, respectively, by minimizing the objective function using a real-coding-based accelerating genetic algorithm. Also, the fraction of substrate electrons diverted to the storage product formation is estimated to be 0.43 mg CODSTO/mg CODS. The validity of our approach is confirmed by the results of independent tests and the kinetic parameter values reported in literature, suggesting that this approach could be useful to evaluate the product formation kinetics of mixed cultures like activated sludge. More importantly, as this integrated approach could estimate the kinetic parameters rapidly and accurately, it could be applied to other biological processes.

  1. Enhanced nonlinear iterative techniques applied to a non-equilibrium plasma flow

    Energy Technology Data Exchange (ETDEWEB)

    Knoll, D.A.; McHugh, P.R. [Idaho National Engineering Lab., Idaho Falls, ID (United States)

    1996-12-31

    We study the application of enhanced nonlinear iterative methods to the steady-state solution of a system of two-dimensional convection-diffusion-reaction partial differential equations that describe the partially-ionized plasma flow in the boundary layer of a tokamak fusion reactor. This system of equations is characterized by multiple time and spatial scales, and contains highly anisotropic transport coefficients due to a strong imposed magnetic field. We use Newton`s method to linearize the nonlinear system of equations resulting from an implicit, finite volume discretization of the governing partial differential equations, on a staggered Cartesian mesh. The resulting linear systems are neither symmetric nor positive definite, and are poorly conditioned. Preconditioned Krylov iterative techniques are employed to solve these linear systems. We investigate both a modified and a matrix-free Newton-Krylov implementation, with the goal of reducing CPU cost associated with the numerical formation of the Jacobian. A combination of a damped iteration, one-way multigrid and a pseudo-transient continuation technique are used to enhance global nonlinear convergence and CPU efficiency. GMRES is employed as the Krylov method with Incomplete Lower-Upper(ILU) factorization preconditioning. The goal is to construct a combination of nonlinear and linear iterative techniques for this complex physical problem that optimizes trade-offs between robustness, CPU time, memory requirements, and code complexity. It is shown that a one-way multigrid implementation provides significant CPU savings for fine grid calculations. Performance comparisons of the modified Newton-Krylov and matrix-free Newton-Krylov algorithms will be presented.

  2. Primal-Dual Interior Point Multigrid Method for Topology Optimization

    Czech Academy of Sciences Publication Activity Database

    Kočvara, Michal; Mohammed, S.

    2016-01-01

    Roč. 38, č. 5 (2016), B685-B709 ISSN 1064-8275 Grant - others:European Commission - EC(XE) 313781 Institutional support: RVO:67985556 Keywords : topology optimization * multigrid method s * interior point method Subject RIV: BA - General Mathematics Impact factor: 2.195, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/kocvara-0462418.pdf

  3. On multigrid-CG for efficient topology optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Aage, Niels; Lazarov, Boyan Stefanov

    2014-01-01

    reduction is obtained by exploiting specific characteristics of a multigrid preconditioned conjugate gradients (MGCG) solver. In particular, the number of MGCG iterations is reduced by relating it to the geometric parameters of the problem. At the same time, accurate outcome of the optimization process...

  4. Algorithms

    Indian Academy of Sciences (India)

    ticians but also forms the foundation of computer science. Two ... with methods of developing algorithms for solving a variety of problems but ... applications of computers in science and engineer- ... numerical calculus are as important. We will ...

  5. The finite volume element (FVE) and multigrid method for the incompressible Navier-Stokes equations

    International Nuclear Information System (INIS)

    Gu Lizhen; Bao Weizhu

    1992-01-01

    The authors apply FVE method to discrete INS equations with the original variable, in which the bilinear square finite element and the square finite volume are chosen. The discrete schemes of INS equations are presented. The FMV multigrid algorithm is applied to solve that discrete system, where DGS iteration is used as smoother, DGS distributive mode for the INS discrete system is also presented. The sample problems for the square cavity flow with Reynolds number Re≤100 are successfully calculated. The numerical solutions show that the results with 1 FMV is satisfactory and when Re is not large, The FVE discrete scheme of the conservative INS equations and that of non-conservative INS equations with linearization both can provide almost same accuracy

  6. CHAM: a fast algorithm of modelling non-linear matter power spectrum in the sCreened HAlo Model

    Science.gov (United States)

    Hu, Bin; Liu, Xue-Wen; Cai, Rong-Gen

    2018-05-01

    We present a fast numerical screened halo model algorithm (CHAM, which stands for the sCreened HAlo Model) for modelling non-linear power spectrum for the alternative models to Λ cold dark matter. This method has three obvious advantages. First of all, it is not being restricted to a specific dark energy/modified gravity model. In principle, all of the screened scalar-tensor theories can be applied. Secondly, the least assumptions are made in the calculation. Hence, the physical picture is very easily understandable. Thirdly, it is very predictable and does not rely on the calibration from N-body simulation. As an example, we show the case of the Hu-Sawicki f(R) gravity. In this case, the typical CPU time with the current parallel PYTHON script (eight threads) is roughly within 10 min. The resulting spectra are in a good agreement with N-body data within a few percentage accuracy up to k ˜ 1 h Mpc-1.

  7. Algorithms

    Indian Academy of Sciences (India)

    algorithm design technique called 'divide-and-conquer'. One of ... Turtle graphics, September. 1996. 5. ... whole list named 'PO' is a pointer to the first element of the list; ..... Program for computing matrices X and Y and placing the result in C *).

  8. Algorithms

    Indian Academy of Sciences (India)

    algorithm that it is implicitly understood that we know how to generate the next natural ..... Explicit comparisons are made in line (1) where maximum and minimum is ... It can be shown that the function T(n) = 3/2n -2 is the solution to the above ...

  9. The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons.

    Science.gov (United States)

    Ren, Pengyu; Li, Bowen; Dong, Shiyao; Chen, Lin; Zhang, Yuelin

    2018-01-01

    Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system.

  10. Rigorous lower bound on the dynamic critical exponent of some multilevel Swendsen-Wang algorithms

    International Nuclear Information System (INIS)

    Li, X.; Sokal, A.D.

    1991-01-01

    We prove the rigorous lower bound z exp ≥α/ν for the dynamic critical exponent of a broad class of multilevel (or ''multigrid'') variants of the Swendsen-Wang algorithm. This proves that such algorithms do suffer from critical slowing down. We conjecture that such algorithms in fact lie in the same dynamic universality class as the stanard Swendsen-Wang algorithm

  11. Design of Robust Supertwisting Algorithm Based Second-Order Sliding Mode Controller for Nonlinear Systems with Both Matched and Unmatched Uncertainty

    Directory of Open Access Journals (Sweden)

    Marwa Jouini

    2017-01-01

    Full Text Available This paper proposes a robust supertwisting algorithm (STA design for nonlinear systems where both matched and unmatched uncertainties are considered. The main contributions reside primarily to conceive a novel structure of STA, in order to ensure the desired performance of the uncertain nonlinear system. The modified algorithm is formed of double closed-loop feedback, in which two linear terms are added to the classical STA. In addition, an integral sliding mode switching surface is proposed to construct the attractiveness and reachability of sliding mode. Sufficient conditions are derived to guarantee the exact differentiation stability in finite time based on Lyapunov function theory. Finally, a comparative study for a variable-length pendulum system illustrates the robustness and the effectiveness of the proposed approach compared to other STA schemes.

  12. An analytical fuzzy-based approach to ?-gain optimal control of input-affine nonlinear systems using Newton-type algorithm

    Science.gov (United States)

    Milic, Vladimir; Kasac, Josip; Novakovic, Branko

    2015-10-01

    This paper is concerned with ?-gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone-Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for ?-gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton's method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system.

  13. Algorithms

    Indian Academy of Sciences (India)

    will become clear in the next article when we discuss a simple logo like programming language. ... Rod B may be used as an auxiliary store. The problem is to find an algorithm which performs this task. ... No disks are moved from A to Busing C as auxiliary rod. • move _disk (A, C);. (No + l)th disk is moved from A to C directly ...

  14. Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation-Maximization (SAEM) Algorithm.

    Science.gov (United States)

    Chow, Sy-Miin; Lu, Zhaohua; Sherwood, Andrew; Zhu, Hongtu

    2016-03-01

    The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation-maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed.

  15. Efficient relaxed-Jacobi smoothers for multigrid on parallel computers

    Science.gov (United States)

    Yang, Xiang; Mittal, Rajat

    2017-03-01

    In this Technical Note, we present a family of Jacobi-based multigrid smoothers suitable for the solution of discretized elliptic equations. These smoothers are based on the idea of scheduled-relaxation Jacobi proposed recently by Yang & Mittal (2014) [18] and employ two or three successive relaxed Jacobi iterations with relaxation factors derived so as to maximize the smoothing property of these iterations. The performance of these new smoothers measured in terms of convergence acceleration and computational workload, is assessed for multi-domain implementations typical of parallelized solvers, and compared to the lexicographic point Gauss-Seidel smoother. The tests include the geometric multigrid method on structured grids as well as the algebraic grid method on unstructured grids. The tests demonstrate that unlike Gauss-Seidel, the convergence of these Jacobi-based smoothers is unaffected by domain decomposition, and furthermore, they outperform the lexicographic Gauss-Seidel by factors that increase with domain partition count.

  16. Towards a multigrid scheme in SU(2) lattice gauge theory

    International Nuclear Information System (INIS)

    Gutbrod, F.

    1992-12-01

    The task of constructing a viable updating multigrid scheme for SU(2) lattice gauge theory is discussed in connection with the classical eigenvalue problem. For a nonlocal overrelaxation Monte Carlo update step, the central numerical problem is the search for the minimum of a quadratic approximation to the action under nonlocal constraints. Here approximate eigenfunctions are essential to reduce the numerical work, and these eigenfunctions are to be constructed with multigrid techniques. A simple implementation on asymmetric lattices is described, where the grids are restricted to 3-dimensional hyperplanes. The scheme is shown to be moderately successful in the early stages of the updating history (starting from a cold configuration). The main results of another, less asymmetric scheme are presented briefly. (orig.)

  17. Multigrid time-accurate integration of Navier-Stokes equations

    Science.gov (United States)

    Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.

    1993-01-01

    Efficient acceleration techniques typical of explicit steady-state solvers are extended to time-accurate calculations. Stability restrictions are greatly reduced by means of a fully implicit time discretization. A four-stage Runge-Kutta scheme with local time stepping, residual smoothing, and multigridding is used instead of traditional time-expensive factorizations. Some applications to natural and forced unsteady viscous flows show the capability of the procedure.

  18. Comparative Performance Analysis of Coarse Solvers for Algebraic Multigrid on Multicore and Manycore Architectures

    Energy Technology Data Exchange (ETDEWEB)

    Druinsky, A; Ghysels, P; Li, XS; Marques, O; Williams, S; Barker, A; Kalchev, D; Vassilevski, P

    2016-04-02

    In this paper, we study the performance of a two-level algebraic-multigrid algorithm, with a focus on the impact of the coarse-grid solver on performance. We consider two algorithms for solving the coarse-space systems: the preconditioned conjugate gradient method and a new robust HSS-embedded low-rank sparse-factorization algorithm. Our test data comes from the SPE Comparative Solution Project for oil-reservoir simulations. We contrast the performance of our code on one 12-core socket of a Cray XC30 machine with performance on a 60-core Intel Xeon Phi coprocessor. To obtain top performance, we optimized the code to take full advantage of fine-grained parallelism and made it thread-friendly for high thread count. We also developed a bounds-and-bottlenecks performance model of the solver which we used to guide us through the optimization effort, and also carried out performance tuning in the solver’s large parameter space. Finally, as a result, significant speedups were obtained on both machines.

  19. Uzawa smoother in multigrid for the coupleD porous medium and stokes flow system

    NARCIS (Netherlands)

    P. Luo (Peiyao); C. Rodrigo (Carmen); F.J. Gaspar Lorenz (Franscisco); C.W. Oosterlee (Kees)

    2017-01-01

    textabstractThe multigrid solution of coupled porous media and Stokes flow problems is considered. The Darcy equation as the saturated porous medium model is coupled to the Stokes equations by means of appropriate interface conditions. We focus on an efficient multigrid solution technique for the

  20. Multigrid for high dimensional elliptic partial differential equations on non-equidistant grids

    NARCIS (Netherlands)

    bin Zubair, H.; Oosterlee, C.E.; Wienands, R.

    2006-01-01

    This work presents techniques, theory and numbers for multigrid in a general d-dimensional setting. The main focus is the multigrid convergence for high-dimensional partial differential equations (PDEs). As a model problem we have chosen the anisotropic diffusion equation, on a unit hypercube. We

  1. Multigrid solution of the convection-diffusion equation with high-Reynolds number

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Jun [George Washington Univ., Washington, DC (United States)

    1996-12-31

    A fourth-order compact finite difference scheme is employed with the multigrid technique to solve the variable coefficient convection-diffusion equation with high-Reynolds number. Scaled inter-grid transfer operators and potential on vectorization and parallelization are discussed. The high-order multigrid method is unconditionally stable and produces solution of 4th-order accuracy. Numerical experiments are included.

  2. Nonlinear Microwave Imaging for Breast-Cancer Screening Using Gauss–Newton's Method and the CGLS Inversion Algorithm

    DEFF Research Database (Denmark)

    Rubæk, Tonny; Meaney, P. M.; Meincke, Peter

    2007-01-01

    is presented which is based on the conjugate gradient least squares (CGLS) algorithm. The iterative CGLS algorithm is capable of solving the update problem by operating on just the Jacobian and the regularizing effects of the algorithm can easily be controlled by adjusting the number of iterations. The new...

  3. Improved binary dragonfly optimization algorithm and wavelet packet based non-linear features for infant cry classification.

    Science.gov (United States)

    Hariharan, M; Sindhu, R; Vijean, Vikneswaran; Yazid, Haniza; Nadarajaw, Thiyagar; Yaacob, Sazali; Polat, Kemal

    2018-03-01

    Infant cry signal carries several levels of information about the reason for crying (hunger, pain, sleepiness and discomfort) or the pathological status (asphyxia, deaf, jaundice, premature condition and autism, etc.) of an infant and therefore suited for early diagnosis. In this work, combination of wavelet packet based features and Improved Binary Dragonfly Optimization based feature selection method was proposed to classify the different types of infant cry signals. Cry signals from 2 different databases were utilized. First database contains 507 cry samples of normal (N), 340 cry samples of asphyxia (A), 879 cry samples of deaf (D), 350 cry samples of hungry (H) and 192 cry samples of pain (P). Second database contains 513 cry samples of jaundice (J), 531 samples of premature (Prem) and 45 samples of normal (N). Wavelet packet transform based energy and non-linear entropies (496 features), Linear Predictive Coding (LPC) based cepstral features (56 features), Mel-frequency Cepstral Coefficients (MFCCs) were extracted (16 features). The combined feature set consists of 568 features. To overcome the curse of dimensionality issue, improved binary dragonfly optimization algorithm (IBDFO) was proposed to select the most salient attributes or features. Finally, Extreme Learning Machine (ELM) kernel classifier was used to classify the different types of infant cry signals using all the features and highly informative features as well. Several experiments of two-class and multi-class classification of cry signals were conducted. In binary or two-class experiments, maximum accuracy of 90.18% for H Vs P, 100% for A Vs N, 100% for D Vs N and 97.61% J Vs Prem was achieved using the features selected (only 204 features out of 568) by IBDFO. For the classification of multiple cry signals (multi-class problem), the selected features could differentiate between three classes (N, A & D) with the accuracy of 100% and seven classes with the accuracy of 97.62%. The experimental

  4. A New Method Based On Modified Shuffled Frog Leaping Algorithm In Order To Solve Nonlinear Large Scale Problem

    Directory of Open Access Journals (Sweden)

    Aliasghar Baziar

    2015-03-01

    Full Text Available Abstract In order to handle large scale problems this study has used shuffled frog leaping algorithm. This algorithm is an optimization method based on natural memetics that uses a new two-phase modification to it to have a better search in the problem space. The suggested algorithm is evaluated by comparing to some well known algorithms using several benchmark optimization problems. The simulation results have clearly shown the superiority of this algorithm over other well-known methods in the area.

  5. Application of the nonlinear time series prediction method of genetic algorithm for forecasting surface wind of point station in the South China Sea with scatterometer observations

    International Nuclear Information System (INIS)

    Zhong Jian; Dong Gang; Sun Yimei; Zhang Zhaoyang; Wu Yuqin

    2016-01-01

    The present work reports the development of nonlinear time series prediction method of genetic algorithm (GA) with singular spectrum analysis (SSA) for forecasting the surface wind of a point station in the South China Sea (SCS) with scatterometer observations. Before the nonlinear technique GA is used for forecasting the time series of surface wind, the SSA is applied to reduce the noise. The surface wind speed and surface wind components from scatterometer observations at three locations in the SCS have been used to develop and test the technique. The predictions have been compared with persistence forecasts in terms of root mean square error. The predicted surface wind with GA and SSA made up to four days (longer for some point station) in advance have been found to be significantly superior to those made by persistence model. This method can serve as a cost-effective alternate prediction technique for forecasting surface wind of a point station in the SCS basin. (paper)

  6. Damage mapping in structural health monitoring using a multi-grid architecture

    Energy Technology Data Exchange (ETDEWEB)

    Mathews, V. John [Dept. of Electrical and Computer Engineering, University of Utah, Salt Lake City, UT 84112 (United States)

    2015-03-31

    This paper presents a multi-grid architecture for tomography-based damage mapping of composite aerospace structures. The system employs an array of piezo-electric transducers bonded on the structure. Each transducer may be used as an actuator as well as a sensor. The structure is excited sequentially using the actuators and the guided waves arriving at the sensors in response to the excitations are recorded for further analysis. The sensor signals are compared to their baseline counterparts and a damage index is computed for each actuator-sensor pair. These damage indices are then used as inputs to the tomographic reconstruction system. Preliminary damage maps are reconstructed on multiple coordinate grids defined on the structure. These grids are shifted versions of each other where the shift is a fraction of the spatial sampling interval associated with each grid. These preliminary damage maps are then combined to provide a reconstruction that is more robust to measurement noise in the sensor signals and the ill-conditioned problem formulation for single-grid algorithms. Experimental results on a composite structure with complexity that is representative of aerospace structures included in the paper demonstrate that for sufficiently high sensor densities, the algorithm of this paper is capable of providing damage detection and characterization with accuracy comparable to traditional C-scan and A-scan-based ultrasound non-destructive inspection systems quickly and without human supervision.

  7. Fast multigrid solution of the advection problem with closed characteristics

    Energy Technology Data Exchange (ETDEWEB)

    Yavneh, I. [Israel Inst. of Technology, Haifa (Israel); Venner, C.H. [Univ. of Twente, Enschede (Netherlands); Brandt, A. [Weizmann Inst. of Science, Rehovot (Israel)

    1996-12-31

    The numerical solution of the advection-diffusion problem in the inviscid limit with closed characteristics is studied as a prelude to an efficient high Reynolds-number flow solver. It is demonstrated by a heuristic analysis and numerical calculations that using upstream discretization with downstream relaxation-ordering and appropriate residual weighting in a simple multigrid V cycle produces an efficient solution process. We also derive upstream finite-difference approximations to the advection operator, whose truncation terms approximate {open_quotes}physical{close_quotes} (Laplacian) viscosity, thus avoiding spurious solutions to the homogeneous problem when the artificial diffusivity dominates the physical viscosity.

  8. A comparative analysis of particle swarm optimization and differential evolution algorithms for parameter estimation in nonlinear dynamic systems

    International Nuclear Information System (INIS)

    Banerjee, Amit; Abu-Mahfouz, Issam

    2014-01-01

    The use of evolutionary algorithms has been popular in recent years for solving the inverse problem of identifying system parameters given the chaotic response of a dynamical system. The inverse problem is reformulated as a minimization problem and population-based optimizers such as evolutionary algorithms have been shown to be efficient solvers of the minimization problem. However, to the best of our knowledge, there has been no published work that evaluates the efficacy of using the two most popular evolutionary techniques – particle swarm optimization and differential evolution algorithm, on a wide range of parameter estimation problems. In this paper, the two methods along with their variants (for a total of seven algorithms) are applied to fifteen different parameter estimation problems of varying degrees of complexity. Estimation results are analyzed using nonparametric statistical methods to identify if an algorithm is statistically superior to others over the class of problems analyzed. Results based on parameter estimation quality suggest that there are significant differences between the algorithms with the newer, more sophisticated algorithms performing better than their canonical versions. More importantly, significant differences were also found among variants of the particle swarm optimizer and the best performing differential evolution algorithm

  9. A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm.

    Science.gov (United States)

    El-Qulity, Said Ali; Mohamed, Ali Wagdy

    2016-01-01

    This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness.

  10. Forecasting nonlinear chaotic time series with function expression method based on an improved genetic-simulated annealing algorithm.

    Science.gov (United States)

    Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

    2015-01-01

    The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.

  11. Fast algorithms for transport models. Final report, June 1, 1993--May 31, 1994

    International Nuclear Information System (INIS)

    Manteuffel, T.

    1994-12-01

    The focus of this project is the study of multigrid and multilevel algorithms for the numerical solution of Boltzmann models of the transport of neutral and charged particles. In previous work a fast multigrid algorithm was developed for the numerical solution of the Boltzmann model of neutral particle transport in slab geometry assuming isotropic scattering. The new algorithm is extremely fast in the thick diffusion limit; the multigrid v-cycle convergence factor approaches zero as the mean-free-path between collisions approaches zero, independent of the mesh. Also, a fast multilevel method was developed for the numerical solution of the Boltzmann model of charged particle transport in the thick Fokker-Plank limit for slab geometry. Parallel implementations were developed for both algorithms

  12. Annual Copper Mountain Conferences on Multigrid and Iterative Methods, Copper Mountain, Colorado

    International Nuclear Information System (INIS)

    McCormick, Stephen F.

    2016-01-01

    This project supported the Copper Mountain Conference on Multigrid and Iterative Methods, held from 2007 to 2015, at Copper Mountain, Colorado. The subject of the Copper Mountain Conference Series alternated between Multigrid Methods in odd-numbered years and Iterative Methods in even-numbered years. Begun in 1983, the Series represents an important forum for the exchange of ideas in these two closely related fields. This report describes the Copper Mountain Conference on Multigrid and Iterative Methods, 2007-2015. Information on the conference series is available at http://grandmaster.colorado.edu/~copper/

  13. Annual Copper Mountain Conferences on Multigrid and Iterative Methods, Copper Mountain, Colorado

    Energy Technology Data Exchange (ETDEWEB)

    McCormick, Stephen F. [Front Range Scientific, Inc., Lake City, CO (United States)

    2016-03-25

    This project supported the Copper Mountain Conference on Multigrid and Iterative Methods, held from 2007 to 2015, at Copper Mountain, Colorado. The subject of the Copper Mountain Conference Series alternated between Multigrid Methods in odd-numbered years and Iterative Methods in even-numbered years. Begun in 1983, the Series represents an important forum for the exchange of ideas in these two closely related fields. This report describes the Copper Mountain Conference on Multigrid and Iterative Methods, 2007-2015. Information on the conference series is available at http://grandmaster.colorado.edu/~copper/.

  14. Estimating model error covariances in nonlinear state-space models using Kalman smoothing and the expectation-maximisation algorithm

    KAUST Repository

    Dreano, Denis; Tandeo, P.; Pulido, M.; Ait-El-Fquih, Boujemaa; Chonavel, T.; Hoteit, Ibrahim

    2017-01-01

    Specification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation-maximisation (EM) algorithm to estimate the model error covariances using classical extended

  15. Observation of the state of the nuclear reactor core by means of non-linear observation algorithms

    International Nuclear Information System (INIS)

    Maciel Palacio, F.E.; Espana, M.D.

    1990-01-01

    A combined, variable-adaptive structure, non-linear observer was designed in order to observe the state of the nuclear reactor core, based on the Absolute Stability Theory. The observer was proved under noise and modelling error conditions. Successful results were obtained in the observation of the states in both cases, showing clear improvement in the observation due to the application of adaptive and variable structure ideas. (Author) [es

  16. Prediction of modified Mercalli intensity from PGA, PGV, moment magnitude, and epicentral distance using several nonlinear statistical algorithms

    Science.gov (United States)

    Alvarez, Diego A.; Hurtado, Jorge E.; Bedoya-Ruíz, Daniel Alveiro

    2012-07-01

    Despite technological advances in seismic instrumentation, the assessment of the intensity of an earthquake using an observational scale as given, for example, by the modified Mercalli intensity scale is highly useful for practical purposes. In order to link the qualitative numbers extracted from the acceleration record of an earthquake and other instrumental data such as peak ground velocity, epicentral distance, and moment magnitude on the one hand and the modified Mercalli intensity scale on the other, simple statistical regression has been generally employed. In this paper, we will employ three methods of nonlinear regression, namely support vector regression, multilayer perceptrons, and genetic programming in order to find a functional dependence between the instrumental records and the modified Mercalli intensity scale. The proposed methods predict the intensity of an earthquake while dealing with nonlinearity and the noise inherent to the data. The nonlinear regressions with good estimation results have been performed using the "Did You Feel It?" database of the US Geological Survey and the database of the Center for Engineering Strong Motion Data for the California region.

  17. Towards a Robust Solution of the Non-Linear Kinematics for the General Stewart Platform with Estimation of Distribution Algorithms

    Directory of Open Access Journals (Sweden)

    Eusebio Eduardo Hernández Martinez

    2013-01-01

    Full Text Available In robotics, solving the direct kinematics problem (DKP for parallel robots is very often more difficult and time consuming than for their serial counterparts. The problem is stated as follows: given the joint variables, the Cartesian variables should be computed, namely the pose of the mobile platform. Most of the time, the DKP requires solving a non-linear system of equations. In addition, given that the system could be non-convex, Newton or Quasi-Newton (Dogleg based solvers get trapped on local minima. The capacity of such kinds of solvers to find an adequate solution strongly depends on the starting point. A well-known problem is the selection of such a starting point, which requires a priori information about the neighbouring region of the solution. In order to circumvent this issue, this article proposes an efficient method to select and to generate the starting point based on probabilistic learning. Experiments and discussion are presented to show the method performance. The method successfully avoids getting trapped on local minima without the need for human intervention, which increases its robustness when compared with a single Dogleg approach. This proposal can be extended to other structures, to any non-linear system of equations, and of course, to non-linear optimization problems.

  18. Optimum Performances for Non-Linear Finite Elements Model of 8/6 Switched Reluctance Motor Based on Intelligent Routing Algorithms

    Directory of Open Access Journals (Sweden)

    Chouaib Labiod

    2017-01-01

    Full Text Available This paper presents torque ripple reduction with speed control of 8/6 Switched Reluctance Motor (SRM by the determination of the optimal parameters of the turn on, turn off angles Theta_(on, Theta_(off, and the supply voltage using Particle Swarm Optimization (PSO algorithm and steady state Genetic Algorithm (ssGA. With SRM model, there is difficulty in the control relapsed into highly non-linear static characteristics. For this, the Finite Elements Method (FEM has been used because it is a powerful tool to get a model closer to reality. The mechanism used in this kind of machine control consists of a speed controller in order to determine current reference which must be produced to get the desired speed, hence, hysteresis controller is used to compare current reference with current measured up to achieve switching signals needed in the inverter. Depending on this control, the intelligent routing algorithms get the fitness equation from torque ripple and speed response so as to give the optimal parameters for better results. Obtained results from the proposed strategy based on metaheuristic methods are compared with the basic case without considering the adjustment of specific parameters. Optimized results found clearly confirmed the ability and the efficiency of the proposed strategy based on metaheuristic methods in improving the performances of the SRM control considering different torque loads.

  19. An application of multigrid methods for a discrete elastic model for epitaxial systems

    International Nuclear Information System (INIS)

    Caflisch, R.E.; Lee, Y.-J.; Shu, S.; Xiao, Y.-X.; Xu, J.

    2006-01-01

    We apply an efficient and fast algorithm to simulate the atomistic strain model for epitaxial systems, recently introduced by Schindler et al. [Phys. Rev. B 67, 075316 (2003)]. The discrete effects in this lattice statics model are crucial for proper simulation of the influence of strain for thin film epitaxial growth, but the size of the atomistic systems of interest is in general quite large and hence the solution of the discrete elastic equations is a considerable numerical challenge. In this paper, we construct an algebraic multigrid method suitable for efficient solution of the large scale discrete strain model. Using this method, simulations are performed for several representative physical problems, including an infinite periodic step train, a layered nanocrystal, and a system of quantum dots. The results demonstrate the effectiveness and robustness of the method and show that the method attains optimal convergence properties, regardless of the problem size, the geometry and the physical parameters. The effects of substrate depth and of invariance due to traction-free boundary conditions are assessed. For a system of quantum dots, the simulated strain energy density supports the observations that trench formation near the dots provides strain relief

  20. Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.

    Science.gov (United States)

    Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger

    2016-11-01

    In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.

  1. Numerical method for the eigenvalue problem and the singular equation by using the multi-grid method and application to ordinary differential equation

    International Nuclear Information System (INIS)

    Kanki, Takashi; Uyama, Tadao; Tokuda, Shinji.

    1995-07-01

    In the numerical method to compute the matching data which are necessary for resistive MHD stability analyses, it is required to solve the eigenvalue problem and the associated singular equation. An iterative method is developed to solve the eigenvalue problem and the singular equation. In this method, the eigenvalue problem is replaced with an equivalent nonlinear equation and a singular equation is derived from Newton's method for the nonlinear equation. The multi-grid method (MGM), a high speed iterative method, can be applied to this method. The convergence of the eigenvalue and the eigenvector, and the CPU time in this method are investigated for a model equation. It is confirmed from the numerical results that this method is effective for solving the eigenvalue problem and the singular equation with numerical stability and high accuracy. It is shown by improving the MGM that the CPU time for this method is 50 times shorter than that of the direct method. (author)

  2. Multiplex protein pattern unmixing using a non-linear variable-weighted support vector machine as optimized by a particle swarm optimization algorithm.

    Science.gov (United States)

    Yang, Qin; Zou, Hong-Yan; Zhang, Yan; Tang, Li-Juan; Shen, Guo-Li; Jiang, Jian-Hui; Yu, Ru-Qin

    2016-01-15

    Most of the proteins locate more than one organelle in a cell. Unmixing the localization patterns of proteins is critical for understanding the protein functions and other vital cellular processes. Herein, non-linear machine learning technique is proposed for the first time upon protein pattern unmixing. Variable-weighted support vector machine (VW-SVM) is a demonstrated robust modeling technique with flexible and rational variable selection. As optimized by a global stochastic optimization technique, particle swarm optimization (PSO) algorithm, it makes VW-SVM to be an adaptive parameter-free method for automated unmixing of protein subcellular patterns. Results obtained by pattern unmixing of a set of fluorescence microscope images of cells indicate VW-SVM as optimized by PSO is able to extract useful pattern features by optimally rescaling each variable for non-linear SVM modeling, consequently leading to improved performances in multiplex protein pattern unmixing compared with conventional SVM and other exiting pattern unmixing methods. Copyright © 2015 Elsevier B.V. All rights reserved.

  3. Calculating the Mean Amplitude of Glycemic Excursions from Continuous Glucose Data Using an Open-Code Programmable Algorithm Based on the Integer Nonlinear Method.

    Science.gov (United States)

    Yu, Xuefei; Lin, Liangzhuo; Shen, Jie; Chen, Zhi; Jian, Jun; Li, Bin; Xin, Sherman Xuegang

    2018-01-01

    The mean amplitude of glycemic excursions (MAGE) is an essential index for glycemic variability assessment, which is treated as a key reference for blood glucose controlling at clinic. However, the traditional "ruler and pencil" manual method for the calculation of MAGE is time-consuming and prone to error due to the huge data size, making the development of robust computer-aided program an urgent requirement. Although several software products are available instead of manual calculation, poor agreement among them is reported. Therefore, more studies are required in this field. In this paper, we developed a mathematical algorithm based on integer nonlinear programming. Following the proposed mathematical method, an open-code computer program named MAGECAA v1.0 was developed and validated. The results of the statistical analysis indicated that the developed program was robust compared to the manual method. The agreement among the developed program and currently available popular software is satisfied, indicating that the worry about the disagreement among different software products is not necessary. The open-code programmable algorithm is an extra resource for those peers who are interested in the related study on methodology in the future.

  4. A novel vehicle dynamics stability control algorithm based on the hierarchical strategy with constrain of nonlinear tyre forces

    Science.gov (United States)

    Li, Liang; Jia, Gang; Chen, Jie; Zhu, Hongjun; Cao, Dongpu; Song, Jian

    2015-08-01

    Direct yaw moment control (DYC), which differentially brakes the wheels to produce a yaw moment for the vehicle stability in a steering process, is an important part of electric stability control system. In this field, most control methods utilise the active brake pressure with a feedback controller to adjust the braked wheel. However, the method might lead to a control delay or overshoot because of the lack of a quantitative project relationship between target values from the upper stability controller to the lower pressure controller. Meanwhile, the stability controller usually ignores the implementing ability of the tyre forces, which might be restrained by the combined-slip dynamics of the tyre. Therefore, a novel control algorithm of DYC based on the hierarchical control strategy is brought forward in this paper. As for the upper controller, a correctional linear quadratic regulator, which not only contains feedback control but also contains feed forward control, is introduced to deduce the object of the stability yaw moment in order to guarantee the yaw rate and side-slip angle stability. As for the medium and lower controller, the quantitative relationship between the vehicle stability object and the target tyre forces of controlled wheels is proposed to achieve smooth control performance based on a combined-slip tyre model. The simulations with the hardware-in-the-loop platform validate that the proposed algorithm can improve the stability of the vehicle effectively.

  5. Fast and high-order numerical algorithms for the solution of multidimensional nonlinear fractional Ginzburg-Landau equation

    Science.gov (United States)

    Mohebbi, Akbar

    2018-02-01

    In this paper we propose two fast and accurate numerical methods for the solution of multidimensional space fractional Ginzburg-Landau equation (FGLE). In the presented methods, to avoid solving a nonlinear system of algebraic equations and to increase the accuracy and efficiency of method, we split the complex problem into simpler sub-problems using the split-step idea. For a homogeneous FGLE, we propose a method which has fourth-order of accuracy in time component and spectral accuracy in space variable and for nonhomogeneous one, we introduce another scheme based on the Crank-Nicolson approach which has second-order of accuracy in time variable. Due to using the Fourier spectral method for fractional Laplacian operator, the resulting schemes are fully diagonal and easy to code. Numerical results are reported in terms of accuracy, computational order and CPU time to demonstrate the accuracy and efficiency of the proposed methods and to compare the results with the analytical solutions. The results show that the present methods are accurate and require low CPU time. It is illustrated that the numerical results are in good agreement with the theoretical ones.

  6. Non-Galerkin Coarse Grids for Algebraic Multigrid

    Energy Technology Data Exchange (ETDEWEB)

    Falgout, Robert D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Schroder, Jacob B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2014-06-26

    Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. And while AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. Particularly, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid hierarchy, and this growth leads to more communication. Therefore, as problem size increases and the number of levels in the hierarchy grows, the overall efficiency of the parallel AMG method decreases, sometimes dramatically. This growth in stencil size is due to the standard Galerkin coarse grid operator, $P^T A P$, where $P$ is the prolongation (i.e., interpolation) operator. For example, the coarse grid stencil size for a simple three-dimensional (3D) seven-point finite differencing approximation to diffusion can increase into the thousands on present day machines, causing an associated increase in communication costs. We therefore consider algebraically truncating coarse grid stencils to obtain a non-Galerkin coarse grid. First, the sparsity pattern of the non-Galerkin coarse grid is determined by employing a heuristic minimal “safe” pattern together with strength-of-connection ideas. Second, the nonzero entries are determined by collapsing the stencils in the Galerkin operator using traditional AMG techniques. The result is a reduction in coarse grid stencil size, overall operator complexity, and parallel AMG solve phase times.

  7. A Robust Algorithm for Optimisation and Customisation of Fractal Dimensions of Time Series Modified by Nonlinearly Scaling Their Time Derivatives: Mathematical Theory and Practical Applications

    Directory of Open Access Journals (Sweden)

    Franz Konstantin Fuss

    2013-01-01

    Full Text Available Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal’s time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.

  8. A robust algorithm for optimisation and customisation of fractal dimensions of time series modified by nonlinearly scaling their time derivatives: mathematical theory and practical applications.

    Science.gov (United States)

    Fuss, Franz Konstantin

    2013-01-01

    Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.

  9. A Cost-Effective Smoothed Multigrid with Modified Neighborhood-Based Aggregation for Markov Chains

    Directory of Open Access Journals (Sweden)

    Zhao-Li Shen

    2015-01-01

    Full Text Available Smoothed aggregation multigrid method is considered for computing stationary distributions of Markov chains. A judgement which determines whether to implement the whole aggregation procedure is proposed. Through this strategy, a large amount of time in the aggregation procedure is saved without affecting the convergence behavior. Besides this, we explain the shortage and irrationality of the Neighborhood-Based aggregation which is commonly used in multigrid methods. Then a modified version is presented to remedy and improve it. Numerical experiments on some typical Markov chain problems are reported to illustrate the performance of these methods.

  10. Multigrid for the Galerkin least squares method in linear elasticity: The pure displacement problem

    Energy Technology Data Exchange (ETDEWEB)

    Yoo, Jaechil [Univ. of Wisconsin, Madison, WI (United States)

    1996-12-31

    Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we prove the convergence of a multigrid (W-cycle) method. This multigrid is robust in that the convergence is uniform as the parameter, v, goes to 1/2 Computational experiments are included.

  11. On the Parallel Elliptic Single/Multigrid Solutions about Aligned and Nonaligned Bodies Using the Virtual Machine for Multiprocessors

    Directory of Open Access Journals (Sweden)

    A. Averbuch

    1994-01-01

    Full Text Available Parallel elliptic single/multigrid solutions around an aligned and nonaligned body are presented and implemented on two multi-user and single-user shared memory multiprocessors (Sequent Symmetry and MOS and on a distributed memory multiprocessor (a Transputer network. Our parallel implementation uses the Virtual Machine for Muli-Processors (VMMP, a software package that provides a coherent set of services for explicitly parallel application programs running on diverse multiple instruction multiple data (MIMD multiprocessors, both shared memory and message passing. VMMP is intended to simplify parallel program writing and to promote portable and efficient programming. Furthermore, it ensures high portability of application programs by implementing the same services on all target multiprocessors. The performance of our algorithm is investigated in detail. It is seen to fit well the above architectures when the number of processors is less than the maximal number of grid points along the axes. In general, the efficiency in the nonaligned case is higher than in the aligned case. Alignment overhead is observed to be up to 200% in the shared-memory case and up to 65% in the message-passing case. We have demonstrated that when using VMMP, the portability of the algorithms is straightforward and efficient.

  12. Asynchronous Task-Based Parallelization of Algebraic Multigrid

    KAUST Repository

    AlOnazi, Amani A.

    2017-06-23

    As processor clock rates become more dynamic and workloads become more adaptive, the vulnerability to global synchronization that already complicates programming for performance in today\\'s petascale environment will be exacerbated. Algebraic multigrid (AMG), the solver of choice in many large-scale PDE-based simulations, scales well in the weak sense, with fixed problem size per node, on tightly coupled systems when loads are well balanced and core performance is reliable. However, its strong scaling to many cores within a node is challenging. Reducing synchronization and increasing concurrency are vital adaptations of AMG to hybrid architectures. Recent communication-reducing improvements to classical additive AMG by Vassilevski and Yang improve concurrency and increase communication-computation overlap, while retaining convergence properties close to those of standard multiplicative AMG, but remain bulk synchronous.We extend the Vassilevski and Yang additive AMG to asynchronous task-based parallelism using a hybrid MPI+OmpSs (from the Barcelona Supercomputer Center) within a node, along with MPI for internode communications. We implement a tiling approach to decompose the grid hierarchy into parallel units within task containers. We compare against the MPI-only BoomerAMG and the Auxiliary-space Maxwell Solver (AMS) in the hypre library for the 3D Laplacian operator and the electromagnetic diffusion, respectively. In time to solution for a full solve an MPI-OmpSs hybrid improves over an all-MPI approach in strong scaling at full core count (32 threads per single Haswell node of the Cray XC40) and maintains this per node advantage as both weak scale to thousands of cores, with MPI between nodes.

  13. Two-Level Adaptive Algebraic Multigrid for a Sequence of Problems with Slowly Varying Random Coefficients [Adaptive Algebraic Multigrid for Sequence of Problems with Slowly Varying Random Coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Kalchev, D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Ketelsen, C. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Vassilevski, P. S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2013-11-07

    Our paper proposes an adaptive strategy for reusing a previously constructed coarse space by algebraic multigrid to construct a two-level solver for a problem with nearby characteristics. Furthermore, a main target application is the solution of the linear problems that appear throughout a sequence of Markov chain Monte Carlo simulations of subsurface flow with uncertain permeability field. We demonstrate the efficacy of the method with extensive set of numerical experiments.

  14. A non-linear multigrid method for the steady Euler equations

    NARCIS (Netherlands)

    Hemker, P.W.; Koren, B.; Dervieux, A.; Leer, van B.; Periaux, J.; Rizzi, A.

    1989-01-01

    Higher-order accurate Euler-flow solutions are presented for some airfoil test cases. Second-order accurate solutions are computed by an Iterative Defect Correction process. For two test cases even higher accuracy is obtained by the additional use of a ~xtrapolation technique. Finite volume

  15. New Multigrid Method Including Elimination Algolithm Based on High-Order Vector Finite Elements in Three Dimensional Magnetostatic Field Analysis

    Science.gov (United States)

    Hano, Mitsuo; Hotta, Masashi

    A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.

  16. Algorithm for the treatment of the material plastic anisotropy and its introduction into a non-linear structural analysis code (NOSA)

    Energy Technology Data Exchange (ETDEWEB)

    Toselli, G. [ENEA, Centro Ricerche Ezio Clementel, Bologna, (Italy). Dipt. Innovazione; Mirco, A. M. [Bologna Univ., Bologna (Italy). Dipt. di Matematica

    1999-07-01

    In this technical report the thesis of doctor's degree in Mathematics of A.M. Mirco is reported; it has been developed at ENEA research centre 'E. Clementel' in Bologna (Italy) in the frame of a collaboration between the section MACO (Applied Physics Division - Innovation Department) of ENEA at Bologna and the Department of Mathematics of the mathematical, physical and natural sciences faculty of Bologna University. Substantially, studies and research work, developed in these last years at MACO section, are here presented; they have led to the development of a constitutive model, based on Hill potential theory, for the treatment, in plastic field, of metal material anisotropy induced by previous workings and to the construction of the corresponding FEM algorithm for the non-linear structural analysis NOSA, oriented in particular to the numerical simulation of metal forming. Subsequently, an algorithm extension (proper object of the thesis), which has given, beyond a more rigorous formalization, also significant improvements. [Italian] In questo rapporto tecnico viene riportata la tesi di laurea in matematica di A. M. Mirco, tesi svolta presso il centro ricerche E. Clementel dell'ENEA di Bologna nell'ambito di un accordo di collaborazione fra la sezione MACO (Divisione Fisica Applicata - Dipartimento di Innovazione) dell'ENEA di Bologna ed il Dipartimento di matematica della facolta' di scienze matematiche, fisiche e naturali dell'universita' degli studi di Bologna. Sostanzialmente, vengono presentati gli studi ed il lavoro di ricerca, svolti in questi ultimi anni presso la sezione MACO, che hanno portato allo sviluppo di un modello costitutivo, basato sulla teoria del potenziale di Hill, per il trattamento in campo plastico, dell'anisotropia indotta da lavorazioni precedenti per un materiale metallico ed alla costruzione del corrispondente algoritmo basato sul metodo degli elementi finiti per il codice di analisi

  17. Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

    NARCIS (Netherlands)

    P. Luo (Peiyao); C. Rodrigo (Carmen); F.J. Gaspar Lorenz (Franscisco); C.W. Oosterlee (Cornelis)

    2018-01-01

    textabstractThe interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled

  18. Analysis of preconditioning and multigrid for Euler flows with low-subsonic regions

    NARCIS (Netherlands)

    Koren, B.; Leer, van B.

    1995-01-01

    For subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of multigrid-accelerated point Gauss-Seidel relaxation is analyzed. Error decay by convection across domain boundaries is also discussed. A fix to poor convergence rates at low Mach numbers is sought in

  19. Two-level Fourier analysis of a multigrid approach for discontinuous Galerkin discretisation

    NARCIS (Netherlands)

    P.W. Hemker (Piet); W. Hoffmann; M.H. van Raalte (Marc)

    2002-01-01

    textabstractIn this paper we study a multigrid method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, andwe give a detailed analysis of the convergence for different block-relaxation strategies.We find that point-wise

  20. Multigrid technique and Optimized Schwarz method on block-structured grids with discontinuous interfaces

    DEFF Research Database (Denmark)

    Kolmogorov, Dmitry; Sørensen, Niels N.; Shen, Wen Zhong

    2013-01-01

    An Optimized Schwarz method using Robin boundary conditions for relaxation scheme is presented in the frame of Multigrid method on discontinuous grids. At each iteration the relaxation scheme is performed in two steps: one step with Dirichlet and another step with Robin boundary conditions at inn...

  1. s-Step Krylov Subspace Methods as Bottom Solvers for Geometric Multigrid

    Energy Technology Data Exchange (ETDEWEB)

    Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Lijewski, Mike [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Almgren, Ann [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Straalen, Brian Van [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Carson, Erin [Univ. of California, Berkeley, CA (United States); Knight, Nicholas [Univ. of California, Berkeley, CA (United States); Demmel, James [Univ. of California, Berkeley, CA (United States)

    2014-08-14

    Geometric multigrid solvers within adaptive mesh refinement (AMR) applications often reach a point where further coarsening of the grid becomes impractical as individual sub domain sizes approach unity. At this point the most common solution is to use a bottom solver, such as BiCGStab, to reduce the residual by a fixed factor at the coarsest level. Each iteration of BiCGStab requires multiple global reductions (MPI collectives). As the number of BiCGStab iterations required for convergence grows with problem size, and the time for each collective operation increases with machine scale, bottom solves in large-scale applications can constitute a significant fraction of the overall multigrid solve time. In this paper, we implement, evaluate, and optimize a communication-avoiding s-step formulation of BiCGStab (CABiCGStab for short) as a high-performance, distributed-memory bottom solver for geometric multigrid solvers. This is the first time s-step Krylov subspace methods have been leveraged to improve multigrid bottom solver performance. We use a synthetic benchmark for detailed analysis and integrate the best implementation into BoxLib in order to evaluate the benefit of a s-step Krylov subspace method on the multigrid solves found in the applications LMC and Nyx on up to 32,768 cores on the Cray XE6 at NERSC. Overall, we see bottom solver improvements of up to 4.2x on synthetic problems and up to 2.7x in real applications. This results in as much as a 1.5x improvement in solver performance in real applications.

  2. Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Kalchev, D

    2012-04-02

    This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-{rho}AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the

  3. Multigrid Algorithms for the Fast Calculation of Space-Charge Effects in Accelerator Design

    NARCIS (Netherlands)

    Pöplau, G.; Rienen, van U.; Geer, van der S.B.; Loos, de M.J.

    2004-01-01

    Numerical prediction of charged particle dynamics in accelerators is essential for the design and understanding of these machines. Methods to calculate the self-fields of the bunch, the so-called space-charge forces, become increasingly important as the demand for high-quality bunches increases. We

  4. Nonlinear acceleration of transport criticality problems

    International Nuclear Information System (INIS)

    Park, H.; Knoll, D.A.; Newman, C.K.

    2011-01-01

    We present a nonlinear acceleration algorithm for the transport criticality problem. The algorithm combines the well-known nonlinear diffusion acceleration (NDA) with a recently developed, Newton-based, nonlinear criticality acceleration (NCA) algorithm. The algorithm first employs the NDA to reduce the system to scalar flux, then the NCA is applied to the resulting drift-diffusion system. We apply a nonlinear elimination technique to eliminate the eigenvalue from the Jacobian matrix. Numerical results show that the algorithm reduces the CPU time a factor of 400 in a very diffusive system, and a factor of 5 in a non-diffusive system. (author)

  5. Multigrid solution of the Navier-Stokes equations at low speeds with large temperature variations

    International Nuclear Information System (INIS)

    Sockol, Peter M.

    2003-01-01

    Multigrid methods for the Navier-Stokes equations at low speeds and large temperature variations are investigated. The compressible equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. Three implicit smoothers have been incorporated into a common multigrid procedure. Both full coarsening and semi-coarsening with directional fine-grid defect correction have been studied. The resulting methods have been tested on four 2D laminar problems over a range of Reynolds numbers on both uniform and highly stretched grids. Two of the three methods show efficient and robust performance over the entire range of conditions. In addition, none of the methods has any difficulty with the large temperature variations

  6. Blockspin and multigrid for staggered fermions in non-abelian gauge fields

    International Nuclear Information System (INIS)

    Kalkreuter, T.; Mack, G.; Speh, M.

    1991-07-01

    We discuss blockspins for staggered fermions, i.e. averaging and interpolation procedures which are needed in a real space renormalization group approach to gauge theories with staggered fermions and in a multigrid approach to the computation of gauge covariant propagators. The discussion starts from the requirement that the symmetries of the free action should be preserved by the blocking procedure in the limit of a pure gauge. A definition of an averaging kernel as a solution of a gauge covariant eigenvalue equation is proposed, and the properties of a corresponding interpolation kernel are examined in the light of general criteria for good choices of blockspins. Some results of multigrid computation of bosonic propagation in an SU(2) gauge field in 4 dimensions are also presented. (orig.)

  7. A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids

    Science.gov (United States)

    Prieto, Manuel; Montero, Ruben S.; Llorente, Ignacio M.; Bushnell, Dennis M. (Technical Monitor)

    2001-01-01

    This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a flat plate. The main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform, we have used Coral, a Beowulf-class system based on Intel Pentium processors and equipped with GigaNet cLAN and switched Fast Ethernet networks. Our study not only examines the scalability of the solver but also includes a performance evaluation of Coral where the investigated solver has been used to compare several of its design choices, namely, the interconnection network (GigaNet versus switched Fast-Ethernet) and the node configuration (dual nodes versus single nodes). As a reference, the performance results have been compared with those obtained with the NAS-MG benchmark.

  8. Adaptive tree multigrids and simplified spherical harmonics approximation in deterministic neutral and charged particle transport

    International Nuclear Information System (INIS)

    Kotiluoto, P.

    2007-05-01

    A new deterministic three-dimensional neutral and charged particle transport code, MultiTrans, has been developed. In the novel approach, the adaptive tree multigrid technique is used in conjunction with simplified spherical harmonics approximation of the Boltzmann transport equation. The development of the new radiation transport code started in the framework of the Finnish boron neutron capture therapy (BNCT) project. Since the application of the MultiTrans code to BNCT dose planning problems, the testing and development of the MultiTrans code has continued in conventional radiotherapy and reactor physics applications. In this thesis, an overview of different numerical radiation transport methods is first given. Special features of the simplified spherical harmonics method and the adaptive tree multigrid technique are then reviewed. The usefulness of the new MultiTrans code has been indicated by verifying and validating the code performance for different types of neutral and charged particle transport problems, reported in separate publications. (orig.)

  9. Multilevel local refinement and multigrid methods for 3-D turbulent flow

    Energy Technology Data Exchange (ETDEWEB)

    Liao, C.; Liu, C. [UCD, Denver, CO (United States); Sung, C.H.; Huang, T.T. [David Taylor Model Basin, Bethesda, MD (United States)

    1996-12-31

    A numerical approach based on multigrid, multilevel local refinement, and preconditioning methods for solving incompressible Reynolds-averaged Navier-Stokes equations is presented. 3-D turbulent flow around an underwater vehicle is computed. 3 multigrid levels and 2 local refinement grid levels are used. The global grid is 24 x 8 x 12. The first patch is 40 x 16 x 20 and the second patch is 72 x 32 x 36. 4th order artificial dissipation are used for numerical stability. The conservative artificial compressibility method are used for further improvement of convergence. To improve the accuracy of coarse/fine grid interface of local refinement, flux interpolation method for refined grid boundary is used. The numerical results are in good agreement with experimental data. The local refinement can improve the prediction accuracy significantly. The flux interpolation method for local refinement can keep conservation for a composite grid, therefore further modify the prediction accuracy.

  10. Fast algorithms for transport models. Final report

    International Nuclear Information System (INIS)

    Manteuffel, T.A.

    1994-01-01

    This project has developed a multigrid in space algorithm for the solution of the S N equations with isotropic scattering in slab geometry. The algorithm was developed for the Modified Linear Discontinuous (MLD) discretization in space which is accurate in the thick diffusion limit. It uses a red/black two-cell μ-line relaxation. This relaxation solves for all angles on two adjacent spatial cells simultaneously. It takes advantage of the rank-one property of the coupling between angles and can perform this inversion in O(N) operations. A version of the multigrid in space algorithm was programmed on the Thinking Machines Inc. CM-200 located at LANL. It was discovered that on the CM-200 a block Jacobi type iteration was more efficient than the block red/black iteration. Given sufficient processors all two-cell block inversions can be carried out simultaneously with a small number of parallel steps. The bottleneck is the need for sums of N values, where N is the number of discrete angles, each from a different processor. These are carried out by machine intrinsic functions and are well optimized. The overall algorithm has computational complexity O(log(M)), where M is the number of spatial cells. The algorithm is very efficient and represents the state-of-the-art for isotropic problems in slab geometry. For anisotropic scattering in slab geometry, a multilevel in angle algorithm was developed. A parallel version of the multilevel in angle algorithm has also been developed. Upon first glance, the shifted transport sweep has limited parallelism. Once the right-hand-side has been computed, the sweep is completely parallel in angle, becoming N uncoupled initial value ODE's. The author has developed a cyclic reduction algorithm that renders it parallel with complexity O(log(M)). The multilevel in angle algorithm visits log(N) levels, where shifted transport sweeps are performed. The overall complexity is O(log(N)log(M))

  11. Multigrid techniques with non-standard coarsening and group relaxation methods

    International Nuclear Information System (INIS)

    Danaee, A.

    1989-06-01

    In the usual (standard) multigrid methods, doubling of grid sizes with different smoothing iterations (pointwise, or blockwise) has been considered by different authors. Some have indicated that a large coarsening can also be used, but is not beneficial (cf. H3, p.59). In this paper, it is shown that with a suitable blockwise smoothing scheme, some advantages could be achieved even with a factor of H l-1 /h l = 3. (author). 10 refs, 2 figs, 6 tabs

  12. Multi-Grid detector for neutron spectroscopy: results obtained on time-of-flight spectrometer CNCS

    Science.gov (United States)

    Anastasopoulos, M.; Bebb, R.; Berry, K.; Birch, J.; Bryś, T.; Buffet, J.-C.; Clergeau, J.-F.; Deen, P. P.; Ehlers, G.; van Esch, P.; Everett, S. M.; Guerard, B.; Hall-Wilton, R.; Herwig, K.; Hultman, L.; Höglund, C.; Iruretagoiena, I.; Issa, F.; Jensen, J.; Khaplanov, A.; Kirstein, O.; Lopez Higuera, I.; Piscitelli, F.; Robinson, L.; Schmidt, S.; Stefanescu, I.

    2017-04-01

    The Multi-Grid detector technology has evolved from the proof-of-principle and characterisation stages. Here we report on the performance of the Multi-Grid detector, the MG.CNCS prototype, which has been installed and tested at the Cold Neutron Chopper Spectrometer, CNCS at SNS. This has allowed a side-by-side comparison to the performance of 3He detectors on an operational instrument. The demonstrator has an active area of 0.2 m2. It is specifically tailored to the specifications of CNCS. The detector was installed in June 2016 and has operated since then, collecting neutron scattering data in parallel to the He-3 detectors of CNCS. In this paper, we present a comprehensive analysis of this data, in particular on instrument energy resolution, rate capability, background and relative efficiency. Stability, gamma-ray and fast neutron sensitivity have also been investigated. The effect of scattering in the detector components has been measured and provides input to comparison for Monte Carlo simulations. All data is presented in comparison to that measured by the 3He detectors simultaneously, showing that all features recorded by one detector are also recorded by the other. The energy resolution matches closely. We find that the Multi-Grid is able to match the data collected by 3He, and see an indication of a considerable advantage in the count rate capability. Based on these results, we are confident that the Multi-Grid detector will be capable of producing high quality scientific data on chopper spectrometers utilising the unprecedented neutron flux of the ESS.

  13. Design and fabrication of multigrid X-ray collimators. [For airborne x-ray spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Acton, L W; Joki, E G; Salmon, R J [Lockheed Missiles and Space Co., Palo Alto, Calif. (USA). Lockheed Palo Alto Research Lab.

    1976-08-01

    Multigrid X-ray collimators continue to find wide application in space research. This paper treats the principles of their design and fabrication and summarizes the experience obtained in making and flying thirteen such collimators ranging in angular resolution from 10 to 0.7 arc min FWHM. Included is a summary of a survey of scientist-users and industrial producers of collimator grids regarding grid materials, precision, plating, hole quality and results of acceptance testing.

  14. A first-order multigrid method for bound-constrained convex optimization

    Czech Academy of Sciences Publication Activity Database

    Kočvara, Michal; Mohammed, S.

    2016-01-01

    Roč. 31, č. 3 (2016), s. 622-644 ISSN 1055-6788 R&D Projects: GA ČR(CZ) GAP201/12/0671 Grant - others:European Commission - EC(XE) 313781 Institutional support: RVO:67985556 Keywords : bound-constrained optimization * multigrid methods * linear complementarity problems Subject RIV: BA - General Mathematics Impact factor: 1.023, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/kocvara-0460326.pdf

  15. Cellular Genetic Algorithm with Communicating Grids for Assembly Line Balancing Problems

    Directory of Open Access Journals (Sweden)

    BRUDARU, O.

    2010-05-01

    Full Text Available This paper presents a new approach with cellular multigrid genetic algorithms for the "I"-shaped and "U"-shaped assembly line balancing problems, including parallel workstations and compatibility constraints. First, a cellular hybrid genetic algorithm that uses a single grid is described. Appropriate operators for mutation, hypermutation, and crossover and two devoration techniques are proposed for creating and maintaining groups based on similarity. This monogrid algorithm is extended for handling many populations placed on different grids. In the multigrid version, the population of each grid is organized in clusters using the positional information of the chromosomes. A similarity preserving communication protocol between the clusters placed on different grids is introduced. The experimental evaluation shows that the multigrid cellular genetic algorithm with communicating grids is better than the hybrid genetic algorithm used for building it, whereas it dominates the monogrid version in all cases. Absolute performance is evaluated using classical benchmarks. The role of certain components of the cellular algorithm is explained and the effect of some parameters is evaluated.

  16. Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations

    Science.gov (United States)

    Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa

    2017-12-01

    Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.

  17. Block-accelerated aggregation multigrid for Markov chains with application to PageRank problems

    Science.gov (United States)

    Shen, Zhao-Li; Huang, Ting-Zhu; Carpentieri, Bruno; Wen, Chun; Gu, Xian-Ming

    2018-06-01

    Recently, the adaptive algebraic aggregation multigrid method has been proposed for computing stationary distributions of Markov chains. This method updates aggregates on every iterative cycle to keep high accuracies of coarse-level corrections. Accordingly, its fast convergence rate is well guaranteed, but often a large proportion of time is cost by aggregation processes. In this paper, we show that the aggregates on each level in this method can be utilized to transfer the probability equation of that level into a block linear system. Then we propose a Block-Jacobi relaxation that deals with the block system on each level to smooth error. Some theoretical analysis of this technique is presented, meanwhile it is also adapted to solve PageRank problems. The purpose of this technique is to accelerate the adaptive aggregation multigrid method and its variants for solving Markov chains and PageRank problems. It also attempts to shed some light on new solutions for making aggregation processes more cost-effective for aggregation multigrid methods. Numerical experiments are presented to illustrate the effectiveness of this technique.

  18. DL_MG: A Parallel Multigrid Poisson and Poisson-Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution.

    Science.gov (United States)

    Womack, James C; Anton, Lucian; Dziedzic, Jacek; Hasnip, Phil J; Probert, Matt I J; Skylaris, Chris-Kriton

    2018-03-13

    The solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential-a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the Poisson equation, featuring nonhomogeneous dielectric permittivities, ionic concentrations with nonlinear dependencies, and diverse boundary conditions. The analytic solutions generally used to solve the Poisson equation in vacuum (or with homogeneous permittivity) are not applicable in these circumstances, and numerical methods must be used. In this work, we present DL_MG, a flexible, scalable, and accurate solver library, developed specifically to tackle the challenges of solving the Poisson equation in modern large-scale electronic structure calculations on parallel computers. Our solver is based on the multigrid approach and uses an iterative high-order defect correction method to improve the accuracy of solutions. Using two chemically relevant model systems, we tested the accuracy and computational performance of DL_MG when solving the generalized Poisson and Poisson-Boltzmann equations, demonstrating excellent agreement with analytic solutions and efficient scaling to ∼10 9 unknowns and 100s of CPU cores. We also applied DL_MG in actual large-scale electronic structure calculations, using the ONETEP linear-scaling electronic structure package to study a 2615 atom protein-ligand complex with routinely available computational resources. In these calculations, the overall execution time with DL_MG was not significantly greater than the time required for calculations using a conventional FFT-based solver.

  19. Nonlinear Elasticity

    Science.gov (United States)

    Fu, Y. B.; Ogden, R. W.

    2001-05-01

    This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.

  20. Multiscale Monte Carlo algorithms in statistical mechanics and quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Lauwers, P G

    1990-12-01

    Conventional Monte Carlo simulation algorithms for models in statistical mechanics and quantum field theory are afflicted by problems caused by their locality. They become highly inefficient if investigations of critical or nearly-critical systems, i.e., systems with important large scale phenomena, are undertaken. We present two types of multiscale approaches that alleveate problems of this kind: Stochastic cluster algorithms and multigrid Monte Carlo simulation algorithms. Another formidable computational problem in simulations of phenomenologically relevant field theories with fermions is the need for frequently inverting the Dirac operator. This inversion can be accelerated considerably by means of deterministic multigrid methods, very similar to the ones used for the numerical solution of differential equations. (orig.).

  1. A Parallel Algebraic Multigrid Solver on Graphics Processing Units

    KAUST Repository

    Haase, Gundolf; Liebmann, Manfred; Douglas, Craig C.; Plank, Gernot

    2010-01-01

    -vector multiplication scheme underlying the PCG-AMG algorithm is presented for the many-core GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster

  2. Algebraic multigrid preconditioning within parallel finite-element solvers for 3-D electromagnetic modelling problems in geophysics

    Science.gov (United States)

    Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María

    2014-06-01

    We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the

  3. A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson–Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

    International Nuclear Information System (INIS)

    Chatterjee, Kausik; Roadcap, John R.; Singh, Surendra

    2014-01-01

    The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications

  4. A new Green's function Monte Carlo algorithm for the solution of the two-dimensional nonlinear Poisson–Boltzmann equation: Application to the modeling of the communication breakdown problem in space vehicles during re-entry

    Energy Technology Data Exchange (ETDEWEB)

    Chatterjee, Kausik, E-mail: kausik.chatterjee@aggiemail.usu.edu [Strategic and Military Space Division, Space Dynamics Laboratory, North Logan, UT 84341 (United States); Center for Atmospheric and Space Sciences, Utah State University, Logan, UT 84322 (United States); Roadcap, John R., E-mail: john.roadcap@us.af.mil [Air Force Research Laboratory, Kirtland AFB, NM 87117 (United States); Singh, Surendra, E-mail: surendra-singh@utulsa.edu [Department of Electrical Engineering, The University of Tulsa, Tulsa, OK 74104 (United States)

    2014-11-01

    The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.

  5. Distance-two interpolation for parallel algebraic multigrid

    International Nuclear Information System (INIS)

    Sterck, H de; Falgout, R D; Nolting, J W; Yang, U M

    2007-01-01

    In this paper we study the use of long distance interpolation methods with the low complexity coarsening algorithm PMIS. AMG performance and scalability is compared for classical as well as long distance interpolation methods on parallel computers. It is shown that the increased interpolation accuracy largely restores the scalability of AMG convergence factors for PMIS-coarsened grids, and in combination with complexity reducing methods, such as interpolation truncation, one obtains a class of parallel AMG methods that enjoy excellent scalability properties on large parallel computers

  6. Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction.

    Science.gov (United States)

    Gilles, Luc; Vogel, Curtis R; Ellerbroek, Brent L

    2002-09-01

    We introduce a multigrid preconditioned conjugate-gradient (MGCG) iterative scheme for computing open-loop wave-front reconstructors for extreme adaptive optics systems. We present numerical simulations for a 17-m class telescope with n = 48756 sensor measurement grid points within the aperture, which indicate that our MGCG method has a rapid convergence rate for a wide range of subaperture average slope measurement signal-to-noise ratios. The total computational cost is of order n log n. Hence our scheme provides for fast wave-front simulation and control in large-scale adaptive optics systems.

  7. Adaptive parallel multigrid for Euler and incompressible Navier-Stokes equations

    Energy Technology Data Exchange (ETDEWEB)

    Trottenberg, U.; Oosterlee, K.; Ritzdorf, H. [and others

    1996-12-31

    The combination of (1) very efficient solution methods (Multigrid), (2) adaptivity, and (3) parallelism (distributed memory) clearly is absolutely necessary for future oriented numerics but still regarded as extremely difficult or even unsolved. We show that very nice results can be obtained for real life problems. Our approach is straightforward (based on {open_quotes}MLAT{close_quotes}). But, of course, reasonable refinement and load-balancing strategies have to be used. Our examples are 2D, but 3D is on the way.

  8. A new perspective for quintic B-spline based Crank-Nicolson-differential quadrature method algorithm for numerical solutions of the nonlinear Schrödinger equation

    Science.gov (United States)

    Başhan, Ali; Uçar, Yusuf; Murat Yağmurlu, N.; Esen, Alaattin

    2018-01-01

    In the present paper, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. For this purpose, first of all, the Schrödinger equation has been converted into coupled real value differential equations and then they have been discretized using both the forward difference formula and the Crank-Nicolson method. After that, Rubin and Graves linearization techniques have been utilized and the differential quadrature method has been applied to obtain an algebraic equation system. Next, in order to be able to test the efficiency of the newly applied method, the error norms, L2 and L_{∞}, as well as the two lowest invariants, I1 and I2, have been computed. Besides those, the relative changes in those invariants have been presented. Finally, the newly obtained numerical results have been compared with some of those available in the literature for similar parameters. This comparison clearly indicates that the currently utilized method, namely CN-DQM, is an effective and efficient numerical scheme and allows us to propose to solve a wide range of nonlinear equations.

  9. A Trust-region-based Sequential Quadratic Programming Algorithm

    DEFF Research Database (Denmark)

    Henriksen, Lars Christian; Poulsen, Niels Kjølstad

    This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints.......This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....

  10. Compiler generation and autotuning of communication-avoiding operators for geometric multigrid

    Energy Technology Data Exchange (ETDEWEB)

    Basu, Protonu [Univ. of Utah, Salt Lake City, UT (United States); Venkat, Anand [Univ. of Utah, Salt Lake City, UT (United States); Hall, Mary [Univ. of Utah, Salt Lake City, UT (United States); Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Van Straalen, Brian [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Oliker, Leonid [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

    2014-04-17

    This paper describes a compiler approach to introducing communication-avoiding optimizations in geometric multigrid (GMG), one of the most popular methods for solving partial differential equations. Communication-avoiding optimizations reduce vertical communication through the memory hierarchy and horizontal communication across processes or threads, usually at the expense of introducing redundant computation. We focus on applying these optimizations to the smooth operator, which successively reduces the error and accounts for the largest fraction of the GMG execution time. Our compiler technology applies both novel and known transformations to derive an implementation comparable to manually-tuned code. To make the approach portable, an underlying autotuning system explores the tradeoff between reduced communication and increased computation, as well as tradeoffs in threading schemes, to automatically identify the best implementation for a particular architecture and at each computation phase. Results show that we are able to quadruple the performance of the smooth operation on the finest grids while attaining performance within 94% of manually-tuned code. Overall we improve the overall multigrid solve time by 2.5× without sacrificing programer productivity.

  11. Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

    Science.gov (United States)

    Luo, P.; Rodrigo, C.; Gaspar, F. J.; Oosterlee, C. W.

    2018-01-01

    The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled Uzawa smoother is employed as an efficient numerical technique for the linear discrete system obtained by finite volumes on staggered grids. A specialty in our modeling approach is that at the interface of the fluid and poroelastic medium, two unknowns from the different subsystems are defined at the same grid point. We propose a special discretization at and near the points on the interface, which combines the approximation of the governing equations and the considered interface conditions. In the decoupled Uzawa smoother, Local Fourier Analysis (LFA) helps us to select optimal values of the relaxation parameter appearing. To implement the monolithic multigrid method, grid partitioning is used to deal with the interface updates when communication is required between two subdomains. Numerical experiments show that the proposed numerical method has an excellent convergence rate. The efficiency and robustness of the method are confirmed in numerical experiments with typically small realistic values of the physical coefficients.

  12. Use of a multigrid technique to study effects of limited sampling of heterogeneity on transport prediction

    International Nuclear Information System (INIS)

    Cole, C.R.; Foote, H.P.

    1987-02-01

    Reliable ground water transport prediction requires accurate spatial and temporal characterization of a hydrogeologic system. However, cost constraints and the desire to maintain site integrity by minimizing drilling can restrict the amount of spatial sampling that can be obtained to resolve the flow parameter variability associated with heterogeneities. This study quantifies the errors in subsurface transport predictions resulting from incomplete characterization of hydraulic conductivity heterogeneity. A multigrid technique was used to simulate two-dimensional flow velocity fields with high resolution. To obtain these velocity fields, the finite difference code MGRID, which implements a multigrid solution technique, was applied to compute stream functions on a 256-by-256 grid for a variety of hypothetical systems having detailed distributions of hydraulic conductivity. Spatial variability in hydraulic conductivity distributions was characterized by the components in the spectrum of spatial frequencies. A low-pass spatial filtering technique was applied to the base case hydraulic conductivity distribution to produce a data set with lower spatial frequency content. Arrival time curves were then calculated for filtered hydraulic conductivity distribution and compared to base case results to judge the relative importance of the higher spatial frequency components. Results indicate a progression from multimode to single-mode arrival time curves as the number and extent of distinct flow pathways are reduced by low-pass filtering. This relationship between transport predictions and spatial frequencies was used to judge the consequences of sampling the hydraulic conductivity with reduced spatial resolution. 22 refs., 17 figs

  13. Fast multigrid-based computation of the induced electric field for transcranial magnetic stimulation

    Science.gov (United States)

    Laakso, Ilkka; Hirata, Akimasa

    2012-12-01

    In transcranial magnetic stimulation (TMS), the distribution of the induced electric field, and the affected brain areas, depends on the position of the stimulation coil and the individual geometry of the head and brain. The distribution of the induced electric field in realistic anatomies can be modelled using computational methods. However, existing computational methods for accurately determining the induced electric field in realistic anatomical models have suffered from long computation times, typically in the range of tens of minutes or longer. This paper presents a matrix-free implementation of the finite-element method with a geometric multigrid method that can potentially reduce the computation time to several seconds or less even when using an ordinary computer. The performance of the method is studied by computing the induced electric field in two anatomically realistic models. An idealized two-loop coil is used as the stimulating coil. Multiple computational grid resolutions ranging from 2 to 0.25 mm are used. The results show that, for macroscopic modelling of the electric field in an anatomically realistic model, computational grid resolutions of 1 mm or 2 mm appear to provide good numerical accuracy compared to higher resolutions. The multigrid iteration typically converges in less than ten iterations independent of the grid resolution. Even without parallelization, each iteration takes about 1.0 s or 0.1 s for the 1 and 2 mm resolutions, respectively. This suggests that calculating the electric field with sufficient accuracy in real time is feasible.

  14. Cellular Automaton Modeling of Dendritic Growth Using a Multi-grid Method

    International Nuclear Information System (INIS)

    Natsume, Y; Ohsasa, K

    2015-01-01

    A two-dimensional cellular automaton model with a multi-grid method was developed to simulate dendritic growth. In the present model, we used a triple-grid system for temperature, solute concentration and solid fraction fields as a new approach of the multi-grid method. In order to evaluate the validity of the present model, we carried out simulations of single dendritic growth, secondary dendrite arm growth, multi-columnar dendritic growth and multi-equiaxed dendritic growth. From the results of the grid dependency from the simulation of single dendritic growth, we confirmed that the larger grid can be used in the simulation and that the computational time can be reduced dramatically. In the simulation of secondary dendrite arm growth, the results from the present model were in good agreement with the experimental data and the simulated results from a phase-field model. Thus, the present model can quantitatively simulate dendritic growth. From the simulated results of multi-columnar and multi-equiaxed dendrites, we confirmed that the present model can perform simulations under practical solidification conditions. (paper)

  15. {sup 10}B multi-grid proportional gas counters for large area thermal neutron detectors

    Energy Technology Data Exchange (ETDEWEB)

    Andersen, K. [ESS, P.O. Box 176, SE-221 00 Lund (Sweden); Bigault, T. [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); Birch, J. [Linköping University, SE-581, 83 Linköping (Sweden); Buffet, J. C.; Correa, J. [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); Hall-Wilton, R. [ESS, P.O. Box 176, SE-221 00 Lund (Sweden); Hultman, L. [Linköping University, SE-581, 83 Linköping (Sweden); Höglund, C. [ESS, P.O. Box 176, SE-221 00 Lund (Sweden); Linköping University, SE-581, 83 Linköping (Sweden); Guérard, B., E-mail: guerard@ill.fr [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); Jensen, J. [Linköping University, SE-581, 83 Linköping (Sweden); Khaplanov, A. [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); ESS, P.O. Box 176, SE-221 00 Lund (Sweden); Kirstein, O. [Linköping University, SE-581, 83 Linköping (Sweden); Piscitelli, F.; Van Esch, P. [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); Vettier, C. [ESS, P.O. Box 176, SE-221 00 Lund (Sweden)

    2013-08-21

    {sup 3}He was a popular material in neutrons detectors until its availability dropped drastically in 2008. The development of techniques based on alternative convertors is now of high priority for neutron research institutes. Thin films of {sup 10}B or {sup 10}B{sub 4}C have been used in gas proportional counters to detect neutrons, but until now, only for small or medium sensitive area. We present here the multi-grid design, introduced at the ILL and developed in collaboration with ESS for LAN (large area neutron) detectors. Typically thirty {sup 10}B{sub 4}C films of 1 μm thickness are used to convert neutrons into ionizing particles which are subsequently detected in a proportional gas counter. The principle and the fabrication of the multi-grid are described and some preliminary results obtained with a prototype of 200 cm×8 cm are reported; a detection efficiency of 48% has been measured at 2.5 Å with a monochromatic neutron beam line, showing the good potential of this new technique.

  16. All-optical and digital non-linear compensation algorithms in flex-coherent grouped and un-grouped contiguous spectrum based networks

    DEFF Research Database (Denmark)

    Asif, Rameez

    2016-01-01

    We have evaluated that in-line non-linear compensation schemes decrease the complexity of digital backward propagation and enhance the transmission performance of 40/112/224 Gbit/s mixed line rate network. Multiple bit rates, i.e. 40/112/224 Gbit/s and modulation formats (i.e. DP-QPSK and DP-16QAM......) are transmitted over 1280 km of Large $$\\hbox {A}_{eff}$$ A e f f Pure-Silica core fiber. Both grouped and un-grouped spectral allocation schemes are investigated. Optical add-drop multiplexers are used to drop the required wavelength for signal processing in the transmission link. Moreover, hybrid mid...

  17. An operational procedure for precipitable and cloud liquid water estimate in non-raining conditions over sea Study on the assessment of the nonlinear physical inversion algorithm

    CERN Document Server

    Nativi, S; Mazzetti, P

    2004-01-01

    In a previous work, an operative procedure to estimate precipitable and liquid water in non-raining conditions over sea was developed and assessed. The procedure is based on a fast non-linear physical inversion scheme and a forward model; it is valid for most of satellite microwave radiometers and it also estimates water effective profiles. This paper presents two improvements of the procedure: first, a refinement to provide modularity of the software components and portability across different computation system architectures; second, the adoption of the CERN MINUIT minimisation package, which addresses the problem of global minimisation but is computationally more demanding. Together with the increased computational performance that allowed to impose stricter requirements on the quality of fit, these refinements improved fitting precision and reliability, and allowed to relax the requirements on the initial guesses for the model parameters. The re-analysis of the same data-set considered in the previous pap...

  18. Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

    Science.gov (United States)

    Atkins, H. L.; Helenbrook, B. T.

    2005-01-01

    This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

  19. Morphing Wing Structural Optimization Using Opposite-Based Population-Based Incremental Learning and Multigrid Ground Elements

    Directory of Open Access Journals (Sweden)

    S. Sleesongsom

    2015-01-01

    Full Text Available This paper has twin aims. Firstly, a multigrid design approach for optimization of an unconventional morphing wing is proposed. The structural design problem is assigned to optimize wing mass, lift effectiveness, and buckling factor subject to structural safety requirements. Design variables consist of partial topology, nodal positions, and component sizes of a wing internal structure. Such a design process can be accomplished by using multiple resolutions of ground elements, which is called a multigrid approach. Secondly, an opposite-based multiobjective population-based incremental learning (OMPBIL is proposed for comparison with the original multiobjective population-based incremental learning (MPBIL. Multiobjective design problems with single-grid and multigrid design variables are then posed and tackled by OMPBIL and MPBIL. The results show that using OMPBIL in combination with a multigrid design approach is the best design strategy. OMPBIL is superior to MPBIL since the former provides better population diversity. Aeroelastic trim for an elastic morphing wing is also presented.

  20. Nonlinear optics

    International Nuclear Information System (INIS)

    Boyd, R.W.

    1992-01-01

    Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics

  1. An efficient flexible-order model for 3D nonlinear water waves

    International Nuclear Information System (INIS)

    Engsig-Karup, A.P.; Bingham, H.B.; Lindberg, O.

    2009-01-01

    The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature

  2. An efficient flexible-order model for 3D nonlinear water waves

    Science.gov (United States)

    Engsig-Karup, A. P.; Bingham, H. B.; Lindberg, O.

    2009-04-01

    The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.

  3. A Line Search Multilevel Truncated Newton Algorithm for Computing the Optical Flow

    Directory of Open Access Journals (Sweden)

    Lluís Garrido

    2015-06-01

    Full Text Available We describe the implementation details and give the experimental results of three optimization algorithms for dense optical flow computation. In particular, using a line search strategy, we evaluate the performance of the unilevel truncated Newton method (LSTN, a multiresolution truncated Newton (MR/LSTN and a full multigrid truncated Newton (FMG/LSTN. We use three image sequences and four models of optical flow for performance evaluation. The FMG/LSTN algorithm is shown to lead to better optical flow estimation with less computational work than both the LSTN and MR/LSTN algorithms.

  4. Nonlinear optics

    CERN Document Server

    Bloembergen, Nicolaas

    1996-01-01

    Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe

  5. Nonlinear Multiantenna Detection Methods

    Directory of Open Access Journals (Sweden)

    Chen Sheng

    2004-01-01

    Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.

  6. A nonlinear QSAR study using oscillating search and SVM as an efficient algorithm to model the inhibition of reverse transcriptase by HEPT derivatives

    International Nuclear Information System (INIS)

    Ferkous, F.; Saihi, Y.

    2018-01-01

    Quantitative structure-activity relationships were constructed for 107 inhibitors of HIV-1 reverse transcriptase that are derivatives of 1-[(2-hydroxyethoxy)methyl]-6-(phenylthio)thymine (HEPT). A combination of a support vector machine (SVM) and oscillating search (OS) algorithms for feature selection was adopted to select the most appropriate descriptors. The application was optimized to obtain an SVM model to predict the biological activity EC50 of the HEPT derivatives with a minimum number of descriptors (SpMax4 B h (e) MLOGP MATS5m) and high values of R2 and Q2 (0.8662, 0.8769). The statistical results showed good correlation between the activity and three best descriptors were included in the best SVM model. The values of R2 and Q2 confirmed the stability and good predictive ability of the model. The SVM technique was adequate to produce an effective QSAR model and outperformed those in the literature and the predictive stages for the inhibitory activity of reverse transcriptase by HEPT derivatives. (author)

  7. Limits to Nonlinear Inversion

    DEFF Research Database (Denmark)

    Mosegaard, Klaus

    2012-01-01

    For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...... pure meta-heuristics. We study problem-adapted inversion algorithms that exploit the knowledge of the smoothness of the misfit function of the problem. Optimal sampling strategies exist for such problems, but many of these problems remain hard. © 2012 Springer-Verlag....

  8. Nonlinear dynamics of structures

    CERN Document Server

    Oller, Sergio

    2014-01-01

    This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics.   This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects.   Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution  are studied, and the theoretical concepts and its programming algorithms are presented.  

  9. Nonlinear Dot Plots.

    Science.gov (United States)

    Rodrigues, Nils; Weiskopf, Daniel

    2018-01-01

    Conventional dot plots use a constant dot size and are typically applied to show the frequency distribution of small data sets. Unfortunately, they are not designed for a high dynamic range of frequencies. We address this problem by introducing nonlinear dot plots. Adopting the idea of nonlinear scaling from logarithmic bar charts, our plots allow for dots of varying size so that columns with a large number of samples are reduced in height. For the construction of these diagrams, we introduce an efficient two-way sweep algorithm that leads to a dense and symmetrical layout. We compensate aliasing artifacts at high dot densities by a specifically designed low-pass filtering method. Examples of nonlinear dot plots are compared to conventional dot plots as well as linear and logarithmic histograms. Finally, we include feedback from an expert review.

  10. Analysis of secondary particle behavior in multiaperture, multigrid accelerator for the ITER neutral beam injector.

    Science.gov (United States)

    Mizuno, T; Taniguchi, M; Kashiwagi, M; Umeda, N; Tobari, H; Watanabe, K; Dairaku, M; Sakamoto, K; Inoue, T

    2010-02-01

    Heat load on acceleration grids by secondary particles such as electrons, neutrals, and positive ions, is a key issue for long pulse acceleration of negative ion beams. Complicated behaviors of the secondary particles in multiaperture, multigrid (MAMuG) accelerator have been analyzed using electrostatic accelerator Monte Carlo code. The analytical result is compared to experimental one obtained in a long pulse operation of a MeV accelerator, of which second acceleration grid (A2G) was removed for simplification of structure. The analytical results show that relatively high heat load on the third acceleration grid (A3G) since stripped electrons were deposited mainly on A3G. This heat load on the A3G can be suppressed by installing the A2G. Thus, capability of MAMuG accelerator is demonstrated for suppression of heat load due to secondary particles by the intermediate grids.

  11. Nonlinear Science

    CERN Document Server

    Yoshida, Zensho

    2010-01-01

    This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl

  12. Nonlinear oscillations

    CERN Document Server

    Nayfeh, Ali Hasan

    1995-01-01

    Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim

  13. Scalable multi-grid preconditioning techniques for the even-parity S_N solver in UNIC

    International Nuclear Information System (INIS)

    Mahadevan, Vijay S.; Smith, Michael A.

    2011-01-01

    The Even-parity neutron transport equation with FE-S_N discretization is solved traditionally using SOR preconditioned CG method at the lowest level of iterations in order to compute the criticality in reactor analysis problems. The use of high order isoparametric finite elements prohibits the formation of the discrete operator explicitly due to memory constraints in peta scale architectures. Hence, a h-p multi-grid preconditioner based on linear tessellation of the higher order mesh is introduced here for the space-angle system and compared against SOR and Algebraic MG black-box solvers. The performance and scalability of the multi-grid scheme was determined for two test problems and found to be competitive in terms of both computational time and memory requirements. The implementation of this preconditioner in an even-parity solver like UNIC from ANL can further enable high fidelity calculations in a scalable manner on peta flop machines. (author)

  14. A matrix-free implicit unstructured multigrid finite volume method for simulating structural dynamics and fluid structure interaction

    Science.gov (United States)

    Lv, X.; Zhao, Y.; Huang, X. Y.; Xia, G. H.; Su, X. H.

    2007-07-01

    A new three-dimensional (3D) matrix-free implicit unstructured multigrid finite volume (FV) solver for structural dynamics is presented in this paper. The solver is first validated using classical 2D and 3D cantilever problems. It is shown that very accurate predictions of the fundamental natural frequencies of the problems can be obtained by the solver with fast convergence rates. This method has been integrated into our existing FV compressible solver [X. Lv, Y. Zhao, et al., An efficient parallel/unstructured-multigrid preconditioned implicit method for simulating 3d unsteady compressible flows with moving objects, Journal of Computational Physics 215(2) (2006) 661-690] based on the immersed membrane method (IMM) [X. Lv, Y. Zhao, et al., as mentioned above]. Results for the interaction between the fluid and an immersed fixed-free cantilever are also presented to demonstrate the potential of this integrated fluid-structure interaction approach.

  15. Nonlinear systems

    CERN Document Server

    Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús

    2018-01-01

    This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many  new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...

  16. A New DOA Algorithm Based on Nonlinear Compress Core Function in Symmetric α-stable Distribution Noise Environment%一种对称琢稳定分布噪声环境下DOA估计新算法

    Institute of Scientific and Technical Information of China (English)

    马金全; 葛临东; 童莉

    2014-01-01

    脉冲噪声环境下波达方向( DOA)估计是阵列信号处理领域一个新兴研究方向。针对α稳定分布噪声环境下经典MUSIC算法性能退化的问题,提出了一种新的基于非线性压缩核函数( NCCF)的DOA估计算法。该算法利用基于NCCF的有界矩阵代替了MUSIC的协方差矩阵,通过对有界矩阵进行特征分解确定信号子空间和噪声子空间,借用MUSIC谱估计公式进行谱峰搜索,得到DOA的估计值。仿真结果表明,NCCF-MUSIC算法运算复杂度较低,相比于基于分数低阶统计量( FLOS)的MUSIC方法和基于广义类相关熵( GCAS)的MUSIC算法,该方法具有更好的准确度和稳定性。%Direction of arrival ( DOA) estimation in the impulse noise environment is a new research direc-tion in the array signal processing field. To solve the problem of performance degradation when applying classic MUSIC algorithm for DOA estimation in the α-stable distribution noise environment,a novel DOA estimation algorithm based on a nonlinear compress core function ( NCCF ) is provided and named as the NCCF-MUSIC. To obtain a DOA estimation,the NCCF-MUSIC method replaces the covariance matrix in MUSIC by a bounded matrix based on the NCCF,and then determines the signal subspace and the noise subspace by feature decomposition, and finally, introduces the MUSIC spectrum estimation algorithm to make a spectral peak searching. Simulation results show that the new NCCF-MUSIC method with a lower computation cost has the higher performance in accuracy and validity than the MUSIC methods based on fractional lower order statistics ( FLOS) or based on generalized correntropy-analogous statistics ( GCAS) .

  17. Angular Multigrid Preconditioner for Krylov-Based Solution Techniques Applied to the Sn Equations with Highly Forward-Peaked Scattering

    Science.gov (United States)

    Turcksin, Bruno; Ragusa, Jean C.; Morel, Jim E.

    2012-01-01

    It is well known that the diffusion synthetic acceleration (DSA) methods for the Sn equations become ineffective in the Fokker-Planck forward-peaked scattering limit. In response to this deficiency, Morel and Manteuffel (1991) developed an angular multigrid method for the 1-D Sn equations. This method is very effective, costing roughly twice as much as DSA per source iteration, and yielding a maximum spectral radius of approximately 0.6 in the Fokker-Planck limit. Pautz, Adams, and Morel (PAM) (1999) later generalized the angular multigrid to 2-D, but it was found that the method was unstable with sufficiently forward-peaked mappings between the angular grids. The method was stabilized via a filtering technique based on diffusion operators, but this filtering also degraded the effectiveness of the overall scheme. The spectral radius was not bounded away from unity in the Fokker-Planck limit, although the method remained more effective than DSA. The purpose of this article is to recast the multidimensional PAM angular multigrid method without the filtering as an Sn preconditioner and use it in conjunction with the Generalized Minimal RESidual (GMRES) Krylov method. The approach ensures stability and our computational results demonstrate that it is also significantly more efficient than an analogous DSA-preconditioned Krylov method.

  18. Nonlinear optics

    CERN Document Server

    Boyd, Robert W

    2013-01-01

    Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q

  19. Recent development of the Multi-Grid detector for large area neutron scattering instruments

    International Nuclear Information System (INIS)

    Guerard, Bruno

    2015-01-01

    Most of the Neutron Scattering facilities are committed in a continuous program of modernization of their instruments, requiring large area and high performance thermal neutron detectors. Beside scintillators detectors, 3 He detectors, like linear PSDs (Position Sensitive Detectors) and MWPCs (Multi-Wires Proportional Chambers), are the most current techniques nowadays. Time Of Flight instruments are using 3 He PSDs mounted side by side to cover tens of m 2 . As a result of the so-called ' 3 He shortage crisis , the volume of 3He which is needed to build one of these instruments is not accessible anymore. The development of alternative techniques requiring no 3He, has been given high priority to secure the future of neutron scattering instrumentation. This is particularly important in the context where the future ESS (European Spallation Source) will start its operation in 2019-2020. Improved scintillators represent one of the alternative techniques. Another one is the Multi-Grid introduced at the ILL in 2009. A Multi-Grid detector is composed of several independent modules of typically 0.8 m x 3 m sensitive area, mounted side by side in air or in a vacuum TOF chamber. One module is composed of segmented boron-lined proportional counters mounted in a gas vessel; the counters, of square section, are assembled with Aluminium grids electrically insulated and stacked together. This design provides two advantages: First, magnetron sputtering techniques can be used to coat B 4 C films on planar substrates, and second, the neutron position along the anode wires can be measured by reading out individually the grid signals with fast shaping amplifiers followed by comparators. Unlike charge division localisation in linear PSDs, the individual readout of the grids allows operating the Multi-Grid at a low amplification gain, hence this detector is tolerant to mechanical defects and its production accessible to laboratories equipped with standard equipment. Prototypes of

  20. 3D inversion based on multi-grid approach of magnetotelluric data from Northern Scandinavia

    Science.gov (United States)

    Cherevatova, M.; Smirnov, M.; Korja, T. J.; Egbert, G. D.

    2012-12-01

    In this work we investigate the geoelectrical structure of the cratonic margin of Fennoscandian Shield by means of magnetotelluric (MT) measurements carried out in Northern Norway and Sweden during summer 2011-2012. The project Magnetotellurics in the Scandes (MaSca) focuses on the investigation of the crust, upper mantle and lithospheric structure in a transition zone from a stable Precambrian cratonic interior to a passive continental margin beneath the Caledonian Orogen and the Scandes Mountains in western Fennoscandia. Recent MT profiles in the central and southern Scandes indicated a large contrast in resistivity between Caledonides and Precambrian basement. The alum shales as a highly conductive layers between the resistive Precambrian basement and the overlying Caledonian nappes are revealed from this profiles. Additional measurements in the Northern Scandes were required. All together data from 60 synchronous long period (LMT) and about 200 broad band (BMT) sites were acquired. The array stretches from Lofoten and Bodo (Norway) in the west to Kiruna and Skeleftea (Sweden) in the east covering an area of 500x500 square kilometers. LMT sites were occupied for about two months, while most of the BMT sites were measured during one day. We have used new multi-grid approach for 3D electromagnetic (EM) inversion and modelling. Our approach is based on the OcTree discretization where the spatial domain is represented by rectangular cells, each of which might be subdivided (recursively) into eight sub-cells. In this simplified implementation the grid is refined only in the horizontal direction, uniformly in each vertical layer. Using multi-grid we manage to have a high grid resolution near the surface (for instance, to tackle with galvanic distortions) and lower resolution at greater depth as the EM fields decay in the Earth according to the diffusion equation. We also have a benefit in computational costs as number of unknowns decrease. The multi-grid forward

  1. Recent development of the Multi-Grid detector for large area neutron scattering instruments

    Energy Technology Data Exchange (ETDEWEB)

    Guerard, Bruno [ILL-ESS-LiU collaboration, CRISP project, Institut Laue Langevin - ILL, Grenoble (France)

    2015-07-01

    Most of the Neutron Scattering facilities are committed in a continuous program of modernization of their instruments, requiring large area and high performance thermal neutron detectors. Beside scintillators detectors, {sup 3}He detectors, like linear PSDs (Position Sensitive Detectors) and MWPCs (Multi-Wires Proportional Chambers), are the most current techniques nowadays. Time Of Flight instruments are using {sup 3}He PSDs mounted side by side to cover tens of m{sup 2}. As a result of the so-called '{sup 3}He shortage crisis{sup ,} the volume of 3He which is needed to build one of these instruments is not accessible anymore. The development of alternative techniques requiring no 3He, has been given high priority to secure the future of neutron scattering instrumentation. This is particularly important in the context where the future ESS (European Spallation Source) will start its operation in 2019-2020. Improved scintillators represent one of the alternative techniques. Another one is the Multi-Grid introduced at the ILL in 2009. A Multi-Grid detector is composed of several independent modules of typically 0.8 m x 3 m sensitive area, mounted side by side in air or in a vacuum TOF chamber. One module is composed of segmented boron-lined proportional counters mounted in a gas vessel; the counters, of square section, are assembled with Aluminium grids electrically insulated and stacked together. This design provides two advantages: First, magnetron sputtering techniques can be used to coat B{sub 4}C films on planar substrates, and second, the neutron position along the anode wires can be measured by reading out individually the grid signals with fast shaping amplifiers followed by comparators. Unlike charge division localisation in linear PSDs, the individual readout of the grids allows operating the Multi-Grid at a low amplification gain, hence this detector is tolerant to mechanical defects and its production accessible to laboratories equipped with standard

  2. Nonlinear systems

    National Research Council Canada - National Science Library

    Drazin, P. G

    1992-01-01

    This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...

  3. Nonlinear analysis

    CERN Document Server

    Gasinski, Leszek

    2005-01-01

    Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.

  4. Spurious Solutions Of Nonlinear Differential Equations

    Science.gov (United States)

    Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

    1992-01-01

    Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.

  5. NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES

    Directory of Open Access Journals (Sweden)

    SILVA R. G.

    1999-01-01

    Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.

  6. Efficiency Analysis of the Parallel Implementation of the SIMPLE Algorithm on Multiprocessor Computers

    Science.gov (United States)

    Lashkin, S. V.; Kozelkov, A. S.; Yalozo, A. V.; Gerasimov, V. Yu.; Zelensky, D. K.

    2017-12-01

    This paper describes the details of the parallel implementation of the SIMPLE algorithm for numerical solution of the Navier-Stokes system of equations on arbitrary unstructured grids. The iteration schemes for the serial and parallel versions of the SIMPLE algorithm are implemented. In the description of the parallel implementation, special attention is paid to computational data exchange among processors under the condition of the grid model decomposition using fictitious cells. We discuss the specific features for the storage of distributed matrices and implementation of vector-matrix operations in parallel mode. It is shown that the proposed way of matrix storage reduces the number of interprocessor exchanges. A series of numerical experiments illustrates the effect of the multigrid SLAE solver tuning on the general efficiency of the algorithm; the tuning involves the types of the cycles used (V, W, and F), the number of iterations of a smoothing operator, and the number of cells for coarsening. Two ways (direct and indirect) of efficiency evaluation for parallelization of the numerical algorithm are demonstrated. The paper presents the results of solving some internal and external flow problems with the evaluation of parallelization efficiency by two algorithms. It is shown that the proposed parallel implementation enables efficient computations for the problems on a thousand processors. Based on the results obtained, some general recommendations are made for the optimal tuning of the multigrid solver, as well as for selecting the optimal number of cells per processor.

  7. Multigrid direct numerical simulation of the whole process of flow transition in 3-D boundary layers

    Science.gov (United States)

    Liu, Chaoqun; Liu, Zhining

    1993-01-01

    A new technology was developed in this study which provides a successful numerical simulation of the whole process of flow transition in 3-D boundary layers, including linear growth, secondary instability, breakdown, and transition at relatively low CPU cost. Most other spatial numerical simulations require high CPU cost and blow up at the stage of flow breakdown. A fourth-order finite difference scheme on stretched and staggered grids, a fully implicit time marching technique, a semi-coarsening multigrid based on the so-called approximate line-box relaxation, and a buffer domain for the outflow boundary conditions were all used for high-order accuracy, good stability, and fast convergence. A new fine-coarse-fine grid mapping technique was developed to keep the code running after the laminar flow breaks down. The computational results are in good agreement with linear stability theory, secondary instability theory, and some experiments. The cost for a typical case with 162 x 34 x 34 grid is around 2 CRAY-YMP CPU hours for 10 T-S periods.

  8. Multigrid solution of incompressible turbulent flows by using two-equation turbulence models

    Energy Technology Data Exchange (ETDEWEB)

    Zheng, X.; Liu, C. [Front Range Scientific Computations, Inc., Denver, CO (United States); Sung, C.H. [David Taylor Model Basin, Bethesda, MD (United States)

    1996-12-31

    Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.

  9. Controller Design of Complex System Based on Nonlinear Strength

    Directory of Open Access Journals (Sweden)

    Rongjun Mu

    2015-01-01

    Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

  10. Nonlinear optimization

    CERN Document Server

    Ruszczynski, Andrzej

    2011-01-01

    Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...

  11. Nonlinear filtering for LIDAR signal processing

    Directory of Open Access Journals (Sweden)

    D. G. Lainiotis

    1996-01-01

    Full Text Available LIDAR (Laser Integrated Radar is an engineering problem of great practical importance in environmental monitoring sciences. Signal processing for LIDAR applications involves highly nonlinear models and consequently nonlinear filtering. Optimal nonlinear filters, however, are practically unrealizable. In this paper, the Lainiotis's multi-model partitioning methodology and the related approximate but effective nonlinear filtering algorithms are reviewed and applied to LIDAR signal processing. Extensive simulation and performance evaluation of the multi-model partitioning approach and its application to LIDAR signal processing shows that the nonlinear partitioning methods are very effective and significantly superior to the nonlinear extended Kalman filter (EKF, which has been the standard nonlinear filter in past engineering applications.

  12. Nonlinear dynamical system approaches towards neural prosthesis

    International Nuclear Information System (INIS)

    Torikai, Hiroyuki; Hashimoto, Sho

    2011-01-01

    An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.

  13. Experimental verification of transient nonlinear acoustical holography.

    Science.gov (United States)

    Jing, Yun; Cannata, Jonathan; Wang, Tianren

    2013-05-01

    This paper presents an experimental study on nonlinear transient acoustical holography. The validity and effectiveness of a recently proposed nonlinear transient acoustical holography algorithm is evaluated in the presence of noise. The acoustic field measured on a post-focal plane of a high-intensity focused transducer is backward projected to reconstruct the pressure distributions on the focal and a pre-focal plane, which are shown to be in good agreement with the measurement. In contrast, the conventional linear holography produces erroneous results in this case where the nonlinearity involved is strong. Forward acoustic field projection was also carried out to further verify the algorithm.

  14. Algorithming the Algorithm

    DEFF Research Database (Denmark)

    Mahnke, Martina; Uprichard, Emma

    2014-01-01

    Imagine sailing across the ocean. The sun is shining, vastness all around you. And suddenly [BOOM] you’ve hit an invisible wall. Welcome to the Truman Show! Ever since Eli Pariser published his thoughts on a potential filter bubble, this movie scenario seems to have become reality, just with slight...... changes: it’s not the ocean, it’s the internet we’re talking about, and it’s not a TV show producer, but algorithms that constitute a sort of invisible wall. Building on this assumption, most research is trying to ‘tame the algorithmic tiger’. While this is a valuable and often inspiring approach, we...

  15. Comparison of multihardware parallel implementations for a phase unwrapping algorithm

    Science.gov (United States)

    Hernandez-Lopez, Francisco Javier; Rivera, Mariano; Salazar-Garibay, Adan; Legarda-Sáenz, Ricardo

    2018-04-01

    Phase unwrapping is an important problem in the areas of optical metrology, synthetic aperture radar (SAR) image analysis, and magnetic resonance imaging (MRI) analysis. These images are becoming larger in size and, particularly, the availability and need for processing of SAR and MRI data have increased significantly with the acquisition of remote sensing data and the popularization of magnetic resonators in clinical diagnosis. Therefore, it is important to develop faster and accurate phase unwrapping algorithms. We propose a parallel multigrid algorithm of a phase unwrapping method named accumulation of residual maps, which builds on a serial algorithm that consists of the minimization of a cost function; minimization achieved by means of a serial Gauss-Seidel kind algorithm. Our algorithm also optimizes the original cost function, but unlike the original work, our algorithm is a parallel Jacobi class with alternated minimizations. This strategy is known as the chessboard type, where red pixels can be updated in parallel at same iteration since they are independent. Similarly, black pixels can be updated in parallel in an alternating iteration. We present parallel implementations of our algorithm for different parallel multicore architecture such as CPU-multicore, Xeon Phi coprocessor, and Nvidia graphics processing unit. In all the cases, we obtain a superior performance of our parallel algorithm when compared with the original serial version. In addition, we present a detailed comparative performance of the developed parallel versions.

  16. On the multi-level solution algorithm for Markov chains

    Energy Technology Data Exchange (ETDEWEB)

    Horton, G. [Univ. of Erlangen, Nuernberg (Germany)

    1996-12-31

    We discuss the recently introduced multi-level algorithm for the steady-state solution of Markov chains. The method is based on the aggregation principle, which is well established in the literature. Recursive application of the aggregation yields a multi-level method which has been shown experimentally to give results significantly faster than the methods currently in use. The algorithm can be reformulated as an algebraic multigrid scheme of Galerkin-full approximation type. The uniqueness of the scheme stems from its solution-dependent prolongation operator which permits significant computational savings in the evaluation of certain terms. This paper describes the modeling of computer systems to derive information on performance, measured typically as job throughput or component utilization, and availability, defined as the proportion of time a system is able to perform a certain function in the presence of component failures and possibly also repairs.

  17. A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

    Science.gov (United States)

    Whiteley, J. P.

    2017-10-01

    Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

  18. Application Of Multi-grid Method On China Seas' Temperature Forecast

    Science.gov (United States)

    Li, W.; Xie, Y.; He, Z.; Liu, K.; Han, G.; Ma, J.; Li, D.

    2006-12-01

    Correlation scales have been used in traditional scheme of 3-dimensional variational (3D-Var) data assimilation to estimate the background error covariance for the numerical forecast and reanalysis of atmosphere and ocean for decades. However there are still some drawbacks of this scheme. First, the correlation scales are difficult to be determined accurately. Second, the positive definition of the first-guess error covariance matrix cannot be guaranteed unless the correlation scales are sufficiently small. Xie et al. (2005) indicated that a traditional 3D-Var only corrects some certain wavelength errors and its accuracy depends on the accuracy of the first-guess covariance. And in general, short wavelength error can not be well corrected until long one is corrected and then inaccurate first-guess covariance may mistakenly take long wave error as short wave ones and result in erroneous analysis. For the purpose of quickly minimizing the errors of long and short waves successively, a new 3D-Var data assimilation scheme, called multi-grid data assimilation scheme, is proposed in this paper. By assimilating the shipboard SST and temperature profiles data into a numerical model of China Seas, we applied this scheme in two-month data assimilation and forecast experiment which ended in a favorable result. Comparing with the traditional scheme of 3D-Var, the new scheme has higher forecast accuracy and a lower forecast Root-Mean-Square (RMS) error. Furthermore, this scheme was applied to assimilate the SST of shipboard, AVHRR Pathfinder Version 5.0 SST and temperature profiles at the same time, and a ten-month forecast experiment on sea temperature of China Seas was carried out, in which a successful forecast result was obtained. Particularly, the new scheme is demonstrated a great numerical efficiency in these analyses.

  19. Nonlinear evolution of f(R) cosmologies. I. Methodology

    International Nuclear Information System (INIS)

    Oyaizu, Hiroaki

    2008-01-01

    We introduce the method and the implementation of a cosmological simulation of a class of metric-variation f(R) models that accelerate the cosmological expansion without a cosmological constant and evade solar-system bounds of small-field deviations to general relativity. Such simulations are shown to reduce to solving a nonlinear Poisson equation for the scalar degree of freedom introduced by the f(R) modifications. We detail the method to efficiently solve the nonlinear Poisson equation by using a Newton-Gauss-Seidel relaxation scheme coupled with the multigrid method to accelerate the convergence. The simulations are shown to satisfy tests comparing the simulated outcome to analytical solutions for simple situations, and the dynamics of the simulations are tested with orbital and Zeldovich collapse tests. Finally, we present several static and dynamical simulations using realistic cosmological parameters to highlight the differences between standard physics and f(R) physics. In general, we find that the f(R) modifications result in stronger gravitational attraction that enhances the dark matter power spectrum by ∼20% for large but observationally allowed f(R) modifications. A more detailed study of the nonlinear f(R) effects on the power spectrum are presented in a companion paper.

  20. Evaluation of the performance of different firefly algorithms to the ...

    African Journals Online (AJOL)

    of firefly algorithms are applied to solve the nonlinear ELD problem. ... problem using those recent variants and the classical firefly algorithm for different test cases. Efficiency ...... International Journal of Machine. Learning and Computing, Vol.

  1. Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems

    National Research Council Canada - National Science Library

    Abramson, Mark A; Audet, Charles; Dennis, Jr, J. E

    2004-01-01

    .... This class combines and extends the Audet-Dennis Generalized Pattern Search (GPS) algorithms for bound constrained mixed variable optimization, and their GPS-filter algorithms for general nonlinear constraints...

  2. Nonlinear dynamics aspects of particle accelerators

    International Nuclear Information System (INIS)

    Jowett, J.M.; Turner, S.; Month, M.

    1986-01-01

    These proceedings contain the lectures presented at the named winter school. They deal with the application of dynamical systems to accelerator theory. Especially considered are the statistical description of charged-beam plasmas, integrable and nonintegrable Hamiltonian systems, single particle dynamics and nonlinear resonances in circular accelerators, nonlinear dynamics aspects of modern storage rings, nonlinear beam-beam resonances, synchro-betatron resonances, observations of the beam-beam interactions, the dynamics of the beam-beam interactions, beam-beam simulations, the perturbation method in nonlinear dynamics, theories of statistical equilibrium in electron-positron storage rings, nonlinear dissipative phenomena in electron storage rings, the dynamical aperture, the transition to chaos for area-preserving maps, special processors for particle tracking, algorithms for tracking of charged particles in circular accelerators, the breakdown of stability, and a personal perspective of nonlinear dynamics. (HSI)

  3. Introduction to nonlinear finite element analysis

    CERN Document Server

    Kim, Nam-Ho

    2015-01-01

    This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: ·         Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems ·         Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory ·    ...

  4. Nonlinear dynamics aspects of particle accelerators. Proceedings

    Energy Technology Data Exchange (ETDEWEB)

    Jowett, J M; Turner, S; Month, M

    1986-01-01

    These proceedings contain the lectures presented at the named winter school. They deal with the application of dynamical systems to accelerator theory. Especially considered are the statistical description of charged-beam plasmas, integrable and nonintegrable Hamiltonian systems, single particle dynamics and nonlinear resonances in circular accelerators, nonlinear dynamics aspects of modern storage rings, nonlinear beam-beam resonances, synchro-betatron resonances, observations of the beam-beam interactions, the dynamics of the beam-beam interactions, beam-beam simulations, the perturbation method in nonlinear dynamics, theories of statistical equilibrium in electron-positron storage rings, nonlinear dissipative phenomena in electron storage rings, the dynamical aperture, the transition to chaos for area-preserving maps, special processors for particle tracking, algorithms for tracking of charged particles in circular accelerators, the breakdown of stability, and a personal perspective of nonlinear dynamics. (HSI).

  5. Sound algorithms

    OpenAIRE

    De Götzen , Amalia; Mion , Luca; Tache , Olivier

    2007-01-01

    International audience; We call sound algorithms the categories of algorithms that deal with digital sound signal. Sound algorithms appeared in the very infancy of computer. Sound algorithms present strong specificities that are the consequence of two dual considerations: the properties of the digital sound signal itself and its uses, and the properties of auditory perception.

  6. Genetic algorithms

    Science.gov (United States)

    Wang, Lui; Bayer, Steven E.

    1991-01-01

    Genetic algorithms are mathematical, highly parallel, adaptive search procedures (i.e., problem solving methods) based loosely on the processes of natural genetics and Darwinian survival of the fittest. Basic genetic algorithms concepts are introduced, genetic algorithm applications are introduced, and results are presented from a project to develop a software tool that will enable the widespread use of genetic algorithm technology.

  7. Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities

    Indian Academy of Sciences (India)

    In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...

  8. Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

    Directory of Open Access Journals (Sweden)

    Y. N. Pavlov

    2015-01-01

    Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

  9. Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

    International Nuclear Information System (INIS)

    Liu Chunliang; Xie Xi; Chen Yinbao

    1991-01-01

    The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

  10. New algorithms for parallel MRI

    International Nuclear Information System (INIS)

    Anzengruber, S; Ramlau, R; Bauer, F; Leitao, A

    2008-01-01

    Magnetic Resonance Imaging with parallel data acquisition requires algorithms for reconstructing the patient's image from a small number of measured lines of the Fourier domain (k-space). In contrast to well-known algorithms like SENSE and GRAPPA and its flavors we consider the problem as a non-linear inverse problem. However, in order to avoid cost intensive derivatives we will use Landweber-Kaczmarz iteration and in order to improve the overall results some additional sparsity constraints.

  11. Fast algorithms for chiral fermions in 2 dimensions

    Directory of Open Access Journals (Sweden)

    Hyka (Xhako Dafina

    2018-01-01

    Full Text Available In lattice QCD simulations the formulation of the theory in lattice should be chiral in order that symmetry breaking happens dynamically from interactions. In order to guarantee this symmetry on the lattice one uses overlap and domain wall fermions. On the other hand high computational cost of lattice QCD simulations with overlap or domain wall fermions remains a major obstacle of research in the field of elementary particles. We have developed the preconditioned GMRESR algorithm as fast inverting algorithm for chiral fermions in U(1 lattice gauge theory. In this algorithm we used the geometric multigrid idea along the extra dimension.The main result of this work is that the preconditioned GMRESR is capable to accelerate the convergence 2 to 12 times faster than the other optimal algorithms (SHUMR for different coupling constant and lattice 32x32. Also, in this paper we tested it for larger lattice size 64x64. From the results of simulations we can see that our algorithm is faster than SHUMR. This is a very promising result that this algorithm can be adapted also in 4 dimension.

  12. Algorithmic cryptanalysis

    CERN Document Server

    Joux, Antoine

    2009-01-01

    Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program.Divided into three parts, the book begins with a short introduction to cryptography and a background chapter on elementary number theory and algebra. It then moves on to algorithms, with each chapter in this section dedicated to a single topic and often illustrated with simple cryptographic applic

  13. Numerical study of propagation properties of surface plasmon polaritons in nonlinear media

    KAUST Repository

    Sagor, Rakibul Hasan; Ghulam Saber, Md.; Alsunaidi, Mohammad

    2016-01-01

    We present a time-domain algorithm for simulating nonlinear propagation of surface plasmon polaritons (SPPs) in chalcogenide glass. Due to the high non-linearity property and strong dispersion and confinement chalcogenide glasses are widely known

  14. Sparse calibration of subsurface flow models using nonlinear orthogonal matching pursuit and an iterative stochastic ensemble method

    KAUST Repository

    Elsheikh, Ahmed H.; Wheeler, Mary Fanett; Hoteit, Ibrahim

    2013-01-01

    is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm. The proposed algorithm is the first ensemble based algorithm that tackels the sparse nonlinear parameter estimation problem. © 2013 Elsevier Ltd.

  15. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

    Science.gov (United States)

    Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

    1990-01-01

    Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

  16. Recent advances in multiparametric nonlinear programming

    KAUST Repository

    Domí nguez, Luis F.; Narciso, Diogo A.; Pistikopoulos, Efstratios N.

    2010-01-01

    In this paper, we present recent developments in multiparametric nonlinear programming. For the case of convex problems, we highlight key issues regarding the full characterization of the parametric solution space and we discuss, through an illustrative example problem, four alternative state-of-the-art multiparametric nonlinear programming algorithms. We also identify a number of main challenges for the non-convex case and highlight future research directions. © 2009 Elsevier Ltd. All rights reserved.

  17. Recent advances in multiparametric nonlinear programming

    KAUST Repository

    Domínguez, Luis F.

    2010-05-01

    In this paper, we present recent developments in multiparametric nonlinear programming. For the case of convex problems, we highlight key issues regarding the full characterization of the parametric solution space and we discuss, through an illustrative example problem, four alternative state-of-the-art multiparametric nonlinear programming algorithms. We also identify a number of main challenges for the non-convex case and highlight future research directions. © 2009 Elsevier Ltd. All rights reserved.

  18. Feedforward Nonlinear Control Using Neural Gas Network

    OpenAIRE

    Machón-González, Iván; López-García, Hilario

    2017-01-01

    Nonlinear systems control is a main issue in control theory. Many developed applications suffer from a mathematical foundation not as general as the theory of linear systems. This paper proposes a control strategy of nonlinear systems with unknown dynamics by means of a set of local linear models obtained by a supervised neural gas network. The proposed approach takes advantage of the neural gas feature by which the algorithm yields a very robust clustering procedure. The direct model of the ...

  19. Nonlinear resonances

    CERN Document Server

    Rajasekar, Shanmuganathan

    2016-01-01

    This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...

  20. Algorithmic mathematics

    CERN Document Server

    Hougardy, Stefan

    2016-01-01

    Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.

  1. Perspectives on Nonlinear Filtering

    KAUST Repository

    Law, Kody

    2015-01-01

    The solution to the problem of nonlinear filtering may be given either as an estimate of the signal (and ideally some measure of concentration), or as a full posterior distribution. Similarly, one may evaluate the fidelity of the filter either by its ability to track the signal or its proximity to the posterior filtering distribution. Hence, the field enjoys a lively symbiosis between probability and control theory, and there are plenty of applications which benefit from algorithmic advances, from signal processing, to econometrics, to large-scale ocean, atmosphere, and climate modeling. This talk will survey some recent theoretical results involving accurate signal tracking with noise-free (degenerate) dynamics in high-dimensions (infinite, in principle, but say d between 103 and 108 , depending on the size of your application and your computer), and high-fidelity approximations of the filtering distribution in low dimensions (say d between 1 and several 10s).

  2. Perspectives on Nonlinear Filtering

    KAUST Repository

    Law, Kody

    2015-01-07

    The solution to the problem of nonlinear filtering may be given either as an estimate of the signal (and ideally some measure of concentration), or as a full posterior distribution. Similarly, one may evaluate the fidelity of the filter either by its ability to track the signal or its proximity to the posterior filtering distribution. Hence, the field enjoys a lively symbiosis between probability and control theory, and there are plenty of applications which benefit from algorithmic advances, from signal processing, to econometrics, to large-scale ocean, atmosphere, and climate modeling. This talk will survey some recent theoretical results involving accurate signal tracking with noise-free (degenerate) dynamics in high-dimensions (infinite, in principle, but say d between 103 and 108 , depending on the size of your application and your computer), and high-fidelity approximations of the filtering distribution in low dimensions (say d between 1 and several 10s).

  3. Total algorithms

    NARCIS (Netherlands)

    Tel, G.

    We define the notion of total algorithms for networks of processes. A total algorithm enforces that a "decision" is taken by a subset of the processes, and that participation of all processes is required to reach this decision. Total algorithms are an important building block in the design of

  4. Analyzing algorithms for nonlinear and spatially nonuniform phase shifts in the liquid crystal point diffraction interferometer. 1998 summer research program for high school juniors at the University of Rochester's Laboratory for Laser Energetics. Student research reports

    International Nuclear Information System (INIS)

    Jain, N.

    1999-03-01

    Phase-shifting interferometry has many advantages, and the phase shifting nature of the Liquid Crystal Point Diffraction Interferometer (LCPDI) promises to provide significant improvement over other current OMEGA wavefront sensors. However, while phase-shifting capabilities improve its accuracy as an interferometer, phase-shifting itself introduces errors. Phase-shifting algorithms are designed to eliminate certain types of phase-shift errors, and it is important to chose an algorithm that is best suited for use with the LCPDI. Using polarization microscopy, the authors have observed a correlation between LC alignment around the microsphere and fringe behavior. After designing a procedure to compare phase-shifting algorithms, they were able to predict the accuracy of two particular algorithms through computer modeling of device-specific phase shift-errors

  5. Numerical Multilevel Upscaling for Incompressible Flow in Reservoir Simulation: An Element-based Algebraic Multigrid (AMGe) Approach

    DEFF Research Database (Denmark)

    Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter

    2017-01-01

    associated with non-planar interfaces between agglomerates, the coarse velocity space has guaranteed approximation properties. The employed AMGe technique provides coarse spaces with desirable local mass conservation and stability properties analogous to the original pair of Raviart-Thomas and piecewise......We study the application of a finite element numerical upscaling technique to the incompressible two-phase porous media total velocity formulation. Specifically, an element agglomeration based Algebraic Multigrid (AMGe) technique with improved approximation proper ties [37] is used, for the first...... discontinuous polynomial spaces, resulting in strong mass conservation for the upscaled systems. Due to the guaranteed approximation properties and the generic nature of the AMGe method, recursive multilevel upscaling is automatically obtained. Furthermore, this technique works for both structured...

  6. Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography.

    Science.gov (United States)

    Yang, Qiang; Vogel, Curtis R; Ellerbroek, Brent L

    2006-07-20

    By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty.

  7. Genetic design of interpolated non-linear controllers for linear plants

    International Nuclear Information System (INIS)

    Ajlouni, N.

    2000-01-01

    The techniques of genetic algorithms are proposed as a means of designing non-linear PID control systems. It is shown that the use of genetic algorithms for this purpose results in highly effective non-linear PID control systems. These results are illustrated by using genetic algorithms to design a non-linear PID control system and contrasting the results with an optimally tuned linear PID controller. (author)

  8. Nonlinear Principal Component Analysis Using Strong Tracking Filter

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The paper analyzes the problem of blind source separation (BSS) based on the nonlinear principal component analysis (NPCA) criterion. An adaptive strong tracking filter (STF) based algorithm was developed, which is immune to system model mismatches. Simulations demonstrate that the algorithm converges quickly and has satisfactory steady-state accuracy. The Kalman filtering algorithm and the recursive leastsquares type algorithm are shown to be special cases of the STF algorithm. Since the forgetting factor is adaptively updated by adjustment of the Kalman gain, the STF scheme provides more powerful tracking capability than the Kalman filtering algorithm and recursive least-squares algorithm.

  9. Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface

    Science.gov (United States)

    Coco, Armando; Russo, Giovanni

    2018-05-01

    In this paper we propose a second-order accurate numerical method to solve elliptic problems with discontinuous coefficients (with general non-homogeneous jumps in the solution and its gradient) in 2D and 3D. The method consists of a finite-difference method on a Cartesian grid in which complex geometries (boundaries and interfaces) are embedded, and is second order accurate in the solution and the gradient itself. In order to avoid the drop in accuracy caused by the discontinuity of the coefficients across the interface, two numerical values are assigned on grid points that are close to the interface: a real value, that represents the numerical solution on that grid point, and a ghost value, that represents the numerical solution extrapolated from the other side of the interface, obtained by enforcing the assigned non-homogeneous jump conditions on the solution and its flux. The method is also extended to the case of matrix coefficient. The linear system arising from the discretization is solved by an efficient multigrid approach. Unlike the 1D case, grid points are not necessarily aligned with the normal derivative and therefore suitable stencils must be chosen to discretize interface conditions in order to achieve second order accuracy in the solution and its gradient. A proper treatment of the interface conditions will allow the multigrid to attain the optimal convergence factor, comparable with the one obtained by Local Fourier Analysis for rectangular domains. The method is robust enough to handle large jump in the coefficients: order of accuracy, monotonicity of the errors and good convergence factor are maintained by the scheme.

  10. Retrieval of high-order susceptibilities of nonlinear metamaterials

    International Nuclear Information System (INIS)

    Wang Zhi-Yu; Qiu Jin-Peng; Chen Hua; Mo Jiong-Jiong; Yu Fa-Xin

    2017-01-01

    Active metamaterials embedded with nonlinear elements are able to exhibit strong nonlinearity in microwave regime. However, existing S -parameter based parameter retrieval approaches developed for linear metamaterials do not apply in nonlinear cases. In this paper, a retrieval algorithm of high-order susceptibilities for nonlinear metamaterials is derived. Experimental demonstration shows that, by measuring the power level of each harmonic while sweeping the incident power, high-order susceptibilities of a thin-layer nonlinear metamaterial can be effectively retrieved. The proposedapproach can be widely used in the research of active metamaterials. (paper)

  11. Flutter analysis of an airfoil with multiple nonlinearities and uncertainties

    Directory of Open Access Journals (Sweden)

    Haitao Liao

    2013-09-01

    Full Text Available An original method for calculating the limit cycle oscillations of nonlinear aero-elastic system is presented. The problem of determining the maximum vibration amplitude of limit cycle is transformed into a nonlinear optimization problem. The harmonic balance method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated and used to analyse the limit cycle oscillations of an airfoil with multiple nonlinearities and uncertainties. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

  12. [Nonlinear magnetohydrodynamics

    International Nuclear Information System (INIS)

    1994-01-01

    Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile

  13. Multigrid Implementation of Cellular Automata for Topology Optimisation of Continuum Structures with Design Dependent loads

    NARCIS (Netherlands)

    Zakhama, R.

    2009-01-01

    Topology optimisation of continuum structures has become mature enough to be often applied in industry and continues to attract the attention of researchers and software companies in various engineering fields. Traditionally, most available algorithms for solving topology optimisation problems are

  14. Scalable Nonlinear Compact Schemes

    Energy Technology Data Exchange (ETDEWEB)

    Ghosh, Debojyoti [Argonne National Lab. (ANL), Argonne, IL (United States); Constantinescu, Emil M. [Univ. of Chicago, IL (United States); Brown, Jed [Univ. of Colorado, Boulder, CO (United States)

    2014-04-01

    In this work, we focus on compact schemes resulting in tridiagonal systems of equations, specifically the fifth-order CRWENO scheme. We propose a scalable implementation of the nonlinear compact schemes by implementing a parallel tridiagonal solver based on the partitioning/substructuring approach. We use an iterative solver for the reduced system of equations; however, we solve this system to machine zero accuracy to ensure that no parallelization errors are introduced. It is possible to achieve machine-zero convergence with few iterations because of the diagonal dominance of the system. The number of iterations is specified a priori instead of a norm-based exit criterion, and collective communications are avoided. The overall algorithm thus involves only point-to-point communication between neighboring processors. Our implementation of the tridiagonal solver differs from and avoids the drawbacks of past efforts in the following ways: it introduces no parallelization-related approximations (multiprocessor solutions are exactly identical to uniprocessor ones), it involves minimal communication, the mathematical complexity is similar to that of the Thomas algorithm on a single processor, and it does not require any communication and computation scheduling.

  15. Dynamic training algorithm for dynamic neural networks

    International Nuclear Information System (INIS)

    Tan, Y.; Van Cauwenberghe, A.; Liu, Z.

    1996-01-01

    The widely used backpropagation algorithm for training neural networks based on the gradient descent has a significant drawback of slow convergence. A Gauss-Newton method based recursive least squares (RLS) type algorithm with dynamic error backpropagation is presented to speed-up the learning procedure of neural networks with local recurrent terms. Finally, simulation examples concerning the applications of the RLS type algorithm to identification of nonlinear processes using a local recurrent neural network are also included in this paper

  16. Convergence criteria for systems of nonlinear elliptic partial differential equations

    International Nuclear Information System (INIS)

    Sharma, R.K.

    1986-01-01

    This thesis deals with convergence criteria for a special system of nonlinear elliptic partial differential equations. A fixed-point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. Conditions are established that help foresee the convergence of the algorithm. Under reasonable hypotheses it is proved that the algorithm converges for such nonlinear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis

  17. Modeling of frequency-domain scalar wave equation with the average-derivative optimal scheme based on a multigrid-preconditioned iterative solver

    Science.gov (United States)

    Cao, Jian; Chen, Jing-Bo; Dai, Meng-Xue

    2018-01-01

    An efficient finite-difference frequency-domain modeling of seismic wave propagation relies on the discrete schemes and appropriate solving methods. The average-derivative optimal scheme for the scalar wave modeling is advantageous in terms of the storage saving for the system of linear equations and the flexibility for arbitrary directional sampling intervals. However, using a LU-decomposition-based direct solver to solve its resulting system of linear equations is very costly for both memory and computational requirements. To address this issue, we consider establishing a multigrid-preconditioned BI-CGSTAB iterative solver fit for the average-derivative optimal scheme. The choice of preconditioning matrix and its corresponding multigrid components is made with the help of Fourier spectral analysis and local mode analysis, respectively, which is important for the convergence. Furthermore, we find that for the computation with unequal directional sampling interval, the anisotropic smoothing in the multigrid precondition may affect the convergence rate of this iterative solver. Successful numerical applications of this iterative solver for the homogenous and heterogeneous models in 2D and 3D are presented where the significant reduction of computer memory and the improvement of computational efficiency are demonstrated by comparison with the direct solver. In the numerical experiments, we also show that the unequal directional sampling interval will weaken the advantage of this multigrid-preconditioned iterative solver in the computing speed or, even worse, could reduce its accuracy in some cases, which implies the need for a reasonable control of directional sampling interval in the discretization.

  18. Implementation of the Vanka-type multigrid solver for the finite element approximation of the Navier-Stokes equations on GPU

    Czech Academy of Sciences Publication Activity Database

    Bauer, Petr; Klement, V.; Oberhuber, T.; Žabka, V.

    2016-01-01

    Roč. 200, March (2016), s. 50-56 ISSN 0010-4655 R&D Projects: GA ČR GB14-36566G Institutional support: RVO:61388998 Keywords : Navier–Stokes equations * mixed finite elements * multigrid * Vanka-type smoothers * Gauss–Seidel * red–black coloring * parallelization * GPU Subject RIV: BK - Fluid Dynamics Impact factor: 3.936, year: 2016

  19. LOO: a low-order nonlinear transport scheme for acceleration of method of characteristics

    International Nuclear Information System (INIS)

    Li, Lulu; Smith, Kord; Forget, Benoit; Ferrer, Rodolfo

    2015-01-01

    This paper presents a new physics-based multi-grid nonlinear acceleration method: the low-order operator method, or LOO. LOO uses a coarse space-angle multi-group method of characteristics (MOC) neutron transport calculation to accelerate the fine space-angle MOC calculation. LOO is designed to capture more angular effects than diffusion-based acceleration methods through a transport-based low-order solver. LOO differs from existing transport-based acceleration schemes in that it emphasizes simplified coarse space-angle characteristics and preserves physics in quadrant phase-space. The details of the method, including the restriction step, the low-order iterative solver and the prolongation step are discussed in this work. LOO shows comparable convergence behavior to coarse mesh finite difference on several two-dimensional benchmark problems while not requiring any under-relaxation, making it a robust acceleration scheme. (author)

  20. SPP propagation in nonlinear glass-metal interface

    KAUST Repository

    Sagor, Rakibul Hasan; Alsunaidi, Mohammad A.; Ooi, Boon S.

    2011-01-01

    The non-linear propagation of Surface-Plasmon-Polaritons (SPP) in single interface of metal and chalcogenide glass (ChG) is considered. A time domain simulation algorithm is developed using the Finite Difference Time Domain (FDTD) method

  1. Nonlinear beam mechanics

    NARCIS (Netherlands)

    Westra, H.J.R.

    2012-01-01

    In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like

  2. Recent Advances in Explicit Multiparametric Nonlinear Model Predictive Control

    KAUST Repository

    Domínguez, Luis F.

    2011-01-19

    In this paper we present recent advances in multiparametric nonlinear programming (mp-NLP) algorithms for explicit nonlinear model predictive control (mp-NMPC). Three mp-NLP algorithms for NMPC are discussed, based on which novel mp-NMPC controllers are derived. The performance of the explicit controllers are then tested and compared in a simulation example involving the operation of a continuous stirred-tank reactor (CSTR). © 2010 American Chemical Society.

  3. On the complexity of computing two nonlinearity measures

    DEFF Research Database (Denmark)

    Find, Magnus Gausdal

    2014-01-01

    We study the computational complexity of two Boolean nonlinearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time 2O(n) given the truth table of length 2n, in fact under the same ...

  4. Ripple distribution for nonlinear fiber-optic channels.

    Science.gov (United States)

    Sorokina, Mariia; Sygletos, Stylianos; Turitsyn, Sergei

    2017-02-06

    We demonstrate data rates above the threshold imposed by nonlinearity on conventional optical signals by applying novel probability distribution, which we call ripple distribution, adapted to the properties of the fiber channel. Our results offer a new direction for signal coding, modulation and practical nonlinear distortions compensation algorithms.

  5. Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem

    Energy Technology Data Exchange (ETDEWEB)

    Alchalabi, R.M. [BOC Group, Murray Hill, NJ (United States); Turinsky, P.J. [North Carolina State Univ., Raleigh, NC (United States)

    1996-12-31

    The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.

  6. Measurement and fitting techniques for the assessment of material nonlinearity using nonlinear Rayleigh waves

    Energy Technology Data Exchange (ETDEWEB)

    Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)

    2015-03-31

    This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.

  7. Algorithm 896: LSA: Algorithms for Large-Scale Optimization

    Czech Academy of Sciences Publication Activity Database

    Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan

    2009-01-01

    Roč. 36, č. 3 (2009), 16-1-16-29 ISSN 0098-3500 R&D Pro jects: GA AV ČR IAA1030405; GA ČR GP201/06/P397 Institutional research plan: CEZ:AV0Z10300504 Keywords : algorithms * design * large-scale optimization * large-scale nonsmooth optimization * large-scale nonlinear least squares * large-scale nonlinear minimax * large-scale systems of nonlinear equations * sparse pro blems * partially separable pro blems * limited-memory methods * discrete Newton methods * quasi-Newton methods * primal interior-point methods Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.904, year: 2009

  8. Ranking scientific publications: the effect of nonlinearity

    Science.gov (United States)

    Yao, Liyang; Wei, Tian; Zeng, An; Fan, Ying; di, Zengru

    2014-10-01

    Ranking the significance of scientific publications is a long-standing challenge. The network-based analysis is a natural and common approach for evaluating the scientific credit of papers. Although the number of citations has been widely used as a metric to rank papers, recently some iterative processes such as the well-known PageRank algorithm have been applied to the citation networks to address this problem. In this paper, we introduce nonlinearity to the PageRank algorithm when aggregating resources from different nodes to further enhance the effect of important papers. The validation of our method is performed on the data of American Physical Society (APS) journals. The results indicate that the nonlinearity improves the performance of the PageRank algorithm in terms of ranking effectiveness, as well as robustness against malicious manipulations. Although the nonlinearity analysis is based on the PageRank algorithm, it can be easily extended to other iterative ranking algorithms and similar improvements are expected.

  9. Ranking scientific publications: the effect of nonlinearity.

    Science.gov (United States)

    Yao, Liyang; Wei, Tian; Zeng, An; Fan, Ying; Di, Zengru

    2014-10-17

    Ranking the significance of scientific publications is a long-standing challenge. The network-based analysis is a natural and common approach for evaluating the scientific credit of papers. Although the number of citations has been widely used as a metric to rank papers, recently some iterative processes such as the well-known PageRank algorithm have been applied to the citation networks to address this problem. In this paper, we introduce nonlinearity to the PageRank algorithm when aggregating resources from different nodes to further enhance the effect of important papers. The validation of our method is performed on the data of American Physical Society (APS) journals. The results indicate that the nonlinearity improves the performance of the PageRank algorithm in terms of ranking effectiveness, as well as robustness against malicious manipulations. Although the nonlinearity analysis is based on the PageRank algorithm, it can be easily extended to other iterative ranking algorithms and similar improvements are expected.

  10. Nonlinear Optimization with Financial Applications

    CERN Document Server

    Bartholomew-Biggs, Michael

    2005-01-01

    The book introduces the key ideas behind practical nonlinear optimization. Computational finance - an increasingly popular area of mathematics degree programs - is combined here with the study of an important class of numerical techniques. The financial content of the book is designed to be relevant and interesting to specialists. However, this material - which occupies about one-third of the text - is also sufficiently accessible to allow the book to be used on optimization courses of a more general nature. The essentials of most currently popular algorithms are described, and their performan

  11. SPP propagation in nonlinear glass-metal interface

    KAUST Repository

    Sagor, Rakibul Hasan

    2011-12-01

    The non-linear propagation of Surface-Plasmon-Polaritons (SPP) in single interface of metal and chalcogenide glass (ChG) is considered. A time domain simulation algorithm is developed using the Finite Difference Time Domain (FDTD) method. The general polarization algorithm incorporated in the auxiliary differential equation (ADE) is used to model frequency-dependent dispersion relation and third-order nonlinearity of ChG. The main objective is to observe the nonlinear behavior of SPP propagation and study the dynamics of the whole structure. © 2011 IEEE.

  12. The (G/G)-expansion method for a discrete nonlinear Schrödinger ...

    Indian Academy of Sciences (India)

    With the aid of symbolic computation, we choose a discrete nonlinear Schrödinger equation to illustrate the validity and advantages of the improved algorithm. As a result ... It is shown that the improved algorithm is effective and can be used for many other nonlinear differential-difference equations in mathematical physics.

  13. The Volterra's integral equation theory for accelerator single-freedom nonlinear components

    International Nuclear Information System (INIS)

    Wang Sheng; Xie Xi

    1996-01-01

    The Volterra's integral equation equivalent to the dynamic equation of accelerator single-freedom nonlinear components is given, starting from which the transport operator of accelerator single-freedom nonlinear components and its inverse transport operator are obtained. Therefore, another algorithm for the expert system of the beam transport operator of accelerator single-freedom nonlinear components is developed

  14. Parameter Estimation and Prediction of a Nonlinear Storage Model: an algebraic approach

    NARCIS (Netherlands)

    Doeswijk, T.G.; Keesman, K.J.

    2005-01-01

    Generally, parameters that are nonlinear in system models are estimated by nonlinear least-squares optimization algorithms. In this paper, if a nonlinear discrete-time model with a polynomial quotient structure in input, output, and parameters, a method is proposed to re-parameterize the model such

  15. New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schroedinger Equation

    International Nuclear Information System (INIS)

    Yang Qin; Dai Chaoqing; Zhang Jiefang

    2005-01-01

    Some new exact travelling wave and period solutions of discrete nonlinear Schroedinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.

  16. FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE) NONLINEAR CALCULATIONS OF PLATES AND SHELLS

    OpenAIRE

    Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.

    2014-01-01

    Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

  17. FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS

    Directory of Open Access Journals (Sweden)

    Bazhenov V.A.

    2014-06-01

    Full Text Available Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

  18. Nonlinear Impairment Compensation Using Expectation Maximization for PDM 16-QAM Systems

    DEFF Research Database (Denmark)

    Zibar, Darko; Winther, Ole; Franceschi, Niccolo

    2012-01-01

    We show experimentally that by using non-linear signal processing based algorithm, expectation maximization, nonlinear system tolerance can be increased by 2 dB. Expectation maximization is also effective in combating I/Q modulator nonlinearities and laser linewidth....

  19. Benchmarking monthly homogenization algorithms

    Science.gov (United States)

    Venema, V. K. C.; Mestre, O.; Aguilar, E.; Auer, I.; Guijarro, J. A.; Domonkos, P.; Vertacnik, G.; Szentimrey, T.; Stepanek, P.; Zahradnicek, P.; Viarre, J.; Müller-Westermeier, G.; Lakatos, M.; Williams, C. N.; Menne, M.; Lindau, R.; Rasol, D.; Rustemeier, E.; Kolokythas, K.; Marinova, T.; Andresen, L.; Acquaotta, F.; Fratianni, S.; Cheval, S.; Klancar, M.; Brunetti, M.; Gruber, C.; Prohom Duran, M.; Likso, T.; Esteban, P.; Brandsma, T.

    2011-08-01

    The COST (European Cooperation in Science and Technology) Action ES0601: Advances in homogenization methods of climate series: an integrated approach (HOME) has executed a blind intercomparison and validation study for monthly homogenization algorithms. Time series of monthly temperature and precipitation were evaluated because of their importance for climate studies and because they represent two important types of statistics (additive and multiplicative). The algorithms were validated against a realistic benchmark dataset. The benchmark contains real inhomogeneous data as well as simulated data with inserted inhomogeneities. Random break-type inhomogeneities were added to the simulated datasets modeled as a Poisson process with normally distributed breakpoint sizes. To approximate real world conditions, breaks were introduced that occur simultaneously in multiple station series within a simulated network of station data. The simulated time series also contained outliers, missing data periods and local station trends. Further, a stochastic nonlinear global (network-wide) trend was added. Participants provided 25 separate homogenized contributions as part of the blind study as well as 22 additional solutions submitted after the details of the imposed inhomogeneities were revealed. These homogenized datasets were assessed by a number of performance metrics including (i) the centered root mean square error relative to the true homogeneous value at various averaging scales, (ii) the error in linear trend estimates and (iii) traditional contingency skill scores. The metrics were computed both using the individual station series as well as the network average regional series. The performance of the contributions depends significantly on the error metric considered. Contingency scores by themselves are not very informative. Although relative homogenization algorithms typically improve the homogeneity of temperature data, only the best ones improve precipitation data

  20. Automatic mesh refinement and local multigrid methods for contact problems: application to the Pellet-Cladding mechanical Interaction

    International Nuclear Information System (INIS)

    Liu, Hao

    2016-01-01

    This Ph.D. work takes place within the framework of studies on Pellet-Cladding mechanical Interaction (PCI) which occurs in the fuel rods of pressurized water reactor. This manuscript focuses on automatic mesh refinement to simulate more accurately this phenomena while maintaining acceptable computational time and memory space for industrial calculations. An automatic mesh refinement strategy based on the combination of the Local Defect Correction multigrid method (LDC) with the Zienkiewicz and Zhu a posteriori error estimator is proposed. The estimated error is used to detect the zones to be refined, where the local sub-grids of the LDC method are generated. Several stopping criteria are studied to end the refinement process when the solution is accurate enough or when the refinement does not improve the global solution accuracy anymore. Numerical results for elastic 2D test cases with pressure discontinuity show the efficiency of the proposed strategy. The automatic mesh refinement in case of unilateral contact problems is then considered. The strategy previously introduced can be easily adapted to the multi-body refinement by estimating solution error on each body separately. Post-processing is often necessary to ensure the conformity of the refined areas regarding the contact boundaries. A variety of numerical experiments with elastic contact (with or without friction, with or without an initial gap) confirms the efficiency and adaptability of the proposed strategy. (author) [fr

  1. Design with Nonlinear Constraints

    KAUST Repository

    Tang, Chengcheng

    2015-12-10

    Most modern industrial and architectural designs need to satisfy the requirements of their targeted performance and respect the limitations of available fabrication technologies. At the same time, they should reflect the artistic considerations and personal taste of the designers, which cannot be simply formulated as optimization goals with single best solutions. This thesis aims at a general, flexible yet e cient computational framework for interactive creation, exploration and discovery of serviceable, constructible, and stylish designs. By formulating nonlinear engineering considerations as linear or quadratic expressions by introducing auxiliary variables, the constrained space could be e ciently accessed by the proposed algorithm Guided Projection, with the guidance of aesthetic formulations. The approach is introduced through applications in different scenarios, its effectiveness is demonstrated by examples that were difficult or even impossible to be computationally designed before. The first application is the design of meshes under both geometric and static constraints, including self-supporting polyhedral meshes that are not height fields. Then, with a formulation bridging mesh based and spline based representations, the application is extended to developable surfaces including origami with curved creases. Finally, general approaches to extend hard constraints and soft energies are discussed, followed by a concluding remark outlooking possible future studies.

  2. Iterative solution of a nonlinear system arising in phase change problems

    International Nuclear Information System (INIS)

    Williams, M.A.

    1987-01-01

    We consider several iterative methods for solving the nonlinear system arising from an enthalpy formulation of a phase change problem. We present the formulation of the problem. Implicit discretization of the governing equations results in a mildly nonlinear system at each time step. We discuss solving this system using Jacobi, Gauss-Seidel, and SOR iterations and a new modified preconditioned conjugate gradient (MPCG) algorithm. The new MPCG algorithm and its properties are discussed in detail. Numerical results are presented comparing the performance of the SOR algorithm and the MPCG algorithm with 1-step SSOR preconditioning. The MPCG algorithm exhibits a superlinear rate of convergence. The SOR algorithm exhibits a linear rate of convergence. Thus, the MPCG algorithm requires fewer iterations to converge than the SOR algorithm. However in most cases, the SOR algorithm requires less total computation time than the MPCG algorithm. Hence, the SOR algorithm appears to be more appropriate for the class of problems considered. 27 refs., 11 figs

  3. On Poisson Nonlinear Transformations

    Directory of Open Access Journals (Sweden)

    Nasir Ganikhodjaev

    2014-01-01

    Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.

  4. Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding

    KAUST Repository

    Desmal, Abdulla; Bagci, Hakan

    2015-01-01

    A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.

  5. Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding

    KAUST Repository

    Desmal, Abdulla

    2015-04-13

    A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.

  6. Algorithms for computational fluid dynamics n parallel processors

    International Nuclear Information System (INIS)

    Van de Velde, E.F.

    1986-01-01

    A study of parallel algorithms for the numerical solution of partial differential equations arising in computational fluid dynamics is presented. The actual implementation on parallel processors of shared and nonshared memory design is discussed. The performance of these algorithms is analyzed in terms of machine efficiency, communication time, bottlenecks and software development costs. For elliptic equations, a parallel preconditioned conjugate gradient method is described, which has been used to solve pressure equations discretized with high order finite elements on irregular grids. A parallel full multigrid method and a parallel fast Poisson solver are also presented. Hyperbolic conservation laws were discretized with parallel versions of finite difference methods like the Lax-Wendroff scheme and with the Random Choice method. Techniques are developed for comparing the behavior of an algorithm on different architectures as a function of problem size and local computational effort. Effective use of these advanced architecture machines requires the use of machine dependent programming. It is shown that the portability problems can be minimized by introducing high level operations on vectors and matrices structured into program libraries

  7. Advances in nonlinear optics

    CERN Document Server

    Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong

    2015-01-01

    This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.

  8. The second order extended Kalman filter and Markov nonlinear filter for data processing in interferometric systems

    International Nuclear Information System (INIS)

    Ermolaev, P; Volynsky, M

    2014-01-01

    Recurrent stochastic data processing algorithms using representation of interferometric signal as output of a dynamic system, which state is described by vector of parameters, in some cases are more effective, compared with conventional algorithms. Interferometric signals depend on phase nonlinearly. Consequently it is expedient to apply algorithms of nonlinear stochastic filtering, such as Kalman type filters. An application of the second order extended Kalman filter and Markov nonlinear filter that allows to minimize estimation error is described. Experimental results of signals processing are illustrated. Comparison of the algorithms is presented and discussed.

  9. Finding all solutions of nonlinear equations using the dual simplex method

    Science.gov (United States)

    Yamamura, Kiyotaka; Fujioka, Tsuyoshi

    2003-03-01

    Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations using the dual simplex method. In this letter, an improved version of the LP test algorithm is proposed. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time.

  10. Algorithmic alternatives

    International Nuclear Information System (INIS)

    Creutz, M.

    1987-11-01

    A large variety of Monte Carlo algorithms are being used for lattice gauge simulations. For purely bosonic theories, present approaches are generally adequate; nevertheless, overrelaxation techniques promise savings by a factor of about three in computer time. For fermionic fields the situation is more difficult and less clear. Algorithms which involve an extrapolation to a vanishing step size are all quite closely related. Methods which do not require such an approximation tend to require computer time which grows as the square of the volume of the system. Recent developments combining global accept/reject stages with Langevin or microcanonical updatings promise to reduce this growth to V/sup 4/3/

  11. Combinatorial algorithms

    CERN Document Server

    Hu, T C

    2002-01-01

    Newly enlarged, updated second edition of a valuable text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discusses binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. 153 black-and-white illus. 23 tables.Newly enlarged, updated second edition of a valuable, widely used text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discussed are binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. New to this edition: Chapter 9

  12. Quantum Nonlinear Optics

    CERN Document Server

    Hanamura, Eiichi; Yamanaka, Akio

    2007-01-01

    This graduate-level textbook gives an introductory overview of the fundamentals of quantum nonlinear optics. Based on the quantum theory of radiation, Quantum Nonlinear Optics incorporates the exciting developments in novel nonlinear responses of materials (plus laser oscillation and superradiance) developed over the past decade. It deals with the organization of radiation field, interaction between electronic system and radiation field, statistics of light, mutual manipulation of light and matter, laser oscillation, dynamics of light, nonlinear optical response, and nonlinear spectroscopy, as well as ultrashort and ultrastrong laser pulse. Also considered are Q-switching, mode locking and pulse compression. Experimental and theoretical aspects are intertwined throughout.

  13. Nonlinear dynamics and complexity

    CERN Document Server

    Luo, Albert; Fu, Xilin

    2014-01-01

    This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

  14. Distributed nonlinear optical response

    DEFF Research Database (Denmark)

    Nikolov, Nikola Ivanov

    2005-01-01

    of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....

  15. Identification of a Class of Non-linear State Space Models using RPE Techniques

    DEFF Research Database (Denmark)

    Zhou, Wei-Wu; Blanke, Mogens

    1989-01-01

    The RPE (recursive prediction error) method in state-space form is developed in the nonlinear systems and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions...... of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows a quite convincing performance of the filter as combined parameter and state estimator...

  16. On the efficiency of chaos optimization algorithms for global optimization

    International Nuclear Information System (INIS)

    Yang Dixiong; Li Gang; Cheng Gengdong

    2007-01-01

    Chaos optimization algorithms as a novel method of global optimization have attracted much attention, which were all based on Logistic map. However, we have noticed that the probability density function of the chaotic sequences derived from Logistic map is a Chebyshev-type one, which may affect the global searching capacity and computational efficiency of chaos optimization algorithms considerably. Considering the statistical property of the chaotic sequences of Logistic map and Kent map, the improved hybrid chaos-BFGS optimization algorithm and the Kent map based hybrid chaos-BFGS algorithm are proposed. Five typical nonlinear functions with multimodal characteristic are tested to compare the performance of five hybrid optimization algorithms, which are the conventional Logistic map based chaos-BFGS algorithm, improved Logistic map based chaos-BFGS algorithm, Kent map based chaos-BFGS algorithm, Monte Carlo-BFGS algorithm, mesh-BFGS algorithm. The computational performance of the five algorithms is compared, and the numerical results make us question the high efficiency of the chaos optimization algorithms claimed in some references. It is concluded that the efficiency of the hybrid optimization algorithms is influenced by the statistical property of chaotic/stochastic sequences generated from chaotic/stochastic algorithms, and the location of the global optimum of nonlinear functions. In addition, it is inappropriate to advocate the high efficiency of the global optimization algorithms only depending on several numerical examples of low-dimensional functions

  17. Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations

    CERN Document Server

    Aliyu, MDS

    2011-01-01

    A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter

  18. Autodriver algorithm

    Directory of Open Access Journals (Sweden)

    Anna Bourmistrova

    2011-02-01

    Full Text Available The autodriver algorithm is an intelligent method to eliminate the need of steering by a driver on a well-defined road. The proposed method performs best on a four-wheel steering (4WS vehicle, though it is also applicable to two-wheel-steering (TWS vehicles. The algorithm is based on coinciding the actual vehicle center of rotation and road center of curvature, by adjusting the kinematic center of rotation. The road center of curvature is assumed prior information for a given road, while the dynamic center of rotation is the output of dynamic equations of motion of the vehicle using steering angle and velocity measurements as inputs. We use kinematic condition of steering to set the steering angles in such a way that the kinematic center of rotation of the vehicle sits at a desired point. At low speeds the ideal and actual paths of the vehicle are very close. With increase of forward speed the road and tire characteristics, along with the motion dynamics of the vehicle cause the vehicle to turn about time-varying points. By adjusting the steering angles, our algorithm controls the dynamic turning center of the vehicle so that it coincides with the road curvature center, hence keeping the vehicle on a given road autonomously. The position and orientation errors are used as feedback signals in a closed loop control to adjust the steering angles. The application of the presented autodriver algorithm demonstrates reliable performance under different driving conditions.

  19. Explicit Nonlinear Model Predictive Control Theory and Applications

    CERN Document Server

    Grancharova, Alexandra

    2012-01-01

    Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø  Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...

  20. Nonlinear observer based fault detection and isolation for a momentum wheel

    DEFF Research Database (Denmark)

    Jensen, Hans-Christian Becker; Wisniewski, Rafal

    2001-01-01

    This article realizes nonlinear Fault Detection and Isolation for a momentum wheel. The Fault Detection and Isolation is based on a Failure Mode and Effect Analysis, which states which faults might occur and can be detected. The algorithms presented in this paper are based on a geometric approach...... toachieve nonlinear Fault Detection and Isolation. The proposed algorithms are tested in a simulation study and the pros and cons of the algorithm are discussed....