Nonlinear Multigrid for Reservoir Simulation
DEFF Research Database (Denmark)
Christensen, Max la Cour; Eskildsen, Klaus Langgren; Engsig-Karup, Allan Peter
2016-01-01
A feasibility study is presented on the effectiveness of applying nonlinear multigrid methods for efficient reservoir simulation of subsurface flow in porous media. A conventional strategy modeled after global linearization by means of Newton’s method is compared with an alternative strategy...... modeled after local linearization, leading to a nonlinear multigrid method in the form of the full-approximation scheme (FAS). It is demonstrated through numerical experiments that, without loss of robustness, the FAS method can outperform the conventional techniques in terms of algorithmic and numerical...... 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...
Multigrid Algorithms for Domain-Wall Fermions
Cohen, Saul D; Clark, M A; Osborn, J C
2012-01-01
We describe an adaptive multigrid algorithm for solving inverses of the domain-wall fermion operator. Our multigrid algorithm uses an adaptive projection of near-null vectors of the domain-wall operator onto coarser four-dimensional lattices. This extension of multigrid techniques to a chiral fermion action will greatly reduce overall computation cost, and the elimination of the fifth dimension in the coarse space reduces the relative cost of using chiral fermions compared to discarding this symmetry. We demonstrate near-elimination of critical slowing as the quark mass is reduced and small volume dependence, which may be suppressed by taking advantage of the recursive nature of the algorithm.
Multigrid Methods for Nonlinear Problems: An Overview
Energy Technology Data Exchange (ETDEWEB)
Henson, V E
2002-12-23
Since their early application to elliptic partial differential equations, multigrid methods have been applied successfully to a large and growing class of problems, from elasticity and computational fluid dynamics to geodetics and molecular structures. Classical multigrid begins with a two-grid process. First, iterative relaxation is applied, whose effect is to smooth the error. Then a coarse-grid correction is applied, in which the smooth error is determined on a coarser grid. This error is interpolated to the fine grid and used to correct the fine-grid approximation. Applying this method recursively to solve the coarse-grid problem leads to multigrid. The coarse-grid correction works because the residual equation is linear. But this is not the case for nonlinear problems, and different strategies must be employed. In this presentation we describe how to apply multigrid to nonlinear problems. There are two basic approaches. The first is to apply a linearization scheme, such as the Newton's method, and to employ multigrid for the solution of the Jacobian system in each iteration. The second is to apply multigrid directly to the nonlinear problem by employing the so-called Full Approximation Scheme (FAS). In FAS a nonlinear iteration is applied to smooth the error. The full equation is solved on the coarse grid, after which the coarse-grid error is extracted from the solution. This correction is then interpolated and applied to the fine grid approximation. We describe these methods in detail, and present numerical experiments that indicate the efficacy of them.
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.
A novel and scalable Multigrid algorithm for many-core architectures
Becerra-Sagredo, Julian; Mandujano, Francisco
2011-01-01
Multigrid algorithms are among the fastest iterative methods known today for solving large linear and some non-linear systems of equations. Greatly optimized for serial operation, they still have a great potential for parallelism not fully realized. In this work, we present a novel multigrid algorithm designed to work entirely inside many-core architectures like the graphics processing units (GPUs), without memory transfers between the GPU and the central processing unit (CPU), avoiding low bandwitdth communications. The algorithm is denoted as the high occupancy multigrid (HOMG) because it makes use of entire grid operations with interpolations and relaxations fused into one task, providing useful work for every thread in the grid. For a given accuracy, its number of operations scale linearly with the total number of nodes in the grid. Perfect scalability is observed for a large number of processors.
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
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...... 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), were less successful due to lack of such good approximation...... 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...
Comparative Convergence Analysis of Nonlinear AMLI-Cycle Multigrid
Energy Technology Data Exchange (ETDEWEB)
Hu, Xiaozhe [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mathematics; Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Xu, Jinchao [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mathematics
2013-04-30
The purpose of our paper is to provide a comprehensive convergence analysis of the nonlinear algebraic multilevel iteration (AMLI)-cycle multigrid (MG) method for symmetric positive definite problems. We show that the nonlinear AMLI-cycle MG method is uniformly convergent, based on classical assumptions for approximation and smoothing properties. Furthermore, under only the assumption that the smoother is convergent, we show that the nonlinear AMLI-cycle method is always better (or not worse) than the respective V-cycle MG method. Finally, numerical experiments are presented to illustrate the theoretical results.
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.
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.
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.
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.
Dynamic Critical Behavior of Multi-Grid Monte Carlo for Two-Dimensional Nonlinear $\\sigma$-Models
Mana, Gustavo; Mendes, Tereza; Pelissetto, Andrea; Sokal, Alan D.
1995-01-01
We introduce a new and very convenient approach to multi-grid Monte Carlo (MGMC) algorithms for general nonlinear $\\sigma$-models: it is based on embedding an $XY$ model into the given $\\sigma$-model, and then updating the induced $XY$ model using a standard $XY$-model MGMC code. We study the dynamic critical behavior of this algorithm for the two-dimensional $O(N)$ $\\sigma$-models with $N = 3,4,8$ and for the $SU(3)$ principal chiral model. We find that the dynamic critical exponent $z$ vari...
An Assessment of Linear Versus Non-linear Multigrid Methods for Unstructured Mesh Solvers
2001-05-01
problems is investigated. The first case consists of a transient radiation-diffusion problem for which an exact linearization is available, while the...to the Jacobian of a second-order accurate discretization. When an exact linearization is employed, the linear and non-linear multigrid methods
Institute of Scientific and Technical Information of China (English)
Hong-ying Man; Zhong-ci Shi
2006-01-01
In this paper, we discuss the finite volume element method of P1-nonconforming quadrilateral element for elliptic problems and obtain optimal error estimates for general quadrilateral partition. An optimal cascadic multigrid algorithm is proposed to solve the nonsymmetric large-scale system resulting from such discretization. Numerical experiments are reported to support our theoretical results.
Multigrid technique incorporated algorithm for CMP lubrication equations
Institute of Scientific and Technical Information of China (English)
ZHANG Chaohui; LUO Jianbin; WEN Shizhu
2004-01-01
Chemical mechanical polishing(CMP)is a manufacturing process used to achieve required high levels of global and local planarity,which involves a combination of chemical erosion and mechanical action.The study on mechanical removal action of CMP with hydrodynamic lubrication involved will help us to get some insights into the mechanism of CMP and to solve the lubrication problem of CMP.In this paper,a full approach scheme of multigrid technique incorporated with line relaxation is introduced for accelerating the convergence.The effects of various parameters on load and moments are simulated and the results of computation are reported.
Directory of Open Access Journals (Sweden)
Yidu Yang
2012-01-01
Full Text Available This paper discusses highly finite element algorithms for the eigenvalue problem of electric field. Combining the mixed finite element method with the Rayleigh quotient iteration method, a new multi-grid discretization scheme and an adaptive algorithm are proposed and applied to the eigenvalue problem of electric field. Theoretical analysis and numerical results show that the computational schemes established in the paper have high efficiency.
Nonlinear algebraic multigrid for constrained solid mechanics problems using Trilinos
Gee, M.W.; R. S. Tuminaro
2012-01-01
The application of the finite element method to nonlinear solid mechanics problems results in the neccessity to repeatedly solve a large nonlinear set of equations. In this paper we limit ourself to problems arising in constrained solid mechanics problems. It is common to apply some variant of Newton?s method or a Newton? Krylov method to such problems. Often, an analytic Jacobian matrix is formed and used in the above mentioned methods. However, if no analytic Jacobian is given, Newton metho...
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.
A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition
Bonito, Andrea
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Ruge, J.; Li, Y.; McCormick, S.F. [and others
1994-12-31
The formulation and time discretization of problems in meteorology are often tailored to the type of efficient solvers available for use on the discrete problems obtained. A common procedure is to formulate the problem so that a constant (or latitude-dependent) coefficient Poisson-like equation results at each time step, which is then solved using spectral methods. This both limits the scope of problems that can be handled and requires linearization by forward extrapolation of nonlinear terms, which, in turn, requires filtering to control noise. Multigrid methods do not suffer these limitations, and can be applied directly to systems of nonlinear equations with variable coefficients. Here, a global barotropic semi-Lagrangian model, developed by the authors, is presented which results in a system of three coupled nonlinear equations to be solved at each time step. A multigrid method for the solution of these equations is described, and results are presented.
Institute of Scientific and Technical Information of China (English)
Zhang Laiping; Zhao Zhong; Chang Xinghua; He Xin
2013-01-01
A hybrid grid generation technique and a multigrid/parallel algorithm are presented in this paper for turbulence flow simulations over three-dimensional (3D) complex geometries.The hybrid grid generation technique is based on an agglomeration method of anisotropic tetrahedrons.Firstly,the complex computational domain is covered by pure tetrahedral grids,in which anisotropic tetrahedrons are adopted to discrete the boundary layer and isotropic tetrahedrons in the outer field.Then,the anisotropic tetrahedrons in the boundary layer are agglomerated to generate prismatic grids.The agglomeration method can improve the grid quality in boundary layer and reduce the grid quantity to enhance the numerical accuracy and efficiency.In order to accelerate the convergence history,a multigrid/parallel algorithm is developed also based on anisotropic agglomeration approach.The numerical results demonstrate the excellent accelerating capability of this multigrid method.
A Multigrid Block LU-SGS Algorithm for Euler Equations on Unstructured Grids
Institute of Scientific and Technical Information of China (English)
Ruo Li; Xin Wang; Weibo Zhao
2008-01-01
We propose an efficient and robust algorithm to solve the steady Euler equations on unstructured grids. The new algorithm is a Newton-iteration method in which each iteration step is a linear multigrid method using block lower-upper symmetric Gauss-Seidel (LU-SGS) iteration as its smoother. To regularize the Jacobian matrix of Newton-iteration, we adopted a local residual dependent regularization as the replace ment of the standard time-stepping relaxation technique based on the local CFL number. The proposed method can be extended to high order approximations and three spatial dimensions in a nature way. The solver was tested on a sequence of benchmark prob lems on both quasi-uniform and local adaptive meshes. The numerical results illustrated the efficiency and robustness of our algorithm.
Algorithms and data structures for adaptive multigrid elliptic solvers
Vanrosendale, J.
1983-01-01
Adaptive refinement and the complicated data structures required to support it are discussed. These data structures must be carefully tuned, especially in three dimensions where the time and storage requirements of algorithms are crucial. Another major issue is grid generation. The options available seem to be curvilinear fitted grids, constructed on iterative graphics systems, and unfitted Cartesian grids, which can be constructed automatically. On several grounds, including storage requirements, the second option seems preferrable for the well behaved scalar elliptic problems considered here. A variety of techniques for treatment of boundary conditions on such grids are reviewed. A new approach, which may overcome some of the difficulties encountered with previous approaches, is also presented.
Energy Technology Data Exchange (ETDEWEB)
Ewing, R.E.; Saevareid, O.; Shen, J. [Texas A& M Univ., College Station, TX (United States)
1994-12-31
A multigrid algorithm for the cell-centered finite difference on equilateral triangular grids for solving second-order elliptic problems is proposed. This finite difference is a four-point star stencil in a two-dimensional domain and a five-point star stencil in a three dimensional domain. According to the authors analysis, the advantages of this finite difference are that it is an O(h{sup 2})-order accurate numerical scheme for both the solution and derivatives on equilateral triangular grids, the structure of the scheme is perhaps the simplest, and its corresponding multigrid algorithm is easily constructed with an optimal convergence rate. They are interested in relaxation of the equilateral triangular grid condition to certain general triangular grids and the application of this multigrid algorithm as a numerically reasonable preconditioner for the lowest-order Raviart-Thomas mixed triangular finite element method. Numerical test results are presented to demonstrate their analytical results and to investigate the applications of this multigrid algorithm on general triangular grids.
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 (pplans was significantly lower than that of the MGS (palgorithms 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.
MAPCUMBA a fast iterative multi-grid map-making algorithm for CMB experiments
Doré, O; Bouchet, F R; Vibert, D; Prunet, S
2001-01-01
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 to 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 N_tod data points along the one dimensional timeline to analyse, the number of operations is O(N_tod ln N_tod) and the memory requirement is O(N_tod). 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.
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.
A multigrid method for the Navier-Stokes and Boussinesq equations
Shi, Zeng; Wesseling, P.
A nonlinear multigrid method is developed for the Navier-Stokes and Boussinesq equations using a discretization of finite volume type on Cartesian staggered grids and a nonlinear collective Gauss-Seidel method for smoothing. A simple multigrid algorithm incorporating the cycles V, F, W and an adaptive multigrid cycle (A cycle) is presented. Numerical experiments are described for a driven square cavity problem and a free convection problem in a rectangular cavity. Of the three cycles tested, namely V, W and A, the A cycle is found to be most efficient. The rate of convergence is shown to improve slightly when the mesh size is decreased. The multigrid method is found to be very much faster than single grid iteration with the smoother.
基于多重网格的SIRT加速算法%Accelerated SIRT Algorithm Based on Multigrid
Institute of Scientific and Technical Information of China (English)
乔灵博; 李亮; 陈志强
2013-01-01
Under the framework of Simultaneous Iterative Reconstruction Technique (SIRT), a new multigrid-based accelerated algorithm is proposed. For each pixel, SIRT updated correction is relevant with pixels which all covered rays go through .In view of this, by using multigrid method, we analyze SIRT and points out its global iterative characteristic .Then inspired by the strategy of "smooth in fine level, correct in coarse level", we achieve the fast SIRT image reconstruction. The new algorithm proposed in this paper aims at reducing computational effort, and does not conflict with other common accelerated algorithms which focus on accelerating the iterative convergence. Numerical experiments show that the new algorithm is better for noise suppression, while the calculation speed in this simulation compared to SIRT is close to double.%在同时迭代重建算法,即SIRT的基础上,提出了一种基于多重网格的加速算法.SIRT算法在对每个像素更新时,更新量与所有穿过该像素的射线所覆盖的其他像素有关.鉴于此,通过运用多重网格的思想,对SIRT算法进行了分析,指出了其全局性的迭代特点,进而根据“细网光滑、粗网校正”,实现较快的SIRT迭代重建.本文提出的新算法主要通过降低计算量来实现加速效果,而与其他常见的加快迭代收敛速度的加速策略并不冲突.数值实验证明,该算法对噪声抑制更好,同时在本文数值实验条件下,计算速度相比SIRT提高接近一倍.
Institute of Scientific and Technical Information of China (English)
SHI; Zhongci
2001-01-01
［1］Bornemann, F., Deuflhard, P., The cascadic multigrid method for elliptic problems, Numer. Math., 996, 75: 35.［2］Bornemann, F., Deuflhard, P., The cascadic multigrid method, The Eighth International Conference on Domain Decomposition Methods for Partial Differential Equations (eds. Glowinski, R., Periaux, J., Shi, Z. et al.), New York: John Wiley and Sons, 997.［3］Bornemann, F., Krause, R., Classical and cascadic multigrid-methodogical comparison, Proceedings of the 9th International Conference on Domain Decomposition (eds. Bjorstad, P., Espedal, M., Keyes, D.), New York: John Wiley and Sons, 998.［4］Shaidurov, V., Some estimates of the rate of convergence for the cascadic conjugate gradient method, Comp. Math. Applic., 996, 3: 6.［5］Shi, Z., Xu, X., Cascadic multigrid method for the second order elliptic problem, East-West J. Numer. Math., 998, 6: 309.［6］Shi, Z., Xu, X., Cascadic multigrid for elliptic problems, East-West J. Numer. Math., 999, 7: 99.［7］Shi, Z., Xu, X., Cascadic multigrid method for the plate bending problem, East-West J. Numer. Math., 998, 6: 37.［8］Braess, D., Dahmen, W., A cascade multigrid algorithm for the Stokes equations, Number. Math., 999, 82: 79.［9］Shi, Z., Xu, X., Cascadic multigrid for parabolic problems, J. Comput. Math., 2000, 8: 450.［10］Ciarlet, P.,The Finite Element Method for Elliptic Problems, Amsterdam: North-Holland, 978.［11］Zienkiewicz, O. C., The Finite Element Method, 3rd. ed., London: McGraw-Hill, 977.［12］Powell, M. J. D., Sabin, M. A., Piecewise quadratic approximations on triangles, ACM Trans. Mat. Software, 977, 3: 36.［13］Xu, J., The auxiliary space method and optimal multigrid precondition techniques for unstructured grids, Computing, 996, 56: 25.［14］Bank, R., Dupont, T., An optimal order process for solving finite element equations, Math. Comput., 980, 36: 35.［15］Brenner, S., Convergence of nonconforming multigrid methods without full elliptic regularity, Math
A multigrid preconditioner for the semiconductor equations
Energy Technology Data Exchange (ETDEWEB)
Meza, J.C. [Sandia National Labs., Albuquerque, NM (United States); Tuminaro, R.S. [Centre European de Recherche et de Formation Avancee en Calcul Scientifique, Toulouse (France)
1994-12-31
Currently, integrated circuits are primarily designed in a {open_quote}trial and error{close_quote} fashion. That is, prototypes are built and improved via experimentation and testing. In the near future, however, it may be possible to significantly reduce the time and cost of designing new devices by using computer simulations. To accurately perform these complex simulations in three dimensions, however, new algorithms and high performance computers are necessary. In this paper the authors discuss the use of multigrid preconditioning inside a semiconductor device modeling code, DANCIR. The DANCIR code is a full three-dimensional simulator capable of computing steady-state solutions of the drift-diffusion equations for a single semiconductor device and has been used to simulate a wide variety of different devices. At the inner core of DANCIR is a solver for the nonlinear equations that arise from the spatial discretization of the drift-diffusion equations on a rectangular grid. These nonlinear equations are resolved using Gummel`s method which requires three symmetric linear systems to be solved within each Gummel iteration. It is the resolution of these linear systems which comprises the dominant computational cost of this code. The original version of DANCIR uses a Cholesky preconditioned conjugate gradient algorithm to solve these linear systems. Unfortunately, this algorithm has a number of disadvantages: (1) it takes many iterations to converge (if it converges), (2) it can require a significant amount of computing time, and (3) it is not very parallelizable. To improve the situation, the authors consider a multigrid preconditioner. The multigrid method uses iterations on a hierarchy of grids to accelerate the convergence on the finest grid.
A NEWTON MULTIGRID METHOD FOR QUASILINEAR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
YU Xijun
2005-01-01
A combination of the classical Newton Method and the multigrid method, i.e.,a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O(NNk) similar to multigrid method for linear parabolic problems.
Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot
2016-01-01
Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which is not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate
Nonlinear evaluations of unconditionally stable explicit algorithms
Institute of Scientific and Technical Information of China (English)
Shuenn-Yih Chang
2009-01-01
Two explicit integration algorithms with unconditional stability for linear elastic systems have been successfully developed for pseudodynamic testing. Their numerical properties in the solution of a linear elastic system have been well explored and their applications to the pseudodynamic testing of a nonlinear system have been shown to be feasible. However, their numerical properties in the solution of a nonlinear system are not apparent. Therefore, the performance of both algorithms for use in the solution of a nonlinear system has been analytically evaluated after introducing an instantaneous degree of nonlinearity. The two algorithms have roughly the same accuracy for a small value of the product of the natural frequency and step size. Meanwhile, the first algorithm is unconditionally stable when the instantaneous degree of nonlinearity is less than or equal to 1, and it becomes conditionally stable when it is greater than 1. The second algorithm is conditionally stable as the instantaneous degree of nonlinearity is less than 1/9, and becomes unstable when it is greater than I. It can have unconditional stability for the range between I/9 and 1. Based on these evaluations, it was concluded that the first algorithm is superior to the second one. Also, both algorithms were found to require commensurate computational efforts, which are much less than needed for the Newmark explicit method in general structural dynamic problems.
Multigrid Methods in Electronic Structure Calculations
Briggs, E L; Bernholc, J
1996-01-01
We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all length scales, thereby permitting efficient calculations for ill-conditioned systems with long length scales or high energy cut-offs. We discuss specific implementations of multigrid and real-space algorithms for electronic structure calculations, including an efficient multigrid-accelerated solver for Kohn-Sham equations, compact yet accurate discretization schemes for the Kohn-Sham and Poisson equations, optimized pseudo\\-potentials for real-space calculations, efficacious computation of ionic forces, and a complex-wavefunction implementation for arbitrary sampling of the Brillioun zone. A particular strength of a real-space multigrid approach is its ready adaptability to massively parallel computer architectures, and we present an implementation for the Cray-T3D with essen...
Combined algorithms in nonlinear problems of magnetostatics
Energy Technology Data Exchange (ETDEWEB)
Gregus, M.; Khoromsky, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.
1988-05-09
To solve boundary problems of magnetostatics in unbounded two- or 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 in nonlinear magnetostatic problems without the preliminary discretization of equations and give some results on the convergence of iterative processes that arise in nonlinear 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.
Self-correcting Multigrid Solver
Energy Technology Data Exchange (ETDEWEB)
Jerome L.V. Lewandowski
2004-06-29
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.
On Multigrid for Overlapping Grids
Energy Technology Data Exchange (ETDEWEB)
Henshaw, W
2004-01-13
The solution of elliptic partial differential equations on composite overlapping grids using multigrid is discussed. An approach is described that provides a fast and memory efficient scheme for the solution of boundary value problems in complex geometries. The key aspects of the new scheme are an automatic coarse grid generation algorithm, an adaptive smoothing technique for adjusting residuals on different component grids, and the use of local smoothing near interpolation boundaries. Other important features include optimizations for Cartesian component grids, the use of over-relaxed Red-Black smoothers and the generation of coarse grid operators through Galerkin averaging. Numerical results in two and three dimensions show that very good multigrid convergence rates can be obtained for both Dirichlet and Neumann/mixed boundary conditions. A comparison to Krylov based solvers shows that the multigrid solver can be much faster and require significantly less memory.
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.
Nonlinear model predictive control theory and algorithms
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...
A Generally Configurable Multigrid Implementation for Transputer Networks
El-Giar, Osama; Hopkins, Tim
1992-01-01
This paper describes the performance of a multigrid method implemented on a transputer-based architecture. We show that the combination of fast floating-point hardware, local memory and fast communication links between processors provide an excellent environment for the parallel implementation of multigrid algorithms. The gain in efficiency obtained by increasing the number of processors is shown to be nearly linear and comparisons are made with published figures for a parallel multigrid Pois...
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Practical Fourier analysis for multigrid methods
Wienands, Roman
2004-01-01
Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detailed and systematic description of local Fourier k-grid (k=1,2,3) analysis for general systems of partial differential equations to provide a framework that answers these questions.This volume contains software that confirms written statements about convergence and efficiency of algorithms and is easily adapted to new applications. Providing theoretical background and the linkage between theory and practice, the text and software quickly combine learning by reading and learning by doing. The book enables understanding of basic principles of multigrid and local Fourier analysis, and also describes the theory important to those who need to delve deeper into the detai...
Iterative restoration algorithms for nonlinear constraint computing
Szu, Harold
A general iterative-restoration principle is introduced to facilitate the implementation of nonlinear optical processors. The von Neumann convergence theorem is generalized to include nonorthogonal subspaces which can be reduced to a special orthogonal projection operator by applying an orthogonality condition. This principle is shown to permit derivation of the Jacobi algorithm, the recursive principle, the van Cittert (1931) deconvolution method, the iteration schemes of Gerchberg (1974) and Papoulis (1975), and iteration schemes using two Fourier conjugate domains (e.g., Fienup, 1981). Applications to restoring the image of a double star and division by hard and soft zeros are discussed, and sample results are presented graphically.
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.
A NEW ALGORITHM OF THE NONLINEAR ADAPTIVE INTERPOLATION
Institute of Scientific and Technical Information of China (English)
Shi Lingfeng; Guo Baolong
2006-01-01
The paper presents a new algorithm of NonLinearly Adaptive Interpolation (NLAI). NLAI is based on both the gradients and the curvature of the signals with the predicted subsection. It is characterized by adaptive nonlinear interpolation method with extracting the characteristics of signals. Experimental research testifies the validity of the algorithm using the echoes of the Ground Penetrating Radar (GPR). A comparison of this algorithm with other traditional algorithms demonstrates that it is feasible.
Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics
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.
Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Adams, Mark F. [Columbia Univ., New York, NY (United States); Samtaney, Ravi [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Brandt, Achi [Weizmann Inst. of Science, Rehovot (Israel)
2013-12-14
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.
Adaptive Algebraic Multigrid Methods
Energy Technology Data Exchange (ETDEWEB)
Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J
2004-04-09
Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
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.
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.
Algorithms for adaptive nonlinear pattern recognition
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
A Genetic Algorithm Approach to Nonlinear Least Squares Estimation
Olinsky, Alan D.; Quinn, John T.; Mangiameli, Paul M.; Chen, Shaw K.
2004-01-01
A common type of problem encountered in mathematics is optimizing nonlinear functions. Many popular algorithms that are currently available for finding nonlinear least squares estimators, a special class of nonlinear problems, are sometimes inadequate. They might not converge to an optimal value, or if they do, it could be to a local rather than…
Block Monotone Iterative Algorithms for Variational Inequalities with Nonlinear Operators
Institute of Scientific and Technical Information of China (English)
Ming-hui Ren; Jin-ping Zeng
2008-01-01
Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established.Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.
A TRUST-REGION ALGORITHM FOR NONLINEAR INEQUALITY CONSTRAINED OPTIMIZATION
Institute of Scientific and Technical Information of China (English)
Xiaojiao Tong; Shuzi Zhou
2003-01-01
This paper presents a new trust-region algorithm for n-dimension nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived,which is the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps, local quadratic convergence theorem is proved for nondegenerate minimizer point. Numerical experiment is presented to show the effectiveness of our approach.
Adaptive Algorithms of Nonlinear Approximation with Finite Terms
Institute of Scientific and Technical Information of China (English)
Wen Bin WEI; Yue Sheng XU; Pei Xin YE
2007-01-01
This paper deals with realizable adaptive algorithms of the nonlinear approximation with finite terms based on wavelets. We present a concrete algorithm by which we may find the required index set Am for the greedy algorithm GPm(·,ψ). This makes the greedy algorithm realize the near best approximation in practice. Moreover, we study the efficiency of the finite-term approximation of another algorithm introduced by Birge and Massart.
Adaptive algebraic multigrid on SIMD architectures
Heybrock, Simon; Georg, Peter; Wettig, Tilo
2015-01-01
We present details of our implementation of the Wuppertal adaptive algebraic multigrid code DD-$\\alpha$AMG on SIMD architectures, with particular emphasis on the Intel Xeon Phi processor (KNC) used in QPACE 2. As a smoother, the algorithm uses a domain-decomposition-based solver code previously developed for the KNC in Regensburg. We optimized the remaining parts of the multigrid code and conclude that it is a very good target for SIMD architectures. Some of the remaining bottlenecks can be eliminated by vectorizing over multiple test vectors in the setup, which is discussed in the contribution of Daniel Richtmann.
Segmental Refinement: A Multigrid Technique for Data Locality
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.
Energy Technology Data Exchange (ETDEWEB)
Vandewalle, S. [Caltech, Pasadena, CA (United States)
1994-12-31
Time-stepping methods for parabolic partial differential equations are essentially sequential. This prohibits the use of massively parallel computers unless the problem on each time-level is very large. This observation has led to the development of algorithms that operate on more than one time-level simultaneously; that is to say, on grids extending in space and in time. The so-called parabolic multigrid methods solve the time-dependent parabolic PDE as if it were a stationary PDE discretized on a space-time grid. The author has investigated the use of multigrid waveform relaxation, an algorithm developed by Lubich and Ostermann. The algorithm is based on a multigrid acceleration of waveform relaxation, a highly concurrent technique for solving large systems of ordinary differential equations. Another method of this class is the time-parallel multigrid method. This method was developed by Hackbusch and was recently subject of further study by Horton. It extends the elliptic multigrid idea to the set of equations that is derived by discretizing a parabolic problem in space and in time.
Variable order variable stepsize algorithm for solving nonlinear Duffing oscillator
Fadly Nurullah Rasedee, Ahmad; Ishak, Norizarina; Raihana Hamzah, Siti; Ijam, Hazizah Mohd; Suleiman, Mohamed; Bibi Ibrahim, Zarina; Sathar, Mohammad Hasan Abdul; Ainna Ramli, Nur; Shuhada Kamaruddin, Nur
2017-09-01
Nonlinear phenomena in science and engineering such as a periodically forced oscillator with nonlinear elasticity are often modeled by the Duffing oscillator (Duffing equation). The Duffling oscillator is a type of nonlinear higher order differential equation. In this research, a numerical approximation for solving the Duffing oscillator directly is introduced using a variable order stepsize (VOS) algorithm coupled with a backward difference formulation. By selecting the appropriate restrictions, the VOS algorithm provides a cost efficient computational code without affecting its accuracy. Numerical results have demonstrated the advantages of a variable order stepsize algorithm over conventional methods in terms of total steps and accuracy.
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...
A Composite Algorithm for Mixed Integer Constrained Nonlinear Optimization.
1980-01-01
algorithm (FLEX) developed by Paviani and Himmelblau [53] is a direct search algorithm for constrained, nonlinear problems. It uses a variation on the...given in an appendix to Himmelblau [32]. Two changes were made to the program as listed in the rcference. Between card number 1340 and 1350 the...1972, pp. 293-308 (32] Himmelblau , D. M., Applied Nonlinear Programming, McGraw-Hill, 1972 (33] Himmelblau , D. M., "A Uniform Evaluation of Unconstrained
Robust Fault Diagnosis Algorithm for a Class of Nonlinear Systems
Directory of Open Access Journals (Sweden)
Hai-gang Xu
2015-01-01
Full Text Available A kind of robust fault diagnosis algorithm to Lipschitz nonlinear system is proposed. The novel disturbances constraint condition of the nonlinear system is derived by group algebra method, and the novel constraint condition can meet the system stability performance. Besides, the defined robust performance index of fault diagnosis observer guarantees the robust. Finally, the effectiveness of the algorithm proposed is proved in the simulations.
An SQP Algorithm for Recourse-based Stochastic Nonlinear Programming
Directory of Open Access Journals (Sweden)
Xinshun Ma
2016-05-01
Full Text Available The stochastic nonlinear programming problem with completed recourse and nonlinear constraints is studied in this paper. We present a sequential quadratic programming method for solving the problem based on the certainty extended nonlinear model. This algorithm is obtained by combing the active set method and filter method. The convergence of the method is established under some standard assumptions. Moreover, a practical design is presented and numerical results are provided.
Non-linear Frequency Scaling Algorithm for FMCW SAR Data
Meta, A.; Hoogeboom, P.; Ligthart, L.P.
2006-01-01
This paper presents a novel approach for processing data acquired with Frequency Modulated Continuous Wave (FMCW) dechirp-on-receive systems by using a non-linear frequency scaling algorithm. The range frequency non-linearity correction, the Doppler shift induced by the continuous motion and the ran
A POSITIVE INTERIOR-POINT ALGORITHM FOR NONLINEAR COMPLEMENTARITY PROBLEMS
Institute of Scientific and Technical Information of China (English)
马昌凤; 梁国平; 陈新美
2003-01-01
A new iterative method, which is called positive interior-point algorithm, is presented for solving the nonlinear complementarity problems. This method is of the desirable feature of robustness. And the convergence theorems of the algorithm is established. In addition, some numerical results are reported.
An Algorithm to Solve Separable Nonlinear Least Square Problem
Directory of Open Access Journals (Sweden)
Wajeb Gharibi
2013-07-01
Full Text Available Separable Nonlinear Least Squares (SNLS problem is a special class of Nonlinear Least Squares (NLS problems, whose objective function is a mixture of linear and nonlinear functions. SNLS has many applications in several areas, especially in the field of Operations Research and Computer Science. Problems related to the class of NLS are hard to resolve having infinite-norm metric. This paper gives a brief explanation about SNLS problem and offers a Lagrangian based algorithm for solving mixed linear-nonlinear minimization problem
Hanyu, Y; Hoshino, K; Ono, A; Sonoda, T; Hirabayashi, H; Karasawa, K; Mitsuhashi, N
2003-01-01
In the convolution/superposition algorithm, the energy spectrum should be modified to make the reconstructed dose distribution consistent with the measured dose distribution. The energy spectrum, which gives the best agreement, is not determined uniquely depending on the reconstruction procedure. In this report, the effects of the characteristics of the energy spectrum on the calculation accuracy are evaluated by comparing the percentage depth dose (PDD) and beam profiles for the reference energy spectrum with those calculated for the modified spectrum in order to optimize the energy spectrum modification procedure when 4 and 10 MV X-ray beams are used. Decreasing the number of energy bins brought a larger decrease rate in the computation accuracy than a decrease rate in computation time. Further, the decrease of the number of energy bins led to a change of the energy spectrum. The balance of the relative fluence weight in a each bin and its average energy, which determines the absoluted dose, are important p...
Coarse-grid selection for parallel algebraic multigrid
Energy Technology Data Exchange (ETDEWEB)
Cleary, A. J., LLNL
1998-06-01
The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG) To date, however, no parallel AMG algorithms exist We introduce a parallel algorithm for the selection of coarse-grid points, a crucial component of AMG, based on modifications of certain paallel independent set algorithms and the application of heuristics designed to insure the quality of the coarse grids A prototype serial version of the algorithm is implemented, and tests are conducted to determine its effect on multigrid convergence, and AMG complexity
Multigrid method for stability problems
Taasan, Shlomo
1988-01-01
The problem of calculating the stability of steady state solutions of differential equations is treated. Leading eigenvalues (i.e., having maximal real part) of large matrices that arise from discretization are to be calculated. An efficient multigrid method for solving these problems is presented. The method begins by obtaining an initial approximation for the dominant subspace on a coarse level using a damped Jacobi relaxation. This proceeds until enough accuracy for the dominant subspace has been obtained. The resulting grid functions are then used as an initial approximation for appropriate eigenvalue problems. These problems are being solved first on coarse levels, followed by refinement until a desired accuracy for the eigenvalues has been achieved. The method employs local relaxation on all levels together with a global change on the coarsest level only, which is designed to separate the different eigenfunctions as well as to update their corresponding eigenvalues. Coarsening is done using the FAS formulation in a non-standard way in which the right hand side of the coarse grid equations involves unknown parameters to be solved for on the coarse grid. This in particular leads to a new multigrid method for calculating the eigenvalues of symmetric problems. Numerical experiments with a model problem demonstrate the effectiveness of the method proposed. Using an FMG algorithm a solution to the level of discretization errors is obtained in just a few work units (less than 10), where a work unit is the work involved in one Jacobi relization on the finest level.
MULTIGRID METHOD FOR A MODIFIED CURVATURE DRIVEN DIFFUSION MODEL FOR IMAGE INPAINTING
Institute of Scientific and Technical Information of China (English)
Carlos Brito-Loeza; Ke Chen
2008-01-01
Digital inpainting is a fundamental problem in image processing and many variational models for this problem have appeared recently in the literature. Among them are the very successfully Total Variation (TV) model [11] designed for local inpainting and its improved version for large scale inpainting: the Curvature-Driven Diffusion (CDD) model [10]. For the above two models, their associated Euler Lagrange equations are highly nonlinear par-tial differential equations. For the TV model there exists a relatively fast and easy to implement fixed point method, so adapting the multigrid method of [24] to here is immedi-ate. For the CDD model however, so far only the well known but usually very slow explicit time marching method has been reported and we explain why the implementation of a fixed point method for the CDD model is not straightforward. Consequently the multigrid method as in [Savage and Chen, Int. J. Comput. Math., 82 (2005), pp. 1001-1015] will not work here. This fact represents a strong limitation to the range of applications of this model since usually fast solutions are expected. In this paper, we introduce a modification designed to enable a fixed point method to work and to preserve the features of the orig-inal CDD model. As a result, a fast and efficient multigrid method is developed for the modified model. Numerical experiments are presented to show the very good performance of the fast algorithm.
Nonlinear smoothing identification algorithm with application to data consistency checks
Idan, M.
1993-01-01
A parameter identification algorithm for nonlinear systems is presented. It is based on smoothing test data with successively improved sets of model parameters. The smoothing, which is iterative, provides all of the information needed to compute the gradients of the smoothing performance measure with respect to the parameters. The parameters are updated using a quasi-Newton procedure, until convergence is achieved. The advantage of this algorithm over standard maximum likelihood identification algorithms is the computational savings in calculating the gradient. This algorithm was used for flight-test data consistency checks based on a nonlinear model of aircraft kinematics. Measurement biases and scale factors were identified. The advantages of the presented algorithm and model are discussed.
Appropriate Algorithms for Nonlinear Time Series Analysis in Psychology
Scheier, Christian; Tschacher, Wolfgang
Chaos theory has a strong appeal for psychology because it allows for the investigation of the dynamics and nonlinearity of psychological systems. Consequently, chaos-theoretic concepts and methods have recently gained increasing attention among psychologists and positive claims for chaos have been published in nearly every field of psychology. Less attention, however, has been paid to the appropriateness of chaos-theoretic algorithms for psychological time series. An appropriate algorithm can deal with short, noisy data sets and yields `objective' results. In the present paper it is argued that most of the classical nonlinear techniques don't satisfy these constraints and thus are not appropriate for psychological data. A methodological approach is introduced that is based on nonlinear forecasting and the method of surrogate data. In artificial data sets and empirical time series we can show that this methodology reliably assesses nonlinearity and chaos in time series even if they are short and contaminated by noise.
An algorithm for earthwork allocation considering non-linear factors
Institute of Scientific and Technical Information of China (English)
WANG Ren-chao; LIU Jin-fei
2008-01-01
For solving the optimization model of earthwork allocation considering non-linear factors, a hybrid al-gorithm combined with the ant algorithm (AA) and particle swarm optimization (PSO) is proposed in this pa-per. Then the proposed method and the LP method are used respectively in solving a linear allocation model of a high rockfill dam project. Results obtained by these two methods are compared each other. It can be conclu-ded that the solution got by the proposed method is extremely approximate to the analytic solution of LP method. The superiority of the proposed method over the LP method in solving a non-linear allocation model is illustrated by a non-linear case. Moreover, further researches on improvement of the algorithm and the allocation model are addressed.
Parallel Algebraic Multigrid Methods - High Performance Preconditioners
Energy Technology Data Exchange (ETDEWEB)
Yang, U M
2004-11-11
The development of high performance, massively parallel computers and the increasing demands of computationally challenging applications have necessitated the development of scalable solvers and preconditioners. One of the most effective ways to achieve scalability is the use of multigrid or multilevel techniques. Algebraic multigrid (AMG) is a very efficient algorithm for solving large problems on unstructured grids. While much of it can be parallelized in a straightforward way, some components of the classical algorithm, particularly the coarsening process and some of the most efficient smoothers, are highly sequential, and require new parallel approaches. This chapter presents the basic principles of AMG and gives an overview of various parallel implementations of AMG, including descriptions of parallel coarsening schemes and smoothers, some numerical results as well as references to existing software packages.
Zeeuw, P.M. de; Tai, X.-C.; Lie, K.A.; Chan, T.F.; Osher, S.
2007-01-01
A second order partial differential operator is applied to an image function. To this end we consider both the Laplacian and a more general elliptic operator. By using a multigrid operator known from the so-called approximation property, we derive a multiresolution decomposition of the image without
Zhao, J.; Vollebregt, E.A.H.; Oosterlee, C.W.
2014-01-01
This paper presents a full multigrid (FMG) technique, which combines a multigrid method, an active set algorithm and a nested iteration technique, to solve a linear complementarity problem (LCP) modeling elastic normal contact problems. The governing system in this LCP is derived from a Fredholm int
Compatible Relaxation and Coarsening in Algebraic Multigrid
Energy Technology Data Exchange (ETDEWEB)
Brannick, J J; Falgout, R D
2009-09-22
We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection. We study its behavior on a number of model problems, and evaluate the performance of an AMG algorithm that incorporates the coarsening approach. Lastly, we introduce a variant of CR that provides a sharper metric of coarse-grid quality and demonstrate its potential with two simple examples.
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.
Impulse position control algorithms for nonlinear systems
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.
A New Subspace Correction Method for Nonlinear Unconstrained Convex Optimization Problems
Institute of Scientific and Technical Information of China (English)
Rong-liang CHEN; Jin-ping ZENG
2012-01-01
This paper gives a new subspace correction algorithm for nonlinear unconstrained convex optimization problems based on the multigrid approach proposed by S.Nash in 2000 and the subspace correction algorithm proposed by X.Tai and J.Xu in 2001.Under some reasonable assumptions,we obtain the convergence as well as a convergence rate estimate for the algorithm.Numerical results show that the algorithm is effective.
A New Superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems
Institute of Scientific and Technical Information of China (English)
Jin-bao Jian; Ran Quan; Qing-jie Hu
2007-01-01
In this paper, the nonlinear minimax problems are discussed. By means of the Sequential Quadratic Programming (SQP), a new descent algorithm for solving the problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a Quadratic Programming (QP) which always has a solution. In order to avoid the Maratos effect, a correction direction is obtained by updating the main direction with a simple explicit formula. Under mild conditions without the strict complementarity, the global and superlinear convergence of the algorithm can be obtained. Finally, some numerical experiments are reported.
An Algorithm for Linearly Constrained Nonlinear Programming Programming Problems.
1980-01-01
ALGORITHM FOR LINEARLY CONSTRAINED NONLINEAR PROGRAMMING PROBLEMS Mokhtar S. Bazaraa and Jamie J. Goode In this paper an algorithm for solving a linearly...distance pro- gramr.ing, as in the works of Bazaraa and Goode 12], and Wolfe [16 can be used for solving this problem. Special methods that take advantage of...34 Pacific Journal of Mathematics, Volume 16, pp. 1-3, 1966. 2. M. S. Bazaraa and J. j. Goode, "An Algorithm for Finding the Shortest Element of a
Sparse Nonlinear Electromagnetic Imaging Accelerated With Projected Steepest Descent Algorithm
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.
Nonlinear Observers for Gyro Calibration Coupled with a Nonlinear Control Algorithm
Thienel, Julie; Sanner, Robert M.
2003-01-01
Nonlinear observers for gyro calibration are presented. The first observer estimates a constant gyro bias. The second observer estimates scale factor errors. The third observer estimates the gyro alignment for three orthogonal gyros. The observers are then combined. The convergence properties of all three observers, and the combined observers, are discussed. Additionally, all three observers are coupled with a nonlinear control algorithm. The stability of each of the resulting closed loop systems is analyzed. Simulated test results are presented for each system.
Concise quantum associative memories with nonlinear search algorithm
Energy Technology Data Exchange (ETDEWEB)
Tchapet Njafa, J.P.; Nana Engo, S.G. [Laboratory of Photonics, Department of Physics, University of Ngaoundere (Cameroon)
2016-02-15
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{sup 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)
A ROBUST TRUST REGION ALGORITHM FOR SOLVING GENERAL NONLINEAR PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Xin-wei Liu; Ya-xiang Yuan
2001-01-01
The trust region approach has been extended to solving nonlinear constrained optimization. Most of these extensions consider only equality constraints and require strong global regularity assumptions. In this paper, a trust region algorithm for solving general nonlinear programming is presented, which solves an unconstrained piecewise quadratic trust region subproblem and a quadratic programming trust region subproblem at each iteration. A new technique for updating the penalty parameter is introduced. Under very mild conditions, the global convergence results are proved. Some local convergence results are also proved. Preliminary numerical results are also reported.
Algebraic dynamics solution to and algebraic dynamics algorithm for nonlinear advection equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
Algebraic dynamics approach and algebraic dynamics algorithm for the solution of nonlinear partial differential equations are applied to the nonlinear advection equa-tion. The results show that the approach is effective for the exact analytical solu-tion and the algorithm has higher precision than other existing algorithms in nu-merical computation for the nonlinear advection equation.
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.
Multigrid Particle-in-cell Simulations of Plasma Microturbulence
Energy Technology Data Exchange (ETDEWEB)
J.L.V. Lewandowski
2003-06-17
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.
On Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms
Institute of Scientific and Technical Information of China (English)
SUN Jie; LU Song-Feng; Samuel L.Braunstein
2013-01-01
In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model — an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.
A General Nonlinear Optimization Algorithm for Lower Bound Limit Analysis
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars
2003-01-01
The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular...... finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound...
Particle Swarm Optimization-Proximal Point Algorithm for Nonlinear Complementarity Problems
Chai Jun-Feng; Wang Shu-Yan
2013-01-01
A new algorithm is presented for solving the nonlinear complementarity problem by combining the particle swarm and proximal point algorithm, which is called the particle swarm optimization-proximal point algorithm. The algorithm mainly transforms nonlinear complementarity problems into unconstrained optimization problems of smooth functions using the maximum entropy function and then optimizes the problem using the proximal point algorithm as the outer algorithm and particle swarm algorithm a...
A multigrid solver for the semiconductor equations
Bachmann, Bernhard
1993-01-01
We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.
A nonlinear regression model-based predictive control algorithm.
Dubay, R; Abu-Ayyad, M; Hernandez, J M
2009-04-01
This paper presents a unique approach for designing a nonlinear regression model-based predictive controller (NRPC) for single-input-single-output (SISO) and multi-input-multi-output (MIMO) processes that are common in industrial applications. The innovation of this strategy is that the controller structure allows nonlinear open-loop modeling to be conducted while closed-loop control is executed every sampling instant. Consequently, the system matrix is regenerated every sampling instant using a continuous function providing a more accurate prediction of the plant. Computer simulations are carried out on nonlinear plants, demonstrating that the new approach is easily implemented and provides tight control. Also, the proposed algorithm is implemented on two real time SISO applications; a DC motor, a plastic injection molding machine and a nonlinear MIMO thermal system comprising three temperature zones to be controlled with interacting effects. The experimental closed-loop responses of the proposed algorithm were compared to a multi-model dynamic matrix controller (MPC) with improved results for various set point trajectories. Good disturbance rejection was attained, resulting in improved tracking of multi-set point profiles in comparison to multi-model MPC.
Investigations on application of multigrid method to MHD equilibrium analysis
Energy Technology Data Exchange (ETDEWEB)
Ikuno, Soichiro [Faculty of Engineering Science, School of Engineering, Tokyo Univ. of Technology, Tokyo (Japan)
2000-06-01
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)
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.
Nonlinear system identification and control using state transition algorithm
Yang, Chunhua; Gui, Weihua
2012-01-01
This paper presents a novel optimization method named state transition algorithm (STA) to solve the problem of identification and control for nonlinear system. In the proposed algorithm, a solution to optimization problem is considered as a state, and the updating of a solution equates to the process of state transition, which makes the STA easy to understand and convenient to be implemented. First, the STA is applied to identify the optimal parameters of the estimated system with previously known structure. With the accurate estimated model, an off-line PID controller is then designed optimally by using the STA as well. Experimental results demonstrate the validity of the methodology, and comparison to STA with other optimization algorithms confirms that STA is a promising alternative method for system identification and control due to its stronger search ability, faster convergence speed and more stable performance.
CASCADIC MULTIGRID FOR FINITE VOLUME METHODS FOR ELLIPTIC PROBLEMS
Institute of Scientific and Technical Information of China (English)
Zhong-ci Shi; Xue-jun Xu; Hong-ying Man
2004-01-01
In this paper, some effective cascadic multigrid methods are proposed for solving the large scale symmetric or nonsymmetric algebraic systems arising from the finite volumemethods for second order elliptic problems. Its is shown that these algorithms are optimal in both accuracy and computational complexity. Numerical expermients are repored to support out theory.
Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver
Livne, Oren E
2011-01-01
Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic partial differential equations discretized on unstructured grids with finite elements. A Lean Algebraic Multigrid (LAMG) solver of the linear system Ax=b is presented, where A is a graph Laplacian. LAMG's run time and storage are linear in the number of graph edges. LAMG consists of a setup phase, in which a sequence of increasingly-coarser Laplacian systems is constructed, and an iterative solve phase using multigrid cycles. General graphs pose algorithmic challenges not encountered in traditional applications of algebraic multigrid. LAMG combines a lean piecewise-constant interpolation, judicious node aggregation based on a new node proximity definition, and an energy correction of the coarse-level systems. This results in fast convergence and substantial overhead and memory s...
Parallel multigrid smoothing: polynomial versus Gauss-Seidel
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.
Bonus algorithm for large scale stochastic nonlinear programming problems
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 ...
A trust region algorithm for optimization with nonlinear equality and linear inequality constraints
Institute of Scientific and Technical Information of China (English)
陈中文; 韩继业
1996-01-01
A new algorithm of trust region type is presented to minimize a differentiable function ofmany variables with nonlinear equality and linear inequality constraints. Under the milder conditions, theglobal convergence of the main algorithm is proved. Moreover, since any nonlinear inequality constraint can beconverted into an equation by introducing a slack variable, the trust region method can be used in solving general nonlinear programming problems.
Multigrid Methods for the Computation of Propagators in Gauge Fields
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.
Application of genetic algorithms in nonlinear heat conduction problems.
Kadri, Muhammad Bilal; Khan, Waqar A
2014-01-01
Genetic algorithms are employed to optimize dimensionless temperature in nonlinear heat conduction problems. Three common geometries are selected for the analysis and the concept of minimum entropy generation is used to determine the optimum temperatures under the same constraints. The thermal conductivity is assumed to vary linearly with temperature while internal heat generation is assumed to be uniform. The dimensionless governing equations are obtained for each selected geometry and the dimensionless temperature distributions are obtained using MATLAB. It is observed that GA gives the minimum dimensionless temperature in each selected geometry.
An SQP algorithm for mathematical programs with nonlinear complementarity constraints
Institute of Scientific and Technical Information of China (English)
Zhi-bin ZHU; Jin-bao JIAN; Cong ZHANG
2009-01-01
In this paper,we describe a successive approximation and smooth sequential quadratic programming (SQP) method for mathematical programs with nonlinear complementarity constraints (MPCC). We introduce a class of smooth programs to approximate the MPCC. Using an l1 penalty function,the line search assures global convergence,while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover,we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints (MPEC) when the algorithm terminates finitely.
Non-linear scalable TFETI domain decomposition based contact algorithm
Dobiáš, J.; Pták, S.; Dostál, Z.; Vondrák, V.; Kozubek, T.
2010-06-01
The paper is concerned with the application of our original variant of the Finite Element Tearing and Interconnecting (FETI) domain decomposition method, called the Total FETI (TFETI), to solve solid mechanics problems exhibiting geometric, material, and contact non-linearities. The TFETI enforces the prescribed displacements by the Lagrange multipliers, so that all the subdomains are 'floating', the kernels of their stiffness matrices are known a priori, and the projector to the natural coarse grid is more effective. The basic theory and relationships of both FETI and TFETI are briefly reviewed and a new version of solution algorithm is presented. It is shown that application of TFETI methodology to the contact problems converts the original problem to the strictly convex quadratic programming problem with bound and equality constraints, so that the effective, in a sense optimal algorithms is to be applied. Numerical experiments show that the method exhibits both numerical and parallel scalabilities.
Novel Approach to Nonlinear PID Parameter Optimization Using Ant Colony Optimization Algorithm
Institute of Scientific and Technical Information of China (English)
Duan Hai-bin; Wang Dao-bo; Yu Xiu-fen
2006-01-01
This paper presents an application of an Ant Colony Optimization (ACO) algorithm to optimize the parameters in the design of a type of nonlinear PID controller. The ACO algorithm is a novel heuristic bionic algorithm, which is based on the behaviour of real ants in nature searching for food. In order to optimize the parameters of the nonlinear PID controller using ACO algorithm,an objective function based on position tracing error was constructed, and elitist strategy was adopted in the improved ACO algorithm. Detailed simulation steps are presented. This nonlinear PID controller using the ACO algorithm has high precision of control and quick response.
Genetic algorithms applied to nonlinear and complex domains
Energy Technology Data Exchange (ETDEWEB)
Barash, D; Woodin, A E
1999-06-01
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.
Genetic algorithms applied to nonlinear and complex domains
Energy Technology Data Exchange (ETDEWEB)
Barash, D; Woodin, A E
1999-06-01
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.
Performance investigation of multigrid optimization for DNS-based optimal control problems
Nita, Cornelia; Vandewalle, Stefan; Meyers, Johan
2016-11-01
Optimal control theory in Direct Numerical Simulation (DNS) or Large-Eddy Simulation (LES) of turbulent flow involves large computational cost and memory overhead for the optimization of the controls. In this context, the minimization of the cost functional is typically achieved by employing gradient-based iterative methods such as quasi-Newton, truncated Newton or non-linear conjugate gradient. In the current work, we investigate the multigrid optimization strategy (MGOpt) in order to speed up the convergence of the damped L-BFGS algorithm for DNS-based optimal control problems. The method consists in a hierarchy of optimization problems defined on different representation levels aiming to reduce the computational resources associated with the cost functional improvement on the finest level. We examine the MGOpt efficiency for the optimization of an internal volume force distribution with the goal of reducing the turbulent kinetic energy or increasing the energy extraction in a turbulent wall-bounded flow; problems that are respectively related to drag reduction in boundary layers, or energy extraction in large wind farms. Results indicate that in some cases the multigrid optimization method requires up to a factor two less DNS and adjoint DNS than single-grid damped L-BFGS. The authors acknowledge support from OPTEC (OPTimization in Engineering Center of Excellence, KU Leuven, Grant No PFV/10/002).
Institute of Scientific and Technical Information of China (English)
张建军; 王德人
2004-01-01
In this paper, based on the resuls presented in part I of this paper[18],we present a numerical crabeding algorithm for soling the nonlinear complementarity problem, and prove its convergence carefully. Numerical experiments show that the algorithm is successful.
Energy Technology Data Exchange (ETDEWEB)
Hillstrom, K. E.
1976-02-01
A simulation test technique was developed to evaluate and compare unconstrained nonlinear optimization computer algorithms. Descriptions of the test technique, test problems, computer algorithms tested, and test results are provided. (auth)
MULTIGRID FOR THE MORTAR ELEMENT METHOD WITH LOCALLY P1 NONCONFORMING ELEMENTS
Institute of Scientific and Technical Information of China (English)
毕春加; 李立康
2003-01-01
In this paper we study the theoretical properties of multigrid algorithm for discretization of the Poisson equation in 2D using a mortar element method under the assumption that the triangulations on every subdomain are uniform.We prove the convergence of the W-cycle with a sufficiently large number of smoothing steps.The variable V-cycle multigrid preconditioner are also available.
Adaptive Aggregation-based Domain Decomposition Multigrid for Twisted Mass Fermions
Alexandrou, Constantia; Finkenrath, Jacob; Frommer, Andreas; Kahl, Karsten; Rottmann, Matthias
2016-01-01
The Adaptive Aggregation-based Domain Decomposition Multigrid method (arXiv:1303.1377) is extended for two degenerate flavors of twisted mass fermions. By fine-tuning the parameters we achieve a speed-up of the order of hundred times compared to the conjugate gradient algorithm for the physical value of the pion mass. A thorough analysis of the aggregation parameters is presented, which provides a novel insight into multigrid methods for lattice QCD independently of the fermion discretization.
A modified WTC algorithm for the Painlevé test of nonlinear variable-coefficient PDEs
Zhao, Yin-Long; Liu, Yin-Ping; Li, Zhi-Bin
2009-11-01
A modified WTC algorithm for the Painlevé test of nonlinear PDEs with variable coefficients is proposed. Compared to the Kruskal's simplification algorithm, the modified algorithm further simplifies the computation in the third step of the Painlevé test for variable-coefficient PDEs to some extent. Two examples illustrate the proposed modified algorithm.
Layout optimization with algebraic multigrid methods
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.
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.
Institute of Scientific and Technical Information of China (English)
Igor Boglaev; Matthew Hardy
2008-01-01
This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type.To solve the nonlinear weighted average finite difference scheme for the partial differential equation,we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition.This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. The rate of convergence of the monotone domain decomposition algorithm is estimated.Numerical experiments are presented.
gpICA: A Novel Nonlinear ICA Algorithm Using Geometric Linearization
Directory of Open Access Journals (Sweden)
Nguyen Thang Viet
2007-01-01
Full Text Available A new geometric approach for nonlinear independent component analysis (ICA is presented in this paper. Nonlinear environment is modeled by the popular post nonlinear (PNL scheme. To eliminate the nonlinearity in the observed signals, a novel linearizing method named as geometric post nonlinear ICA (gpICA is introduced. Thereafter, a basic linear ICA is applied on these linearized signals to estimate the unknown sources. The proposed method is motivated by the fact that in a multidimensional space, a nonlinear mixture is represented by a nonlinear surface while a linear mixture is represented by a plane, a special form of the surface. Therefore, by geometrically transforming the surface representing a nonlinear mixture into a plane, the mixture can be linearized. Through simulations on different data sets, superior performance of gpICA algorithm has been shown with respect to other algorithms.
gpICA: A Novel Nonlinear ICA Algorithm Using Geometric Linearization
Nguyen, Thang Viet; Patra, Jagdish Chandra; Emmanuel, Sabu
2006-12-01
A new geometric approach for nonlinear independent component analysis (ICA) is presented in this paper. Nonlinear environment is modeled by the popular post nonlinear (PNL) scheme. To eliminate the nonlinearity in the observed signals, a novel linearizing method named as geometric post nonlinear ICA (gpICA) is introduced. Thereafter, a basic linear ICA is applied on these linearized signals to estimate the unknown sources. The proposed method is motivated by the fact that in a multidimensional space, a nonlinear mixture is represented by a nonlinear surface while a linear mixture is represented by a plane, a special form of the surface. Therefore, by geometrically transforming the surface representing a nonlinear mixture into a plane, the mixture can be linearized. Through simulations on different data sets, superior performance of gpICA algorithm has been shown with respect to other algorithms.
A NONMONOTONE TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION SUBJECT TO GENERAL CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
Hongchao Zhang
2003-01-01
In this paper we present a nonmonotone trust region algorithm for general nonlinear constrained optimization problems. The main idea of this paper is to combine Yuan's technique[1] with a nonmonotone method similar to Ke and Han [2]. This new algorithm may not only keep the robust properties of the algorithm given by Yuan, but also have some advantages led by the nonmonotone technique. Under very mild conditions, global convergence for the algorithm is given. Numerical experiments demonstrate the efficiency of the algorithm.
Double precision nonlinear cell for fast independent component analysis algorithm
Jain, V. K.
2006-05-01
Several advanced algorithms in defense and security objectives require high-speed computation of nonlinear functions. These include detection, localization, and identification. Increasingly, such computations must be performed in double precision accuracy in real time. In this paper, we develop a significance-based interpolative approach to such evaluations for double precision arguments. It is shown that our approach requires only one major multiplication, which leads to a unified and fast, two-cycle, VLSI architecture for mantissa computations. In contrast, the traditional iterative computations require several cycles to converge and typically these computations vary a lot from one function to another. Moreover, when the evaluation pertains to a compound or concatenated function, the overall time required becomes the sum of the times required by the individual operations. For our approach, the time required remains two cycles even for such compound or concatenated functions. Very importantly, the paper develops a key formula for predicting and bounding the worst case arithmetic error. This new result enables the designer to quickly select the architectural parameters without the expensive and intolerably long simulations, while guaranteeing the desired accuracy. The specific application focus is the mapping of the Independent Component Analysis (ICA) technique to a coarse-grain parallel-processing architecture.
A BPTT-like Min-Max Optimal Control Algorithm for Nonlinear Systems
Milić, Vladimir; Kasać, Josip; Majetić, Dubravko; Šitum, Željko
2010-09-01
This paper presents a conjugate gradient-based algorithm for feedback min-max optimal control of nonlinear systems. The algorithm has a backward-in-time recurrent structure similar to the back propagation through time (BPTT) algorithm. The control law is given as the output of the one-layer neural network. Main contribution of the paper includes the integration of BPTT techniques, conjugate gradient methods, Adams method for solving ODEs and automatic differentiation (AD), to provide an effective, novel algorithm for solving numerically optimally min-max control problems. The proposed algorithm is applied to the rotational/translational actuator (RTAC) nonlinear benchmark problem with control and state vector constraints.
[Non-linear rectification of sensor based on immune genetic algorithm].
Lu, Lirong; Zhou, Jinyang; Niu, Xiaodong
2014-08-01
A non-linear rectification based on immune genetic algorithm (IGA) is proposed in this paper, for the shortcoming of the non-linearity rectification. This algorithm introducing the biologic immune mechanism into the genetic algorithm can restrain the disadvantages that the poor precision, slow convergence speed and early maturity of the genetic algorithm. Computer simulations indicated that the algorithm not only keeps population diversity, but also increases the convergent speed, precision and the stability greatly. The results have shown the correctness and effectiveness of the method.
An Approximate Algorithm for a Class of Nonlinear Bilevel Integer Programming
Institute of Scientific and Technical Information of China (English)
LI Lei; TENG Chun-xian; TIAN Guang-yue
2002-01-01
The algorithm for a class of nonlinear bilevel integer programming is discussed in this paper. It is based on the theory and algorithm for nonlinear integer programming. The continuity methods for integer programming are studied in this paper. After simulated annealing algorithm is applied to the upper-level programming problem and the thought of filled function method for continuous global optimization is applied to the corresponding lower-level programming, an approximate algorithm is established. The satisfactory algorithm is elaborated in the following example.
[Non-linear rectification of sensor based on immune genetic Algorithm].
Lu, Lirong; Zhou, Jinyang; Niu, Xiaodong
2014-08-01
A non-linear rectification based on immune genetic algorithm (IGA) is proposed in this paper, for the shortcoming of the non-linearity rectification. This algorithm introducing the biologic immune mechanism into the genetic algorithm can restrain the disadvantages that the poor precision, slow convergence speed and early maturity of the genetic algorithm. Computer simulations indicated that the algorithm not only keeps population diversity, but also increases the convergent speed, precision and the stability greatly. The results have shown the correctness and effectiveness of the method.
Altmann, Yoann; Tourneret, Jean-Yves
2013-01-01
This paper presents a nonlinear mixing model for hyperspectral image unmixing. The proposed model assumes that the pixel reflectances are post-nonlinear functions of unknown pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated using polynomials leading to a polynomial post-nonlinear mixing model. A Bayesian algorithm is proposed to estimate the parameters involved in the model yielding an unsupervised nonlinear unmixing algorithm. Due to the large number of parameters to be estimated, an efficient Hamiltonian Monte Carlo algorithm is investigated. The classical leapfrog steps of this algorithm are modified to handle the parameter constraints. The performance of the unmixing strategy, including convergence and parameter tuning, is first evaluated on synthetic data. Simulations conducted with real data finally show the accuracy of the proposed unmixing strategy for the analysis of hyperspectral images.
Achieving Textbook Multigrid Efficiency for Hydrostatic Ice Sheet Flow
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.
MINIMAL INVERSION AND ITS ALGORITHMS OF DISCRETE-TIME NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
ZHENG Yufan
2005-01-01
The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.
Energy Technology Data Exchange (ETDEWEB)
Huang, Xiaobiao; 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.
MULTIGRID METHODS FOR THE GENERALIZED STOKES EQUATIONS BASED ON MIXED FINITE ELEMENT METHODS
Institute of Scientific and Technical Information of China (English)
Qing-ping Deng; Xiao-ping Feng
2002-01-01
Multigrid methods are developed and analyzed for the generalized stationary Stokes equations which are discretized by various mixed finite element methods. In this paper, the multigrid algorithm, the criterion for prolongation operators and the convergence analysis are all established in an abstract and element-independent fashion. It is proven that the multigrid algorithm converges optimally if the prolongation operator satisfies the criterion.To utilize the abstract result, more than ten well-known mixed finite elements for the Stokes problems are discussed in detail and examples of prolongation operators are constructed explicitly. For nonconforming elements, it is shown that the usual local averaging technique for constructing prolongation operators can be replaced by a computationally cheaper alternative, random choice technique. Moreover, since the algorithm and analysis allows using of nonnested meshes, the abstract result also applies to low order mixed finite elements, which are usually stable only for some special mesh structures.
Directory of Open Access Journals (Sweden)
Yongquan Zhou
2013-01-01
Full Text Available In view of the traditional numerical method to solve the nonlinear equations exist is sensitive to initial value and the higher accuracy of defects. This paper presents an invasive weed optimization (IWO algorithm which has population diversity with the heuristic global search of differential evolution (DE algorithm. In the iterative process, the global exploration ability of invasive weed optimization algorithm provides effective search area for differential evolution; at the same time, the heuristic search ability of differential evolution algorithm provides a reliable guide for invasive weed optimization. Based on the test of several typical nonlinear equations and a circle packing problem, the results show that the differential evolution invasive weed optimization (DEIWO algorithm has a higher accuracy and speed of convergence, which is an efficient and feasible algorithm for solving nonlinear systems of equations.
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.
Multigrid methods for propagators in lattice gauge theories
Kalkreuter, T
1994-01-01
Multigrid methods were invented for the solution of discretized partial differential equations in ordered systems. The slowness of traditional algorithms is overcome by updates on various length scales. In this article we discuss generalizations of multigrid methods for disordered systems, in particular for propagators in lattice gauge theories. A discretized nonabelian gauge theory can be formulated as a system of statistical mechanics where the gauge field degrees of freedom are SU(N) matrices on the links of the lattice. These SU(N) matrices appear as random coefficients in Dirac equations. We aim at finding an efficient method by which one can solve Dirac equations without critical slowing down. If this could be achieved, Monte Carlo simulations of Quantum Chromodynamics (the theory of the strong interaction) would be accelerated considerably. In principle, however, the methods discussed can be used in arbitrary space-time dimension and for arbitrary gauge group. Moreover, there are applications in multig...
Comparison of Algebraic Multigrid Preconditioners for Solving Helmholtz Equations
Directory of Open Access Journals (Sweden)
Dandan Chen
2012-01-01
Full Text Available An algebraic multigrid (AMG with aggregation technique to coarsen is applied to construct a better preconditioner for solving Helmholtz equations in this paper. The solution process consists of constructing the preconditioner by AMG and solving the preconditioned Helmholtz problems by Krylov subspace methods. In the setup process of AMG, we employ the double pairwise aggregation (DPA scheme firstly proposed by Y. Notay (2006 as the coarsening method. We compare it with the smoothed aggregation algebraic multigrid and meanwhile show shifted Laplacian preconditioners. According to numerical results, we find that DPA algorithm is a good choice in AMG for Helmholtz equations in reducing time and memory. Spectral estimation of system preconditioned by the three methods and the influence of second-order and fourth-order accurate discretizations on the three techniques are also considered.
An efficient artificial bee colony algorithm with application to nonlinear predictive control
Ait Sahed, Oussama; Kara, Kamel; Benyoucef, Abousoufyane; Laid Hadjili, Mohamed
2016-05-01
In this paper a constrained nonlinear predictive control algorithm, that uses the artificial bee colony (ABC) algorithm to solve the optimization problem, is proposed. The main objective is to derive a simple and efficient control algorithm that can solve the nonlinear constrained optimization problem with minimal computational time. Indeed, a modified version, enhancing the exploring and the exploitation capabilities, of the ABC algorithm is proposed and used to design a nonlinear constrained predictive controller. This version allows addressing the premature and the slow convergence drawbacks of the standard ABC algorithm, using a modified search equation, a well-known organized distribution mechanism for the initial population and a new equation for the limit parameter. A convergence statistical analysis of the proposed algorithm, using some well-known benchmark functions is presented and compared with several other variants of the ABC algorithm. To demonstrate the efficiency of the proposed algorithm in solving engineering problems, the constrained nonlinear predictive control of the model of a Multi-Input Multi-Output industrial boiler is considered. The control performances of the proposed ABC algorithm-based controller are also compared to those obtained using some variants of the ABC algorithms.
A MODIFIED LEVENBERG-MARQUARDT ALGORITHM FOR SINGULAR SYSTEM OF NONLINEAR EQUATIONS
Institute of Scientific and Technical Information of China (English)
Jin-yan Fan
2003-01-01
Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithmfor solving singular system of nonlinear equations F(x) = 0, where F(x): Rn -→ Rn iscontinuously differentiable and F′ (x) is Lipschitz continuous. The algorithm is equivalentto a trust region algorithm in some sense, and the global convergence result is given. Thesequence generated by the algorithm converges to the solution quadratically, if ‖F(x)‖2provides a local error bound for the system of nonlinear equations. Numerical results showthat the algorithm performs well.
Directory of Open Access Journals (Sweden)
Wang Pidong
2016-01-01
Full Text Available Blind source separation is a hot topic in signal processing. Most existing works focus on dealing with linear combined signals, while in practice we always encounter with nonlinear mixed signals. To address the problem of nonlinear source separation, in this paper we propose a novel algorithm using radial basis function neutral network, optimized by multi-universe parallel quantum genetic algorithm. Experiments show the efficiency of the proposed method.
Development of numerical algorithms for practical computation of nonlinear normal modes
2008-01-01
When resorting to numerical algorithms, we show that nonlinear normal mode (NNM) computation is possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems. The proposed method relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. In addition, sensitivity analysis is used to reduce the computational burden of the algorithm. A simplified discrete model of a...
A Parallel Algebraic Multigrid Solver on Graphics Processing Units
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.
Nonlinear unmixing of hyperspectral images: models and algorithms
Dobigeon, Nicolas; Richard, Cédric; Bermudez, José C M; McLaughlin, Stephen; Hero, Alfred O
2013-01-01
When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas rely on the widely acknowledged linear mixing model (LMM). However, in specific but common contexts, the LMM may be not valid and other nonlinear models should be invoked. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this paper, we present an overview of recent advances that deal with the nonlinear unmixing problem. The main nonlinear models are introduced and their validity discussed. Then, we describe the main classes of unmixing strategies designed to solve the problem in supervised and unsupervised frameworks. Finally, the problem of detecting nonlinear mixtures in hyperspectral images is addressed.
THE APPLICATION OF GENETIC ALGORITHM IN NON-LINEAR INVERSION OF ROCK MECHANICS PARAMETERS
Institute of Scientific and Technical Information of China (English)
赵晓东
1998-01-01
The non-linear inversion of rock mechanics parameters based on genetic algorithm ispresented. The principle and step of genetic algorithm is also given. A brief discussion of thismethod and an application example is presented at the end of this paper. From the satisfied re-sult, quick, convenient and practical new approach is developed to solve this kind of problems.
Teren, F.
1977-01-01
Minimum time accelerations of aircraft turbofan engines are presented. The calculation of these accelerations was made by using a piecewise linear engine model, and an algorithm based on nonlinear programming. Use of this model and algorithm allows such trajectories to be readily calculated on a digital computer with a minimal expenditure of computer time.
Model algorithm control using neural networks for input delayed nonlinear control system
Institute of Scientific and Technical Information of China (English)
Yuanliang Zhang; Kil To Chong
2015-01-01
The performance of the model algorithm control method is partial y based on the accuracy of the system’s model. It is diffi-cult to obtain a good model of a nonlinear system, especial y when the nonlinearity is high. Neural networks have the ability to“learn”the characteristics of a system through nonlinear mapping to rep-resent nonlinear functions as wel as their inverse functions. This paper presents a model algorithm control method using neural net-works for nonlinear time delay systems. Two neural networks are used in the control scheme. One neural network is trained as the model of the nonlinear time delay system, and the other one pro-duces the control inputs. The neural networks are combined with the model algorithm control method to control the nonlinear time delay systems. Three examples are used to il ustrate the proposed control method. The simulation results show that the proposed control method has a good control performance for nonlinear time delay systems.
Nonlinear Model Algorithmic Control of a pH Neutralization Process
Institute of Scientific and Technical Information of China (English)
ZOU Zhiyun; YU Meng; WANG Zhizhen; LIU Xinghong; GUO Yuqing; ZHANG Fengbo; GUO Ning
2013-01-01
Control of pH neutralization processes is challenging in the chemical process industry because of their inherent strong nonlinearity.In this paper,the model algorithmic control (MAC) strategy is extended to nonlinear processes using Hammerstein model that consists of a static nonlinear polynomial function followed in series by a linear impulse response dynamic element.A new nonlinear Hammerstein MAC algorithm (named NLH-MAC) is presented in detail.The simulation control results of a pH neutralization process show that NLH-MAC gives better control performance than linear MAC and the commonly used industrial nonlinear propotional plus integral plus derivative (PID) controller.Further simulation experiment demonstrates that NLH-MAC not only gives good control response,but also possesses good stability and robustness even with large modeling errors.
Institute of Scientific and Technical Information of China (English)
LIN Xiangguo; LIANG Yong
2005-01-01
The processing of nonlinear data was one of hot topics in surveying and mapping field in recent years.As a result, many linear methods and nonlinear methods have been developed.But the methods for processing generalized nonlinear surveying and mapping data, especially for different data types and including unknown parameters with random or nonrandom, are seldom noticed.A new algorithm model is presented in this paper for processing nonlinear dynamic multiple-period and multiple-accuracy data derived from deformation monitoring network.
Directory of Open Access Journals (Sweden)
Suxiang He
2014-01-01
Full Text Available An implementable nonlinear Lagrange algorithm for stochastic minimax problems is presented based on sample average approximation method in this paper, in which the second step minimizes a nonlinear Lagrange function with sample average approximation functions of original functions and the sample average approximation of the Lagrange multiplier is adopted. Under a set of mild assumptions, it is proven that the sequences of solution and multiplier obtained by the proposed algorithm converge to the Kuhn-Tucker pair of the original problem with probability one as the sample size increases. At last, the numerical experiments for five test examples are performed and the numerical results indicate that the algorithm is promising.
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.
Algorithms for non-linear M-estimation
DEFF Research Database (Denmark)
Madsen, Kaj; Edlund, O; Ekblom, H
1997-01-01
a sequence of estimation problems for linearized models is solved. In the testing we apply four estimators to ten non-linear data fitting problems. The test problems are also solved by the Generalized Levenberg-Marquardt method and standard optimization BFGS method. It turns out that the new method...
AN ALGORITHM FOR FINDING GLOBAL MINIMUM OF NONLINEAR INTEGER PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Wei-wenTian; Lian-shengZhang
2004-01-01
A filled function is proposed by R.Ge[2] for finding a global minimizer of a function of several continuous variables. In [4], an approach for finding a global integer minimizer of nonlinear flmction using the above filled function is given. Meanwhile a major obstacle is met: if ρ > 0 is small, and ‖xI- xI* is large, where xI - an integer point, xI* - a current local integer minimizer, then the value of the filled function almost equals zero. Thus it is difficult to recognize the size of the value of the filled flmction and can not to find the global integer minimizer of nonlinear function. In this paper, two new filled functions are proposed for finding global integer minimizer of nonlinear flmction, the new filled function improves some properties of the filled function proposed by R. Ge [2]. Some numerical results are given, which indicate the new filled function (4.1) to find global integer minimizer of nonlinear function is efficient.
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.
Adaptive aggregation-based domain decomposition multigrid for twisted mass fermions
Alexandrou, Constantia; Bacchio, Simone; Finkenrath, Jacob; Frommer, Andreas; Kahl, Karsten; Rottmann, Matthias
2016-12-01
The adaptive aggregation-base domain decomposition multigrid method [A. Frommer et al., SIAM J. Sci. Comput. 36, A1581 (2014)] is extended for two degenerate flavors of twisted mass fermions. By fine-tuning the parameters we achieve a speed-up of the order of a hundred times compared to the conjugate gradient algorithm for the physical value of the pion mass. A thorough analysis of the aggregation parameters is presented, which provides a novel insight into multigrid methods for lattice quantum chromodynamics independently of the fermion discretization.
Inverse airfoil design procedure using a multigrid Navier-Stokes method
Malone, J. B.; Swanson, R. C.
1991-01-01
The Modified Garabedian McFadden (MGM) design procedure was incorporated into an existing 2-D multigrid Navier-Stokes airfoil analysis method. The resulting design method is an iterative procedure based on a residual correction algorithm and permits the automated design of airfoil sections with prescribed surface pressure distributions. The new design method, Multigrid Modified Garabedian McFadden (MG-MGM), is demonstrated for several different transonic pressure distributions obtained from both symmetric and cambered airfoil shapes. The airfoil profiles generated with the MG-MGM code are compared to the original configurations to assess the capabilities of the inverse design method.
Simulation of viscous flows using a multigrid-control volume finite element method
Energy Technology Data Exchange (ETDEWEB)
Hookey, N.A. [Memorial Univ., Newfoundland (Canada)
1994-12-31
This paper discusses a multigrid control volume finite element method (MG CVFEM) for the simulation of viscous fluid flows. The CVFEM is an equal-order primitive variables formulation that avoids spurious solution fields by incorporating an appropriate pressure gradient in the velocity interpolation functions. The resulting set of discretized equations is solved using a coupled equation line solver (CELS) that solves the discretized momentum and continuity equations simultaneously along lines in the calculation domain. The CVFEM has been implemented in the context of both FMV- and V-cycle multigrid algorithms, and preliminary results indicate a five to ten fold reduction in execution times.
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 inner...... block boundaries. A Robin parameter that depends on grid geometry and grid discontinuity at block interfaces is introduced. The general solution algorithm is based on SIMPLE method and a conservative _nite-volume scheme on block-structured grids with discontinuous interfaces. The multigrid method...
Multiblock, Multigrid Solution Of Euler Equations
Melson, N. Duane; Cannizzaro, Frank E.; Von Lavante, E.
1994-01-01
Method of numerical solution of Euler equations of three-dimensional flow of compressible fluid involves combination of multiblock and multigrid strategies. In multiblock strategy, flow field divided, into multiple smaller, more computationally-convenient zones and computational grid fitted to applicable flow boundaries generated in each block. In multigrid strategy used here, different quantities computed, variously, on finer or coarser grids. Minimizing cost of computation by using fewest grid points yielding acceptably accurate values of affected variable. Multigrid strategy found effective in accelerating convergence to steady state, while multiblock strategy provides geometric flexibility.
Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver (Journal Version)
Livne, Oren E
2011-01-01
Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic partial differential equations discretized on unstructured grids with finite elements. A Lean Algebraic Multigrid (LAMG) solver of the symmetric linear system Ax=b is presented, where A is a graph Laplacian. LAMG's run time and storage are linear in the number of graph edges. It is robust and requires no fine tuning. LAMG consists of a setup phase, in which a sequence of increasingly-coarser Laplacian systems is constructed, and an iterative solve phase using multigrid cycles. General graphs pose algorithmic challenges not encountered in traditional applications of algebraic multigrid. LAMG combines a lean piecewise-constant interpolation, judicious node aggregation based on a new node proximity definition, and a novel energy correction of the coarse-level systems. This results ...
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.
Smoothing Newton Algorithm for Nonlinear Complementarity Problem with a P* Function
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
By using a smoothing function, the P* nonlinear complementarity problem (P* NCP) can be reformulated as a parameterized smooth equation. A Newton method is proposed to solve this equation. The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P* NCP has a nonempty solution set. This assumption is weaker than the ones used in most existing smoothing algorithms. In particular, the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P* NCP without any additional assumption.
Institute of Scientific and Technical Information of China (English)
Zi-you Gao; Tian-de Guo; Guo-ping He; Fang Wu
2002-01-01
In this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations having a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration. Moreover, for the SQPtype algorithms, there exist so-called inconsistent problems, i.e., quadratic programming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the related systems of linear equations always have solutions. Some numerical results are reported.
Institute of Scientific and Technical Information of China (English)
高自友; 贺国平; 吴方
1997-01-01
For current sequential quadratic programming (SQP) type algorithms, there exist two problems; (i) in order to obtain a search direction, one must solve one or more quadratic programming subproblems per iteration, and the computation amount of this algorithm is very large. So they are not suitable for the large-scale problems; (ii) the SQP algorithms require that the related quadratic programming subproblems be solvable per iteration, but it is difficult to be satisfied. By using e-active set procedure with a special penalty function as the merit function, a new algorithm of sequential systems of linear equations for general nonlinear optimization problems with arbitrary initial point is presented This new algorithm only needs to solve three systems of linear equations having the same coefficient matrix per iteration, and has global convergence and local superlinear convergence. To some extent, the new algorithm can overcome the shortcomings of the SQP algorithms mentioned above.
Institute of Scientific and Technical Information of China (English)
DAI Chao-Qing; MENG Jian-Ping; ZHANG Jie-Fang
2005-01-01
The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.
Research on an augmented Lagrangian penalty function algorithm for nonlinear programming
Frair, L.
1978-01-01
The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.
One-parameter quasi-filled function algorithm for nonlinear integer programming
Institute of Scientific and Technical Information of China (English)
SHANG You-lin; HAN Bo-shun
2005-01-01
A definition of the quasi-filled function for nonlinear integer programming problem is given in this paper. A quasi-filled function satisfying our definition is presented. This function contains only one parameter. The properties of the proposed quasi-filled function and the method using this quasi-filled function to solve nonlinear integer programming problem are also discussed in this paper. Numerical results indicated the efficiency and reliability of the proposed quasi-filled function algorithm.
A NEW ALGORITHM IN NONLINEAR ANALYSIS OF STRUCTURES USING PARTICLE SWARM OPTIMIZATION
Iman Mansouri; Ali Shahri; Hassan Zahedifar
2016-01-01
Solving systems of nonlinear equations is a difficult problem in numerical computation. Probably the best known and most widely used algorithm to solve a system of nonlinear equations is Newton-Raphson method. A significant shortcoming of this method becomes apparent when attempting to solve problems with limit points. Once a fixed load is defined in the first step, there is no way to modify the load vector should a limit point occur within the increment. To overcome this defect, displacement...
A time integral formulation and algorithm for structural dynamics with nonlinear stiffness
Institute of Scientific and Technical Information of China (English)
Kaiping Yu; Jie Zhao
2006-01-01
A newly-developed numerical algorithm, which is called the new Generalized-α(G-α)method, is presented for solving structural dynamics problems with nonlinear stiffness. The traditional G-α method has undesired overshoot properties as for a class of α-method. In the present work, seven independent parameters are introduced into the single-step three-stage algorithmic formulations and the nonlinear internal force at every time interval is approximated by means of the generalized trapezoidal rule, and then the algorithm is implemented based on the finite difference theory. An analysis on the stability, accuracy, energy and overshoot properties of the proposed scheme is performed in the nonlinear regime. The values or the ranges of values of the seven independent parameters are determined in the analysis process. The computational results obtained by the new algorithm show that the displacement accuracy is of order two, and the acceleration can also be improved to a second order accuracy by a suitable choice of parameters. Obviously, the present algorithm is zerostable, and the energy conservation or energy decay can be realized in the high-frequency range, which can be regarded as stable in an energy sense. The algorithmic overshoot can be completely avoided by using the new algorithm without any constraints with respect to the damping force and initial conditions.
Two-parameters quasi-filled function algorithm for nonlinear integer programming
Institute of Scientific and Technical Information of China (English)
WANG Wei-xiang; SHANG You-lin; ZHANG Lian-sheng
2006-01-01
A quasi-filled function for nonlinear integer programming problem is given in this paper. This function contains two parameters which are easily to be chosen. Theoretical properties of the proposed quasi-filled function are investigated. Moreover,we also propose a new solution algorithm using this quasi-filled function to solve nonlinear integer programming problem in this paper. The examples with 2 to 6 variables are tested and computational results indicated the efficiency and reliability of the proposed quasi-filled function algorithm.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
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.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Algorithms of estimation for nonlinear systems a differential and algebraic viewpoint
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.
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.
A nonlinear model reference adaptive inverse control algorithm with pre-compensator
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In this paper, the reduced-order modeling (ROM)technology and its corresponding linear theory are expanded from the linear dynamic system to the nonlinear one, and H∞ control theory is employed in the frequency domain to design some nonlinear system' s pre-compensator in some special way. The adaptive model inverse control (AMIC)theory coping with nonlinear system is improved as well. Such is the model reference adaptive inverse control with pre-compensator (PCMRAIC). The aim of that algorithm is to construct a strategy of control as a whole. As a practical example of the application, the numerical simulation has been given on matlab software packages. The numerical result is given. The proposed strategy realizes the linearization control of nonlinear dynamic system. And it carries out a good performance to deal with the nonlinear system.
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.
A Projected Lagrangian Algorithm for Nonlinear Minimax Optimization.
1979-11-01
T Problem 5: Charalambous and Bandler (1976) # 1. f 1(x ) 2- + _ f3(x) = 2 exp(-x+ X2) Starting Pointz xO (1,..1)T 61 Problem 6: Rosen and Suzuki...Charalambous and Bandler ,#l) 2 3 1 6 6 6 (Rosen and Suzuki) 4 4 2 7 10 The results demonstrate that at least on a limited set of test problems the...and Numerical Methods for Stiff Differential Equations. Charalambous, C. and J.W. Bandler (1974). Nonlinear minimax optimization as a sequence of least
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.
Comparison and analysis of nonlinear algorithms for compressed sensing in MRI.
Yu, Yeyang; Hong, Mingjian; Liu, Feng; Wang, Hua; Crozier, Stuart
2010-01-01
Compressed sensing (CS) theory has been recently applied in Magnetic Resonance Imaging (MRI) to accelerate the overall imaging process. In the CS implementation, various algorithms have been used to solve the nonlinear equation system for better image quality and reconstruction speed. However, there are no explicit criteria for an optimal CS algorithm selection in the practical MRI application. A systematic and comparative study of those commonly used algorithms is therefore essential for the implementation of CS in MRI. In this work, three typical algorithms, namely, the Gradient Projection For Sparse Reconstruction (GPSR) algorithm, Interior-point algorithm (l(1)_ls), and the Stagewise Orthogonal Matching Pursuit (StOMP) algorithm are compared and investigated in three different imaging scenarios, brain, angiogram and phantom imaging. The algorithms' performances are characterized in terms of image quality and reconstruction speed. The theoretical results show that the performance of the CS algorithms is case sensitive; overall, the StOMP algorithm offers the best solution in imaging quality, while the GPSR algorithm is the most efficient one among the three methods. In the next step, the algorithm performances and characteristics will be experimentally explored. It is hoped that this research will further support the applications of CS in MRI.
Nonlinear Algorithms for Channel Equalization and Map Symbol Detection.
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
Institute of Scientific and Technical Information of China (English)
Zhi Hong-Yan; Zhao Xue-Qin; Zhang Hong-Qing
2005-01-01
Based on the study of tanh function method and the coupled projective Riccati equation method, we propose a new algorithm to search for explicit exact solutions of nonlinear evolution equations. We use the higher-order Schrodinger equation and mKdV equation to illustrate this algorithm. As a result, more new solutions are obtained, which include new solitary solutions, periodic solutions, and singular solutions. Some new solutions are illustrated in figures.
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.
A general-purpose contact detection algorithm for nonlinear structural analysis codes
Energy Technology Data Exchange (ETDEWEB)
Heinstein, M.W.; Attaway, S.W.; Swegle, J.W.; Mello, F.J.
1993-05-01
A new contact detection algorithm has been developed to address difficulties associated with the numerical simulation of contact in nonlinear finite element structural analysis codes. Problems including accurate and efficient detection of contact for self-contacting surfaces, tearing and eroding surfaces, and multi-body impact are addressed. The proposed algorithm is portable between dynamic and quasi-static codes and can efficiently model contact between a variety of finite element types including shells, bricks, beams and particles. The algorithm is composed of (1) a location strategy that uses a global search to decide which slave nodes are in proximity to a master surface and (2) an accurate detailed contact check that uses the projected motions of both master surface and slave node. In this report, currently used contact detection algorithms and their associated difficulties are discussed. Then the proposed algorithm and how it addresses these problems is described. Finally, the capability of the new algorithm is illustrated with several example problems.
Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem
DEFF Research Database (Denmark)
Delbary, Fabrice; Knudsen, Kim
2014-01-01
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...
A Taylor-Galerkin finite element algorithm for transient nonlinear thermal-structural analysis
Thornton, E. A.; Dechaumphai, P.
1986-01-01
A Taylor-Galerkin finite element method for solving large, nonlinear thermal-structural problems is presented. The algorithm is formulated for coupled transient and uncoupled quasistatic thermal-structural problems. Vectorizing strategies ensure computational efficiency. Two applications demonstrate the validity of the approach for analyzing transient and quasistatic thermal-structural problems.
A separated bias identification and state estimation algorithm for nonlinear systems
Caglayan, A. K.; Lancraft, R. E.
1983-01-01
A computational algorithm for the identification of biases in discrete-time, nonlinear, stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.
Active suppression of nonlinear composite beam vibrations by selected control algorithms
Warminski, Jerzy; Bochenski, Marcin; Jarzyna, Wojciech; Filipek, Piotr; Augustyniak, Michal
2011-05-01
This paper is focused on application of different control algorithms for a flexible, geometrically nonlinear beam-like structure with Macro Fiber Composite (MFC) actuator. Based on the mathematical model of a geometrically nonlinear beam, analytical solutions for Nonlinear Saturation Controller (NSC) are obtained using Multiple Scale Method. Effectiveness of different control strategies is evaluated by numerical simulations in Matlab-Simulink software. Then, the Digital Signal Processing (DSP) controller and selected control algorithms are implemented to the physical system to compare numerical and experimental results. Detailed analysis for the NSC system is carried out, especially for high level of amplitude and wide range of frequencies of excitation. Finally, the efficiency of the considered controllers is tested experimentally for a more complex autoparametric " L-shape" beam system.
Institute of Scientific and Technical Information of China (English)
Chunxia Jia; Detong Zhu
2008-01-01
In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables.By employing the affine scaling conjugate gradient path search strategy,we obtain an iterative direction by solving the linearize model.By using the line search technique,we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective function nonmonotonically decreasing.The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions.Furthermore,the numerical results of the proposed algorithm indicate to be effective.
Parameter estimation of cutting tool temperature nonlinear model using PSO algorithm
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In cutting tool temperature experiment, a large number of related data could be available. In order to define the relationship among the experiment data, the nonlinear regressive curve of cutting tool temperature must be constructed based on the data. This paper proposes the Particle Swarm Optimization (PSO) algorithm for estimating the parameters such a curve. The PSO algorithm is an evolutional method based on a very simple concept. Comparison of PSO results with those of GA and LS methods showed that the PSO algorithm is more effective for estimating the parameters of the above curve.
Efficient Multigrid Preconditioners for Anisotropic Problems in Geophysical Modelling
Dedner, Andreas; Scheichl, Robert
2014-01-01
Many problems in geophysical modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the pressure correction has to be solved at every time step in a thin spherical shell representing the global atmosphere. This elliptic solve can be one of the computationally most demanding components in semi-implicit semi-Lagrangian time stepping methods which are very popular as they allow for larger model time steps and better overall performance. With increasing model resolution, algorithmically efficient and scalable algorithms are essential to run the code under tight operational time constraints. We discuss the theory and practical application of bespoke geometric multigrid preconditioners for equations of this type. The algorithms deal with the strong anisotropy in the vertical direction by using the tensor-product approach originally analysed by B\\"{o}rm and Hiptmair ...
Improved simple optimization (SOPT algorithm for unconstrained non-linear optimization problems
Directory of Open Access Journals (Sweden)
J. Thomas
2016-09-01
Full Text Available In the recent years, population based meta-heuristic are developed to solve non-linear optimization problems. These problems are difficult to solve using traditional methods. Simple optimization (SOPT algorithm is one of the simple and efficient meta-heuristic techniques to solve the non-linear optimization problems. In this paper, SOPT is compared with some of the well-known meta-heuristic techniques viz. Artificial Bee Colony algorithm (ABC, Particle Swarm Optimization (PSO, Genetic Algorithm (GA and Differential Evolutions (DE. For comparison, SOPT algorithm is coded in MATLAB and 25 standard test functions for unconstrained optimization having different characteristics are run for 30 times each. The results of experiments are compared with previously reported results of other algorithms. Promising and comparable results are obtained for most of the test problems. To improve the performance of SOPT, an improvement in the algorithm is proposed which helps it to come out of local optima when algorithm gets trapped in it. In almost all the test problems, improved SOPT is able to get the actual solution at least once in 30 runs.
Indian Academy of Sciences (India)
A Rama Mohan Rao; T V S R Appa Rao; B Dattaguru
2004-02-01
The work reported in this paper is motivated by the need to develop portable parallel processing algorithms and codes which can run on a variety of hardware platforms without any modiﬁcations. The prime aim of the research work reported here is to test the portability of the parallel algorithms and also to study and understand the comparative efﬁciencies of three parallel algorithms developed for implicit time integration technique. The standard message passing interface (MPI) is used to develop parallel algorithms for computing nonlinear dynamic response of large structures employing implicit time-marching scheme. The parallel algorithms presented in this paper are developed under the broad framework of non-overlapped domain decomposition technique. Numerical studies indicate that the parallel algorithm devised employing the conventional form of Newmark time integration algorithm is faster than the predictor–corrector form. It is also accurate and highly adaptive to ﬁne grain computations. The group implicit algorithm is found to be extremely superior in performance when compared to the other two parallel algorithms. This algorithm is better suited for large size problems on coarse grain environment as the resulting submeshes will obviously be large and thus permit larger time steps without losing accuracy.
Some Nonlinear Reconstruction Algorithms for Electrical Impedance Tomography
Energy Technology Data Exchange (ETDEWEB)
Berryman, J G
2001-03-09
An impedance camera [Henderson and Webster, 1978; Dines and Lytle, 1981]--or what is now more commonly called electrical impedance tomography--attempts to image the electrical impedance (or just the conductivity) distribution inside a body using electrical measurements on its boundary. The method has been used successfully in both biomedical [Brown, 1983; Barber and Brown, 1986; J. C. Newell, D. G. Gisser, and D. Isaacson, 1988; Webster, 1990] and geophysical applications [Wexler, Fry, and Neurnan, 1985; Daily, Lin, and Buscheck, 1987], but the analysis of optimal reconstruction algorithms is still progressing [Murai and Kagawa, 1985; Wexler, Fry, and Neurnan, 1985; Kohn and Vogelius, 1987; Yorkey and Webster, 1987; Yorkey, Webster, and Tompkins, 1987; Berryman and Kohn, 1990; Kohn and McKenney, 1990; Santosa and Vogelius, 1990; Yorkey, 1990]. The most common application is monitoring the influx or efflux of a highly conducting fluid (such as brine in a porous rock or blood in the human body) through the volume being imaged. For biomedical applications, this met hod does not have the resolution of radiological methods, but it is comparatively safe and inexpensive and therefore provides a valuable alternative when continuous monitoring of a patient or process is desired. The following discussion is intended first t o summarize the physics of electrical impedance tomography, then to provide a few details of the data analysis and forward modeling requirements, and finally to outline some of the reconstruction algorithms that have proven to be most useful in practice. Pointers to the literature are provided throughout this brief narrative and the reader is encouraged to explore the references for more complete discussions of the various issues raised here.
Parallel algorithm of trigonometric collocation method in nonlinear dynamics of rotors
Directory of Open Access Journals (Sweden)
Musil T.
2007-11-01
Full Text Available A parallel algorithm of a numeric procedure based on a method of trigonometric collocation is presented for investigating an unbalance response of a rotor supported by journal bearings. After a condensation process the trigonometric collocation method results in a set of nonlinear algebraic equations which is solved by the Newton-Raphson method. The order of the set is proportional to the number of nonlinear bearing coordinates and terms of the finite Fourier series. The algorithm, realized in the MATLAB parallel computing environment (DCT/DCE, uses message passing technique for interacting among processes on nodes of a parallel computer. This technique enables portability of the source code both on parallel computers with distributed and shared memory. Tests, made on a Beowulf cluster and a symmetric multiprocessor, have revealed very good speed-up and scalability of this algorithm.
Chin, Siu A
2007-01-01
Since the kinetic and the potential energy term of the real time nonlinear Schr\\"odinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even when the total energy is very well conserved. A detail error analysis reveals that the noise, or elementary excitations of the nonlinear Schr\\"odinger, obeys the Bogoliubov spectrum and the instability is due to the exponential growth of high wave number noises caused by the splitting process. For a continuum wave function, this instability is unavoidable no matter how small the time step. For a discrete wave function, the instability can be avoided only for $\\dt k_{max}^2{<\\atop\\sim}2 \\pi$, where $k_{max}=\\pi/\\Delta x$.
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.
An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE
Baysal, Oktay; Lessard, Victor R.
1990-01-01
The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.
Kazemi, Mahdi; Arefi, Mohammad Mehdi
2016-12-15
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.
Directory of Open Access Journals (Sweden)
Chein-Shan Liu
2014-01-01
Full Text Available To solve an unconstrained nonlinear minimization problem, we propose an optimal algorithm (OA as well as a globally optimal algorithm (GOA, by deflecting the gradient direction to the best descent direction at each iteration step, and with an optimal parameter being derived explicitly. An invariant manifold defined for the model problem in terms of a locally quadratic function is used to derive a purely iterative algorithm and the convergence is proven. Then, the rank-two updating techniques of BFGS are employed, which result in several novel algorithms as being faster than the steepest descent method (SDM and the variable metric method (DFP. Six numerical examples are examined and compared with exact solutions, revealing that the new algorithms of OA, GOA, and the updated ones have superior computational efficiency and accuracy.
The Contraction-Expansion Algorithm and Its Use in Fitting Nonlinear Equation
Institute of Scientific and Technical Information of China (English)
Gu Shiliang; Hui Dafeng; Bian Aihua
1998-01-01
A new optimization method, contraction-expansion algorithm, is developed and applied to fit nonlinear equations. Five points with equal distance are allocated in the given initial intervals, then the algorithm searches for the points of better objective function one round after another, with contracting and expanding intervals alternatively.The step length (l), a critical factor to optimal solution, is determined and adjusted by feedback information of the searching process. The experiments with number of simulated and real data sets show that the new algorithm is much easier to the optimization than other methods. The algorithm does not need to provide derivatives of the equation.This algorithm can also be used in other optimization problems.
CHAOS-REGULARIZATION HYBRID ALGORITHM FOR NONLINEAR TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEM
Institute of Scientific and Technical Information of China (English)
王登刚; 刘迎曦; 李守巨
2002-01-01
A numerical model of nonlinear two-dimensional steady inverse heat conduction problem was established considering the thermal conductivity changing with temperature.Combining the chaos optimization algorithm with the gradient regularization method, a chaos-regularization hybrid algorithm was proposed to solve the established numerical model.The hybrid algorithm can give attention to both the advantages of chaotic optimization algorithm and those of gradient regularization method. The chaos optimization algorithm was used to help the gradient regalarization method to escape from local optima in the hybrid algorithm. Under the assumption of temperature-dependent thermal conductivity changing with temperature in linear rule, the thermal conductivity and the linear rule were estimated by using the present method with the aid of boundary temperature measurements. Numerical simulation results show that good estimation on the thermal conductivity and the linear function can be obtained with arbitrary initial guess values, and that the present hybrid algorithm is much more efficient than conventional genetic algorithm and chaos optimization algorithm.
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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.
Murphy, Patrick Charles
1985-01-01
An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.
A nonlinear filtering algorithm for denoising HR(S)TEM micrographs
Energy Technology Data Exchange (ETDEWEB)
Du, Hongchu, E-mail: h.du@fz-juelich.de [Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Jülich Research Centre, Jülich, 52425 (Germany); Central Facility for Electron Microscopy (GFE), RWTH Aachen University, Aachen 52074 (Germany); Peter Grünberg Institute, Jülich Research Centre, Jülich 52425 (Germany)
2015-04-15
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.
Shemer, A.; Schwarz, A.; Gur, E.; Cohen, E.; Zalevsky, Z.
2015-04-01
In this paper, the authors describe a novel technique for image nonlinearity and non-uniformity corrections in imaging systems based on gamma detectors. The limitation of the gamma detector prevents the producing of high quality images due to the radionuclide distribution. This problem causes nonlinearity and non-uniformity distortions in the obtained image. Many techniques have been developed to correct or compensate for these image artifacts using complex calibration processes. The presented method is based on the Papoulis - Gerchberg(PG) iterative algorithm and is obtained without need of detector calibration, tuning process or using any special test phantom.
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.
An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics.
Ahmad, Jamshad; Mohyud-Din, Syed Tauseef
2014-01-01
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.
Directory of Open Access Journals (Sweden)
Mahdi Sohrabi-Haghighat
2014-06-01
Full Text Available In this paper, a new algorithm based on SQP method is presented to solve the nonlinear inequality constrained optimization problem. As compared with the other existing SQP methods, per single iteration, the basic feasible descent direction is computed by solving at most two equality constrained quadratic programming. Furthermore, there is no need for any auxiliary problem to obtain the coefficients and update the parameters. Under some suitable conditions, the global and superlinear convergence are shown. Keywords: Global convergence, Inequality constrained optimization, Nonlinear programming problem, SQP method, Superlinear convergence rate.
Institute of Scientific and Technical Information of China (English)
YAN Zhen-Ya
2004-01-01
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the correspondingsystem of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2+1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.
Institute of Scientific and Technical Information of China (English)
YANZhen-Ya
2004-01-01
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the corresponding system of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2+1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.
Nonlinear Random Effects Mixture Models: Maximum Likelihood Estimation via the EM Algorithm.
Wang, Xiaoning; Schumitzky, Alan; D'Argenio, David Z
2007-08-15
Nonlinear random effects models with finite mixture structures are used to identify polymorphism in pharmacokinetic/pharmacodynamic phenotypes. An EM algorithm for maximum likelihood estimation approach is developed and uses sampling-based methods to implement the expectation step, that results in an analytically tractable maximization step. A benefit of the approach is that no model linearization is performed and the estimation precision can be arbitrarily controlled by the sampling process. A detailed simulation study illustrates the feasibility of the estimation approach and evaluates its performance. Applications of the proposed nonlinear random effects mixture model approach to other population pharmacokinetic/pharmacodynamic problems will be of interest for future investigation.
Improvements to the Levenberg-Marquardt algorithm for nonlinear least-squares minimization
Transtrum, Mark K
2012-01-01
When minimizing a nonlinear least-squares function, the Levenberg-Marquardt algorithm can suffer from a slow convergence, particularly when it must navigate a narrow canyon en route to a best fit. On the other hand, when the least-squares function is very flat, the algorithm may easily become lost in parameter space. We introduce several improvements to the Levenberg-Marquardt algorithm in order to improve both its convergence speed and robustness to initial parameter guesses. We update the usual step to include a geodesic acceleration correction term, explore a systematic way of accepting uphill steps that may increase the residual sum of squares due to Umrigar and Nightingale, and employ the Broyden method to update the Jacobian matrix. We test these changes by comparing their performance on a number of test problems with standard implementations of the algorithm. We suggest that these two particular challenges, slow convergence and robustness to initial guesses, are complimentary problems. Schemes that imp...
Institute of Scientific and Technical Information of China (English)
Fadhil H. T. Al-dulaimy; WANG Zuoying
2005-01-01
This work describes an improved feature extractor algorithm to extract the peripheral features of point x(ti,fj) using a nonlinear algorithm to compute the nonlinear time spectrum (NL-TS) pattern. The algorithm observes n×n neighborhoods of the point in all directions, and then incorporates the peripheral features using the Mel frequency cepstrum components (MFCCs)-based feature extractor of the Tsinghua electronic engineering speech processing (THEESP) for Mandarin automatic speech recognition (MASR) system as replacements of the dynamic features with different feature combinations. In this algorithm, the orthogonal bases are extracted directly from the speech data using discrite cosime transformation (DCT) with 3×3 blocks on an NL-TS pattern as the peripheral features. The new primal bases are then selected and simplified in the form of the operator in the time direction and the operator in the frequency direction. The algorithm has 23.29% improvements of the relative error rate in comparison with the standard MFCC feature-set and the dynamic features in tests using THEESP with the duration distribution-based hidden Markov model (DDBHMM) based on MASR system.
SOLUTION OF NONLINEAR PROBLEMS IN WATER RESOURCES SYSTEMS BY GENETIC ALGORITHM
Directory of Open Access Journals (Sweden)
Ahmet BAYLAR
1998-03-01
Full Text Available Genetic Algorithm methodology is a genetic process treated on computer which is considering evolution process in the nature. The genetic operations takes place within the chromosomes stored in computer memory. By means of various operators, the genetic knowledge in chromosomes change continuously and success of the community progressively increases as a result of these operations. The primary purpose of this study is calculation of nonlinear programming problems in water resources systems by Genetic Algorithm. For this purpose a Genetic Algoritm based optimization program were developed. It can be concluded that the results obtained from the genetic search based method give the precise results.
Long step homogeneous interior point algorithm for the p* nonlinear complementarity problems
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Lešaja Goran
2002-01-01
Full Text Available A P*-Nonlinear Complementarity Problem as a generalization of the P*-Linear Complementarity Problem is considered. We show that the long-step version of the homogeneous self-dual interior-point algorithm could be used to solve such a problem. The algorithm achieves linear global convergence and quadratic local convergence under the following assumptions: the function satisfies a modified scaled Lipschitz condition, the problem has a strictly complementary solution, and certain submatrix of the Jacobian is nonsingular on some compact set.
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Houda Salhi
2016-01-01
Full Text Available This paper deals with the parameter estimation problem for multivariable nonlinear systems described by MIMO state-space Wiener models. Recursive parameters and state estimation algorithms are presented using the least squares technique, the adjustable model, and the Kalman filter theory. The basic idea is to estimate jointly the parameters, the state vector, and the internal variables of MIMO Wiener models based on a specific decomposition technique to extract the internal vector and avoid problems related to invertibility assumption. The effectiveness of the proposed algorithms is shown by an illustrative simulation example.
A multigrid method applied to reactor kinetics
Energy Technology Data Exchange (ETDEWEB)
Nguyen, T.S
2006-07-01
The control and safety analysis of a nuclear reactor strongly relies on numerical simulation of reactor dynamics, in which the neutronics computation is one of the most important tasks. It is necessary to utilize a full three-dimensional model of neutron kinetics for satisfactory results but this requires an extensive computation. The purpose of this research is to explore an efficient method for accurate solution of the spatial neutron kinetics problem. The kinetics of neutrons in a nuclear reactor of practical interest is adequately represented by the few-group diffusion equations with delayed neutron effects taken into account. For solving such a space-time equation system, finite difference methods, though the simplest, must work with a very fine-mesh grid, resulting in an extremely large algebraic system whose solution by basic numerical methods encounters inefficiency. Coarse-mesh methods increase computational efficiency by reducing the number of discretized equations. However, by adding more complexity and limitations, the coarse-mesh computation is still rather time-consuming. Multigrid methods may provide an optimal solution for a large, sparse algebraic system arising from discretization of a partial differential equation or system but have not found many applications in reactor physics due to inherent difficulties. In this research, a finite difference method is used for discretization of the kinetics equations and a multigrid solver is developed to solve the discretized equation system. The Additive Correction Multigrid, the simplest and cheapest method in the multigrid family, is used for grid coarsening, allowing for reaching the coarsest grid without any difficulties. By avoiding the singularity and indefiniteness of the discretized system, the Red-Black Gauss-Seidel method is suited for multigrid smoothing and favours an implementation of parallel computation. Numerical experiments show that our multigrid solver is not only much faster than any
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.
An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints
Hurley, R. C.; Vorobiev, O. Y.; Ezzedine, S. M.
2017-08-01
We present a numerical method for modeling the mechanical effects of nonlinearly-compliant joints in elasto-plastic media. The method uses a series of strain-rate and stress update algorithms to determine joint closure, slip, and solid stress within computational cells containing multiple "embedded" joints. This work facilitates efficient modeling of nonlinear wave propagation in large spatial domains containing a large number of joints that affect bulk mechanical properties. We implement the method within the massively parallel Lagrangian code GEODYN-L and provide verification and examples. We highlight the ability of our algorithms to capture joint interactions and multiple weakness planes within individual computational cells, as well as its computational efficiency. We also discuss the motivation for developing the proposed technique: to simulate large-scale wave propagation during the Source Physics Experiments (SPE), a series of underground explosions conducted at the Nevada National Security Site (NNSS).
A general non-linear optimization algorithm for lower bound limit analysis
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars
2003-01-01
The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular...... finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound...... load optimization problem. and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non-linear yield criteria. Copyright (C) 2002 John Wiley Sons. Ltd....
Acikmese, Ahmet Behcet; Carson, John M., III
2006-01-01
A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.
Rajput, Sudheesh K; Nishchal, Naveen K
2014-01-20
We propose a novel nonlinear image-encryption scheme based on a Gerchberg-Saxton (G-S) phase-retrieval algorithm in the Fresnel transform domain. The decryption process can be performed using conventional double random phase encoding (DRPE) architecture. The encryption is realized by applying G-S phase-retrieval algorithm twice, which generates two asymmetric keys from intermediate phases. The asymmetric keys are generated in such a way that decryption is possible optically with a conventional DRPE method. Due to the asymmetric nature of the keys, the proposed encryption process is nonlinear and offers enhanced security. The cryptanalysis has been carried out, which proves the robustness of proposed scheme against known-plaintext, chosen-plaintext, and special attacks. A simple optical setup for decryption has also been suggested. Results of computer simulation support the idea of the proposed cryptosystem.
Han, Honggui; Wu, Xiao-Long; Qiao, Jun-Fei
2014-04-01
In this paper, a self-organizing fuzzy-neural-network with adaptive computation algorithm (SOFNN-ACA) is proposed for modeling a class of nonlinear systems. This SOFNN-ACA is constructed online via simultaneous structure and parameter learning processes. In structure learning, a set of fuzzy rules can be self-designed using an information-theoretic methodology. The fuzzy rules with high spiking intensities (SI) are divided into new ones. And the fuzzy rules with a small relative mutual information (RMI) value will be pruned in order to simplify the FNN structure. In parameter learning, the consequent part parameters are learned through the use of an ACA that incorporates an adaptive learning rate strategy into the learning process to accelerate the convergence speed. Then, the convergence of SOFNN-ACA is analyzed. Finally, the proposed SOFNN-ACA is used to model nonlinear systems. The modeling results demonstrate that this proposed SOFNN-ACA can model nonlinear systems effectively.
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Mahsa Khoeiniha
2012-01-01
Full Text Available This paper investigated study of dynamics of nonlinear electrical circuit by means of modern nonlinear techniques and the control of a class of chaotic system by using backstepping method based on Lyapunov function. The behavior of such nonlinear system when they are under the influence of external sinusoidal disturbances with unknown amplitudes has been considered. The objective is to analyze the performance of this system at different amplitudes of disturbances. We illustrate the proposed approach for controlling duffing oscillator problem to stabilize this system at the equilibrium point. Also Genetic Algorithm method (GA for computing the parameters of controller has been used. GA can be successfully applied to achieve a better controller. Simulation results have shown the effectiveness of the proposed method.
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Aijia Ouyang
2015-01-01
Full Text Available Nonlinear Muskingum models are important tools in hydrological forecasting. In this paper, we have come up with a class of new discretization schemes including a parameter θ to approximate the nonlinear Muskingum model based on general trapezoid formulas. The accuracy of these schemes is second order, if θ≠1/3, but interestingly when θ=1/3, the accuracy of the presented scheme gets improved to third order. Then, the present schemes are transformed into an unconstrained optimization problem which can be solved by a hybrid invasive weed optimization (HIWO algorithm. Finally, a numerical example is provided to illustrate the effectiveness of the present methods. The numerical results substantiate the fact that the presented methods have better precision in estimating the parameters of nonlinear Muskingum models.
Constructive interference II: Semi-chaotic multigrid methods
Energy Technology Data Exchange (ETDEWEB)
Douglas, C.C. [Yale Univ., New Haven, CT (United States)
1994-12-31
Parallel computer vendors have mostly decided to move towards multi-user, multi-tasking per node machines. A number of these machines already exist today. Self load balancing on these machines is not an option to the users except when the user can convince someone to boot the entire machine in single user mode, which may have to be done node by node. Chaotic relaxation schemes were considered for situations like this as far back as the middle 1960`s. However, very little convergence theory exists. Further, what exists indicates that this is not really a good method. Besides chaotic relaxation, chaotic conjugate direction and minimum residual methods are explored as smoothers for symmetric and nonsymmetric problems. While having each processor potentially going off in a different direction from the rest is not what one would strive for in a unigrid situation, the change of grid procedures in multigrid provide a natural way of aiming all of the processors in the right direction. The author presents some new results for multigrid methods in which synchronization of the calculations on one or more levels is not assumed. However, he assumes that he knows how far out of synch neighboring subdomains are with respect to each other. Thus the author can show that the combination of a limited chaotic smoother and coarse level corrections produces a better algorithm than would be expected.
Fault Diagnosis of Nonlinear Systems Based on Hybrid PSOSA Optimization Algorithm
Institute of Scientific and Technical Information of China (English)
Ling-Lai Li; Dong-Hua Zhou; Ling Wang
2007-01-01
Fault diagnosis of nonlinear systems is of great importance in theory and practice, and the parameter estimation method is an effective strategy. Based on the framework of moving horizon estimation, fault parameters are identified by a proposed intelligent optimization algorithm called PSOSA, which could avoid premature convergence of standard particle swarm optimization (PSO) by introducing the probabilistic jumping property of simulated annealing (SA). Simulations on a three-tank system show the effectiveness of this optimization based fault diagnosis strategy.
A multigrid method for steady Euler equations on unstructured adaptive grids
Riemslagh, Kris; Dick, Erik
1993-01-01
A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.
Nonlinear Inversion of Potential-Field Data Using an Improved Genetic Algorithm
Institute of Scientific and Technical Information of China (English)
Feng Gangding; Chen Chao
2004-01-01
The genetic algorithm is useful for solving an inversion of complex nonlinear geophysical equations. The multi-point search of the genetic algorithm makes it easier to find a globally optimal solution and avoid falling into a local extremum. The search efficiency of the genetic algorithm is a key to producing successful solutions in a huge multi-parameter model space. The encoding mechanism of the genetic algorithm affects the searching processes in the evolution. Not all genetic operations perform perfectly in a search under either a binary or decimal encoding system. As such, a standard genetic algorithm (SGA) is sometimes unable to resolve an optimization problem such as a simple geophysical inversion. With the binary encoding system the operation of the crossover may produce more new individuals. The decimal encoding system, on the other hand, makes the mutation generate more new genes. This paper discusses approaches of exploiting the search potentials of genetic operations with different encoding systems and presents a hybrid-encoding mechanism for the genetic algorithm. This is referred to as the hybrid-encoding genetic algorithm (HEGA). The method is based on the routine in which the mutation operation is executed in decimal code and other operations in binary code. HEGA guarantees the birth of better genes by mutation processing with a high probability, so that it is beneficial for resolving the inversions of complicated problems. Synthetic and real-world examples demonstrate the advantages of using HEGA in the inversion of potential-field data.
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
Furuichi, Mikito; Nishiura, Daisuke
2017-10-01
We developed dynamic load-balancing algorithms for Particle Simulation Methods (PSM) involving short-range interactions, such as Smoothed Particle Hydrodynamics (SPH), Moving Particle Semi-implicit method (MPS), and Discrete Element method (DEM). These are needed to handle billions of particles modeled in large distributed-memory computer systems. Our method utilizes flexible orthogonal domain decomposition, allowing the sub-domain boundaries in the column to be different for each row. The imbalances in the execution time between parallel logical processes are treated as a nonlinear residual. Load-balancing is achieved by minimizing the residual within the framework of an iterative nonlinear solver, combined with a multigrid technique in the local smoother. Our iterative method is suitable for adjusting the sub-domain frequently by monitoring the performance of each computational process because it is computationally cheaper in terms of communication and memory costs than non-iterative methods. Numerical tests demonstrated the ability of our approach to handle workload imbalances arising from a non-uniform particle distribution, differences in particle types, or heterogeneous computer architecture which was difficult with previously proposed methods. We analyzed the parallel efficiency and scalability of our method using Earth simulator and K-computer supercomputer systems.
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.
Institute of Scientific and Technical Information of China (English)
WANG Shundin; ZHANG Hua
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.
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...
Mitchell, Lawrence
2016-01-01
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element discretisations on unstructured grids an efficient implementation can be very time consuming and requires the programmer to have in-depth knowledge of the mathematical theory, parallel computing and optimisation techniques on manycore CPUs. In this paper we show how the development of bespoke multigrid preconditioners can be simplified significantly by using a framework which allows the expression of the each component of the algorithm at the correct abstraction level. Our approach (1) allows the expression of the finite element problem in a language which is close to the mathematical formulation of the problem, (2) guarantees the automatic generation and efficient execution of parallel optimised low-level computer code and (3) is flexible enough to support different abstra...
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
Gaussian Sum PHD Filtering Algorithm for Nonlinear Non-Gaussian Models
Institute of Scientific and Technical Information of China (English)
Yin Jianjun; Zhang Jianqiu; Zhuang Zesen
2008-01-01
A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density (GSPHD) filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussiaa sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaassian mixture probability hypothesis density (GMPHD) filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special ease of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.
Parallel Algebraic Multigrids for Structural mechanics
Energy Technology Data Exchange (ETDEWEB)
Brezina, M; Tong, C; Becker, R
2004-05-11
This paper presents the results of a comparison of three parallel algebraic multigrid (AMG) preconditioners for structural mechanics applications. In particular, they are interested in investigating both the scalability and robustness of the preconditioners. Numerical results are given for a range of structural mechanics problems with various degrees of difficulty.
Multigrid for steady gas dynamics problems
Hemker, P.W.; Koren, B.; Lioen, W.M.; Nool, M.; van der Maarel, H.T.M.; Hafez, M.; Oshima, K.
1995-01-01
This paper consists of two parts. In the first part we give a review of a good multigrid method for solving the steady Euler equations of gas dynamics on a locally refined mesh. The method is selfadaptive and makes use of unstructured grids that can be considered as parts of a nested sequence of str
A multigrid approach to image processing
Zeeuw, P.M. de; Kimmel, R.; Sochen, N.; Weickert, J.
2005-01-01
A second order partial differential operator is applied to an image function. By using a multigrid operator known from the so-called approximation property, we derive a new type of multiresolution decomposition of the image. As an example, the Poisson case is treated in-depth. Using the new transfor
Conduct of the International Multigrid Conference
Mccormick, S.
1984-01-01
The 1983 International Multigrid Conference was held at Colorado's Copper Mountain Ski Resort, April 5-8. It was organized jointly by the Institute for Computational Studies at Colorado State University, U.S.A., and the Gasellschaft fur Mathematik und Datenverarbeitung Bonn, F.R. Germany, and was sponsored by the Air Force Office of Sponsored Research and National Aeronautics and Space Administration Headquarters. The conference was attended by 80 scientists, divided by institution almost equally into private industry, research laboratories, and academia. Fifteen attendees came from countries other than the U.S.A. In addition to the fruitful discussions, the most significant factor of the conference was of course the lectures. The lecturers include most of the leaders in the field of multigrid research. The program offered a nice integrated blend of theory, numerical studies, basic research, and applications. Some of the new areas of research that have surfaced since the Koln-Porz conference include: the algebraic multigrid approach; multigrid treatment of Euler equations for inviscid fluid flow problems; 3-D problems; and the application of MG methods on vector and parallel computers.
PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS
Institute of Scientific and Technical Information of China (English)
Yun-qing Huang; Shi Shu; Xi-jun Yu
2006-01-01
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.
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
Directory of Open Access Journals (Sweden)
E. L. Dmitrieva
2016-05-01
Full Text Available Basic peculiarities of nonlinear Kalman filtering algorithm applied to processing of interferometric signals are considered. Analytical estimates determining statistical characteristics of signal values prediction errors were obtained and analysis of errors histograms taking into account variations of different parameters of interferometric signal was carried out. Modeling of the signal prediction procedure with known fixed parameters and variable parameters of signal in the algorithm of nonlinear Kalman filtering was performed. Numerical estimates of prediction errors for interferometric signal values were obtained by formation and analysis of the errors histograms under the influence of additive noise and random variations of amplitude and frequency of interferometric signal. Nonlinear Kalman filter is shown to provide processing of signals with randomly variable parameters, however, it does not take into account directly the linearization error of harmonic function representing interferometric signal that is a filtering error source. The main drawback of the linear prediction consists in non-Gaussian statistics of prediction errors including cases of random deviations of signal amplitude and/or frequency. When implementing stochastic filtering of interferometric signals, it is reasonable to use prediction procedures based on local statistics of a signal and its parameters taken into account.
A Multi-Grid Iterative Method for Photoacoustic Tomography.
Javaherian, Ashkan; Holman, Sean
2016-11-04
Inspired by the recent advances on minimizing nonsmooth or bound-constrained convex functions on models using varying degrees of fidelity, we propose a line search multigrid (MG) method for full-wave iterative image reconstruction in photoacoustic tomography (PAT) in heterogeneous media. To compute the search direction at each iteration, we decide between the gradient at the target level, or alternatively an approximate error correction at a coarser level, relying on some predefined criteria. To incorporate absorption and dispersion, we derive the analytical adjoint directly from the first-order acoustic wave system. The effectiveness of the proposed method is tested on a total-variation penalized Iterative Shrinkage Thresholding algorithm (ISTA) and its accelerated variant (FISTA), which have been used in many studies of image reconstruction in PAT. The results show the great potential of the proposed method in improving speed of iterative image reconstruction.
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.
A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schr(o)dinger system
Institute of Scientific and Technical Information of China (English)
Cai Jia-Xiang; Wang Yu-Shun
2013-01-01
We derive a new method for a coupled nonlinear Schr(o)dinger system by using the square of first-order Fourier spectral differentiation matrix D1 instead of traditional second-order Fourier spectral differentiation matrix D2 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.
Yang, Ji Seung; Cai, Li
2014-01-01
The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard…
Yang, Ji Seung; Cai, Li
2014-01-01
The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard…
DEFF Research Database (Denmark)
Ghoreishi, Newsha; Sørensen, Jan Corfixen; Jørgensen, Bo Nørregaard
2015-01-01
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...
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.
A Non-linear Scaling Algorithm Based on chirp-z Transform for Squint Mode FMCW-SAR
Directory of Open Access Journals (Sweden)
Yu Bin-bin
2012-03-01
Full Text Available A non-linear scaling chirp-z imaging algorithm for squint mode Frequency Modulated Continuous Wave Synthetic Aperture Radar (FMCW-SAR is presented to solve the problem of the focus accuracy decline. Based on the non-linear characteristics in range direction for the echo signal in Doppler domain, a non-linear modulated signal is introduced to perform a non-linear scaling based on chirp-z transform. Then the error due to range compression and range migration correction can be reduced, therefore the range resolution of radar image is improved. By using the imaging algorithm proposed, the imaging performances for point targets, compared with that from the original chirp-z algorithm, are demonstrated to be improved in range resolution and image contrast, and to be maintained the same in azimuth resolution.
Integral and integrable algorithms for a nonlinear shallow-water wave equation
Camassa, Roberto; Huang, Jingfang; Lee, Long
2006-08-01
An asymptotic higher-order model of wave dynamics in shallow water is examined in a combined analytical and numerical study, with the aim of establishing robust and efficient numerical solution methods. Based on the Hamiltonian structure of the nonlinear equation, an algorithm corresponding to a completely integrable particle lattice is implemented first. Each "particle" in the particle method travels along a characteristic curve. The resulting system of nonlinear ordinary differential equations can have solutions that blow-up in finite time. We isolate the conditions for global existence and prove l1-norm convergence of the method in the limit of zero spatial step size and infinite particles. The numerical results show that this method captures the essence of the solution without using an overly large number of particles. A fast summation algorithm is introduced to evaluate the integrals of the particle method so that the computational cost is reduced from O( N2) to O( N), where N is the number of particles. The method possesses some analogies with point vortex methods for 2D Euler equations. In particular, near singular solutions exist and singularities are prevented from occurring in finite time by mechanisms akin to those in the evolution of vortex patches. The second method is based on integro-differential formulations of the equation. Two different algorithms are proposed, based on different ways of extracting the time derivative of the dependent variable by an appropriately defined inverse operator. The integro-differential formulations reduce the order of spatial derivatives, thereby relaxing the stability constraint and allowing large time steps in an explicit numerical scheme. In addition to the Cauchy problem on the infinite line, we include results on the study of the nonlinear equation posed in the quarter (space-time) plane. We discuss the minimum number of boundary conditions required for solution uniqueness and illustrate this with numerical
Extension of the SAEM algorithm for nonlinear mixed models with 2 levels of random effects.
Panhard, Xavière; Samson, Adeline
2009-01-01
This article focuses on parameter estimation of multilevel nonlinear mixed-effects models (MNLMEMs). These models are used to analyze data presenting multiple hierarchical levels of grouping (cluster data, clinical trials with several observation periods, ...). The variability of the individual parameters of the regression function is thus decomposed as a between-subject variability and higher levels of variability (e.g. within-subject variability). We propose maximum likelihood estimates of parameters of those MNLMEMs with 2 levels of random effects, using an extension of the stochastic approximation version of expectation-maximization (SAEM)-Monte Carlo Markov chain algorithm. The extended SAEM algorithm is split into an explicit direct expectation-maximization (EM) algorithm and a stochastic EM part. Compared to the original algorithm, additional sufficient statistics have to be approximated by relying on the conditional distribution of the second level of random effects. This estimation method is evaluated on pharmacokinetic crossover simulated trials, mimicking theophylline concentration data. Results obtained on those data sets with either the SAEM algorithm or the first-order conditional estimates (FOCE) algorithm (implemented in the nlme function of R software) are compared: biases and root mean square errors of almost all the SAEM estimates are smaller than the FOCE ones. Finally, we apply the extended SAEM algorithm to analyze the pharmacokinetic interaction of tenofovir on atazanavir, a novel protease inhibitor, from the Agence Nationale de Recherche sur le Sida 107-Puzzle 2 study. A significant decrease of the area under the curve of atazanavir is found in patients receiving both treatments.
A filter algorithm for multi-measurement nonlinear system with parameter perturbation
Institute of Scientific and Technical Information of China (English)
GUO Yun-fei; WEI Wei; XUE An-ke; MAO Dong-cai
2006-01-01
An improved interacting multiple models particle filter (IMM-PF) algorithm is proposed for multi-measurement nonlinear system with parameter perturbation. It divides the perturbation region into sub-regions and assigns each of them a particle filter. Hence the perturbation problem is converted into a multi-model filters problem. It combines the multiple measurements into a fusion value according to their likelihood function. In the simulation study, we compared it with the IMM-KF and the H-infinite filter; the results testify to its advantage over the other two methods.
Karabiber, Fethullah; Vecchio, Pietro; Grassi, Giuseppe
2011-12-01
The Bio-inspired (Bi-i) Cellular Vision System is a computing platform consisting of sensing, array sensing-processing, and digital signal processing. The platform is based on the Cellular Neural/Nonlinear Network (CNN) paradigm. This article presents the implementation of a novel CNN-based segmentation algorithm onto the Bi-i system. Each part of the algorithm, along with the corresponding implementation on the hardware platform, is carefully described through the article. The experimental results, carried out for Foreman and Car-phone video sequences, highlight the feasibility of the approach, which provides a frame rate of about 26 frames/s. Comparisons with existing CNN-based methods show that the conceived approach is more accurate, thus representing a good trade-off between real-time requirements and accuracy.
Directory of Open Access Journals (Sweden)
Vecchio Pietro
2011-01-01
Full Text Available Abstract The Bio-inspired (Bi-i Cellular Vision System is a computing platform consisting of sensing, array sensing-processing, and digital signal processing. The platform is based on the Cellular Neural/Nonlinear Network (CNN paradigm. This article presents the implementation of a novel CNN-based segmentation algorithm onto the Bi-i system. Each part of the algorithm, along with the corresponding implementation on the hardware platform, is carefully described through the article. The experimental results, carried out for Foreman and Car-phone video sequences, highlight the feasibility of the approach, which provides a frame rate of about 26 frames/s. Comparisons with existing CNN-based methods show that the conceived approach is more accurate, thus representing a good trade-off between real-time requirements and accuracy.
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.
A Parallel Multigrid Method for the Finite Element Analysis of Mechanical Contact
Energy Technology Data Exchange (ETDEWEB)
Hales, J D; Parsons, I D
2002-03-21
A geometrical multigrid method for solving the linearized matrix equations arising from node-on-face three-dimensional finite element contact is described. The development of an efficient implementation of this combination that minimizes both the memory requirements and the computational cost requires careful construction and storage of the portion of the coarse mesh stiffness matrices that are associated with the contact stiffness on the fine mesh. The multigrid contact algorithm is parallelized in a manner suitable for distributed memory architectures: results are presented that demonstrates the scheme's scalability. The solution of a large contact problem derived from an analysis of the factory joints present in the Space Shuttle reusable solid rocket motor demonstrates the usefulness of the general approach.
Guo, Hongbo; He, Xiaowei; Liu, Muhan; Zhang, Zeyu; Hu, Zhenhua; Tian, Jie
2017-03-01
Cerenkov luminescence tomography (CLT), as a promising optical molecular imaging modality, can be applied to cancer diagnostic and therapeutic. Most researches about CLT reconstruction are based on the finite element method (FEM) framework. However, the quality of FEM mesh grid is still a vital factor to restrict the accuracy of the CLT reconstruction result. In this paper, we proposed a multi-grid finite element method framework, which was able to improve the accuracy of reconstruction. Meanwhile, the multilevel scheme adaptive algebraic reconstruction technique (MLS-AART) based on a modified iterative algorithm was applied to improve the reconstruction accuracy. In numerical simulation experiments, the feasibility of our proposed method were evaluated. Results showed that the multi-grid strategy could obtain 3D spatial information of Cerenkov source more accurately compared with the traditional single-grid FEM.
Sidilkover, David
1994-01-01
We present a new approach towards the construction of a genuinely multidimensional high-resolution scheme for computing steady-state solutions of the Euler equations of gas dynamics. The unique advantage of this approach is that the Gauss-Seidel relaxation is stable when applied directly to the high-resolution discrete equations, thus allowing us to construct a very efficient and simple multigrid steady-state solver. This is the only high-resolution scheme known to us that has this property. The two-dimensional scheme is presented in detail. It is formulated on triangular (structured and unstructured) meshes and can be interpreted as a genuinely two-dimensional extension of the Roe scheme. The quality of the solutions obtained using this scheme and the performance of the multigrid algorithm are illustrated by the numerical experiments. Construction of the three dimensional scheme is outlined briefly as well.
The Closest Point Method and Multigrid Solvers for Elliptic Equations on Surfaces
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.
Multigrid-based grid-adaptive solution of the Navier-Stokes equations
Michelsen, Jess
A finite volume scheme for solution of the incompressible Navier-Stokes equations in two dimensions and axisymmetry is described. Solutions are obtained on nonorthogonal, solution adaptive BFC grids, based on the Brackbill-Saltzman generator. Adaptivity is achieved by the use of a single control function based on the local kinetic energy production. Nonstaggered allocation of pressure and Cartesian velocity components avoids the introduction of curvature terms associated with the use of a grid-direction vector-base. A special interpolation of the pressure correction equation in the SIMPLE algorithm ensures firm coupling between velocity and pressure field. Steady-state solutions are accelerated by a full approximation multigrid scheme working on the decoupled grid-flow problem, while an algebraic multigrid scheme is employed for the pressure correction equation.
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 inner...... block boundaries. A Robin parameter that depends on grid geometry and grid discontinuity at block interfaces is introduced. The general solution algorithm is based on SIMPLE method and a conservative _nite-volume scheme on block-structured grids with discontinuous interfaces. The multigrid method...... is used to obtain the solution of pressure-correction equation where an Incomplete Block LU factorization is used as the relaxation scheme. Solution on the coarsest grid is done with an Incomplete Block LU preconditioned Conjugate Gradient method. Results from computations of laminar ows around a circular...
Multilayer perceptron for robust nonlinear interval regression analysis using genetic algorithms.
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.
Multilayer Perceptron for Robust Nonlinear Interval Regression Analysis Using Genetic Algorithms
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. PMID:25110755
Multigrid with red black SOR revisited
Energy Technology Data Exchange (ETDEWEB)
Yavneh, I. [Technion-Israel Institute of Technology, Haifa (Israel)
1994-12-31
Optimal relaxation parameters are obtained for red-black point Gauss-Seidel relaxation in multigrid solvers of a family of elliptic equations. The resulting relaxation schemes are found to retain high efficiency over an appreciable range of coefficients of the elliptic operator, yielding simple, inexpensive and fully parallelizable smoothers in many situations where more complicated and less cost-effective block-relaxation and/or partial coarsening are commonly used.
Grandchild of the frequency: Decomposition multigrid method
Energy Technology Data Exchange (ETDEWEB)
Dendy, J.E. Jr. [Los Alamos National Lab., NM (United States); Tazartes, C.C. [Univ. of California, Los Angeles, CA (United States)
1994-12-31
Previously the authors considered the frequency decomposition multigrid method and rejected it because it was not robust for problems with discontinuous coefficients. In this paper they show how to modify the method so as to obtain such robustness while retaining robustness for problems with anisotropic coefficients. They also discuss application of this method to a problem arising in global ocean modeling on the CM-5.
Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm
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
Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems.
Liu, Derong; Wei, Qinglai
2014-03-01
This paper is concerned with a new discrete-time policy iteration adaptive dynamic programming (ADP) method for solving the infinite horizon optimal control problem of nonlinear systems. The idea is to use an iterative ADP technique to obtain the iterative control law, which optimizes the iterative performance index function. The main contribution of this paper is to analyze the convergence and stability properties of policy iteration method for discrete-time nonlinear systems for the first time. It shows that the iterative performance index function is nonincreasingly convergent to the optimal solution of the Hamilton-Jacobi-Bellman equation. It is also proven that any of the iterative control laws can stabilize the nonlinear systems. Neural networks are used to approximate the performance index function and compute the optimal control law, respectively, for facilitating the implementation of the iterative ADP algorithm, where the convergence of the weight matrices is analyzed. Finally, the numerical results and analysis are presented to illustrate the performance of the developed method.
Lee, Ping-Chang
2014-03-01
Computed tomography (CT) plays a key role in modern medical system, whether it be for diagnosis or therapy. As an increased risk of cancer development is associated with exposure to radiation, reducing radiation exposure in CT becomes an essential issue. Based on the compressive sensing (CS) theory, iterative based method with total variation (TV) minimization is proven to be a powerful framework for few-view tomographic image reconstruction. Multigrid method is an iterative method for solving both linear and nonlinear systems, especially when the system contains a huge number of components. In medical imaging, image background is often defined by zero intensity, thus attaining spatial support of the image, which is helpful for iterative reconstruction. In the proposed method, the image support is not considered as a priori knowledge. Rather, it evolves during the reconstruction process. Based on the CS framework, we proposed a multigrid method with adaptive spatial support constraint. The simultaneous algebraic reconstruction (SART) with TV minimization is implemented for comparison purpose. The numerical result shows: 1. Multigrid method has better performance while less than 60 views of projection data were used, 2. Spatial support highly improves the CS reconstruction, and 3. When few views of projection data were measured, our method performs better than the SART+TV method with spatial support constraint.
Multigrid Acceleration of Time-Accurate DNS of Compressible Turbulent Flow
Broeze, Jan; Geurts, Bernard; Kuerten, Hans; Streng, Martin
1996-01-01
An efficient scheme for the direct numerical simulation of 3D transitional and developed turbulent flow is presented. Explicit and implicit time integration schemes for the compressible Navier-Stokes equations are compared. The nonlinear system resulting from the implicit time discretization is solved with an iterative method and accelerated by the application of a multigrid technique. Since we use central spatial discretizations and no artificial dissipation is added to the equations, the smoothing method is less effective than in the more traditional use of multigrid in steady-state calculations. Therefore, a special prolongation method is needed in order to obtain an effective multigrid method. This simulation scheme was studied in detail for compressible flow over a flat plate. In the laminar regime and in the first stages of turbulent flow the implicit method provides a speed-up of a factor 2 relative to the explicit method on a relatively coarse grid. At increased resolution this speed-up is enhanced correspondingly.
Liver disorder diagnosis using linear, nonlinear and decision tree classification algorithms
Directory of Open Access Journals (Sweden)
Aman Singh
2016-10-01
Full Text Available In India and across the globe, liver disease is a serious area of concern in medicine. Therefore, it becomes essential to use classification algorithms for assessing the disease in order to improve the efficiency of medical diagnosis which eventually leads to appropriate and timely treatment. The study accordingly implemented various classification algorithms including linear discriminant analysis (LDA, diagonal linear discriminant analysis (DLDA, quadratic discriminant analysis (QDA, diagonal quadratic discriminant analysis (DQDA, naive bayes (NB, feed-forward neural network (FFNN and classification and regression tree (CART in an attempt to enhance the diagnostic accuracy of liver disorder and to reduce the inefficiencies caused by false diagnosis. The results demonstrated that CART had emerged as the best model by achieving higher diagnostic accuracy than LDA, DLDA, QDA, DQDA, NB and FFNN. FFNN stood second in comparison and performed better than rest of the classifiers. After evaluation, it can be said that the precision of a classification algorithm depends on the type and features of a dataset. For the given dataset, decision tree classifier CART outperforms all other linear and nonlinear classifiers. It also showed the capability of assisting clinicians in determining the existence of liver disorder, in attaining better diagnosis and in avoiding delay in treatment.
DEFF Research Database (Denmark)
Rubæk, Tonny; Meaney, P. M.; Meincke, Peter;
2007-01-01
Breast-cancer screening using microwave imaging is emerging as a new promising technique as a supplement to X-ray mammography. To create tomographic images from microwave measurements, it is necessary to solve a nonlinear inversion problem, for which an algorithm based on the iterative Gauss-Newton...... method has been developed at Dartmouth College. This algorithm determines the update values at each iteration by solving the set of normal equations of the problem using the Tikhonov algorithm. In this paper, a new algorithm for determining the iteration update values in the Gauss-Newton algorithm...... algorithm is compared to the Gauss-Newton algorithm with Tikhonov regularization and is shown to reconstruct images of similar quality using fewer iterations....
MULTIGRID FOR THE MORTAR FINITE ELEMENT FOR PARABOLIC PROBLEM
Institute of Scientific and Technical Information of China (English)
Xue-jun Xu; Jin-ru Chen
2003-01-01
In this paper, a mortar finite element method for parabolic problem is presented. Multigrid method is used for solving the resulting discrete system. It is shown that the multigrid method is optimal, I.e, the convergence rate is independent of the mesh size L and the time step parameter т.
ON CONVERGENCE OF MULTIGRID METHOD FOR NONNEGATIVE DEFINITE SYSTEMS
Institute of Scientific and Technical Information of China (English)
Qian-shun Chang; Wei-wei Sun
2005-01-01
In this paper, we consider multigrid methods for solving symmetric nonnegative definite matrix equations. We present some interesting features of the multigrid method and prove that the method is convergent in L2 space and the convergent solution is unique for such nonnegative definite system and given initial guess.
Chen, Yunjie; Zhan, Tianming; Zhang, Ji; Wang, Hongyuan
2016-01-01
We propose a novel segmentation method based on regional and nonlocal information to overcome the impact of image intensity inhomogeneities and noise in human brain magnetic resonance images. With the consideration of the spatial distribution of different tissues in brain images, our method does not need preestimation or precorrection procedures for intensity inhomogeneities and noise. A nonlocal information based Gaussian mixture model (NGMM) is proposed to reduce the effect of noise. To reduce the effect of intensity inhomogeneity, the multigrid nonlocal Gaussian mixture model (MNGMM) is proposed to segment brain MR images in each nonoverlapping multigrid generated by using a new multigrid generation method. Therefore the proposed model can simultaneously overcome the impact of noise and intensity inhomogeneity and automatically classify 2D and 3D MR data into tissues of white matter, gray matter, and cerebral spinal fluid. To maintain the statistical reliability and spatial continuity of the segmentation, a fusion strategy is adopted to integrate the clustering results from different grid. The experiments on synthetic and clinical brain MR images demonstrate the superior performance of the proposed model comparing with several state-of-the-art algorithms.
Nonlinear System Identification with a Real–Coded Genetic Algorithm (RCGA
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Cherif Imen
2015-12-01
Full Text Available This paper is devoted to the blind identification problem of a special class of nonlinear systems, namely, Volterra models, using a real-coded genetic algorithm (RCGA. The model input is assumed to be a stationary Gaussian sequence or an independent identically distributed (i.i.d. process. The order of the Volterra series is assumed to be known. The fitness function is defined as the difference between the calculated cumulant values and analytical equations in which the kernels and the input variances are considered. Simulation results and a comparative study for the proposed method and some existing techniques are given. They clearly show that the RCGA identification method performs better in terms of precision, time of convergence and simplicity of programming.
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.
Yukita, Kazuto; Kato, Shinya; Goto, Yasuyuki; Ichiyanagi, Katsuhiro; Kawashima, Yasuhiro
Recently, the independent power producers (IPPs) and the distributed power generations (DGs) are increase on by the electric power system with the power system deregulation. And the power system becomes more complicated. It is necessary to carry out the electric power demand forecasting in order to the power system is operated for the high economical and the high-efficient. For the improvement of electric power demand forecasting, many methods, such as the methods using fuzzy theory, neural network and SDP data, are proposed. In this paper, we proposed the method using STROGANOFF (STructured Re-presentation on Genetic Algorithms for Non-linear Function Fitting) that approximate the value of predictive to the future data by the past data is obtained. Also, the weather condition was considered for the forecasting that is improvement, and the daily peak load forecasting in next day on Chubu district in Japan was carried out, and the effectiveness of proposed method was examined.
Development of Algorithms for Control of Motor Boat as Multidimensional Nonlinear Object
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Gaiduk Anatoliy
2015-01-01
Full Text Available In this paper authors develop and research system for motor boat control, that allows to move along the stated paths with the given speed. It is assumed, that boat is equipped by the measuring system that provides current coordinates, linear and angular velocities. Control system is based upon the mathematical model, presented earlier (see references. In order to analytically find the necessary controls, all equations were transformed to Jordan controllable form. Besides solution this transformation also allows to handle model nonlinearities and get required quality of movement along the stated paths. Control system includes algorithms for control of longtitudal velocity and boat course. Research of the proposed control system according to boat design limitations for the values of control variables was performed by simulation in MATLAB. Results of two experiments, different in value of the required velocity are discussed.
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.
Nonlinear model-based control algorithm for a distillation column using software sensor.
Jana, Amiya Kumar; Samanta, Amar Nath; Ganguly, Saibal
2005-04-01
This paper presents the design of model-based globally linearizing control (GLC) structure for a distillation process within the differential geometric framework. The model of a nonideal binary distillation column, whose characteristics were highly nonlinear and strongly interactive, is used as a real process. The classical GLC law is comprised of a transformer (input-output linearizing state feedback), a nonlinear state observer, and an external PI controller. The tray temperature based short-cut observer (TTBSCO) has been used as a state estimator within the control structure, in which all tray temperatures were considered to be measured. Accordingly, the liquid phase composition of each tray was calculated online using the derived temperature-composition correlation. In the simulation experiment, the proposed GLC coupled with TTBSCO (GLC-TTBSCO) outperformed a conventional PI controller based on servo performances with and without measurement noise as well as on regulatory behaviors. In the subsequent part, the GLC law has been synthesized in conjunction with tray temperature based reduced-order observer (GLC-TTBROO) where the distillate and bottom compositions of the distillation process have been inferred from top and bottom product temperatures respectively, which were measured online. Finally, the comparative performance of the GLC-TTBSCO and the GLC-TTBROO has been addressed under parametric uncertainty and the GLC-TTBSCO algorithm provided slightly better performance than the GLC-TTBROO. The resulting control laws are rather general and can be easily adopted for other binary distillation columns.
Directory of Open Access Journals (Sweden)
Deyuan Meng
2014-05-01
Full Text Available The dynamics of pneumatic systems are highly nonlinear, and there normally exists a large extent of model uncertainties; the precision motion trajectory tracking control of pneumatic cylinders is still a challenge. In this paper, two typical nonlinear controllers—adaptive controller and deterministic robust controller—are constructed firstly. Considering that they have both benefits and limitations, an adaptive robust controller (ARC is further proposed. The ARC is a combination of the first two controllers; it employs online recursive least squares estimation (RLSE to reduce the extent of parametric uncertainties, and utilizes the robust control method to attenuate the effects of parameter estimation errors, unmodeled dynamics, and disturbances. In order to solve the conflicts between the robust control design and the parameter adaption law design, the projection mapping is used to condition the RLSE algorithm so that the parameter estimates are kept within a known bounded convex set. Theoretically, ARC possesses the advantages of the adaptive control and the deterministic robust control, and thus an even better tracking performance can be expected. Extensive comparative experimental results are presented to illustrate the achievable performance of the three proposed controllers and their performance robustness to the parameter variations and sudden disturbance.
Scalable Parallel Algebraic Multigrid Solvers
Energy Technology Data Exchange (ETDEWEB)
Bank, R; Lu, S; Tong, C; Vassilevski, P
2005-03-23
The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.
Is the Multigrid Method Fault Tolerant? The Two-Grid Case
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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.
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Xingwen Zhu
2015-01-01
Full Text Available Smoothing analysis process of distributive red-black Jacobi relaxation in multigrid method for solving 2D Stokes flow is mainly investigated on the nonstaggered grid by using local Fourier analysis (LFA. For multigrid relaxation, the nonstaggered discretizing scheme of Stokes flow is generally stabilized by adding an artificial pressure term. Therefore, an important problem is how to determine the zone of parameter in adding artificial pressure term in order to make stabilization of the algorithm for multigrid relaxation. To end that, a distributive red-black Jacobi relaxation technique for the 2D Stokes flow is established. According to the 2h-harmonics invariant subspaces in LFA, the Fourier representation of the distributive red-black Jacobi relaxation for discretizing Stokes flow is given by the form of square matrix, whose eigenvalues are meanwhile analytically computed. Based on optimal one-stage relaxation, a mathematical relation of the parameter in artificial pressure term between the optimal relaxation parameter and related smoothing factor is well yielded. The analysis results show that the numerical schemes for solving 2D Stokes flow by multigrid method on the distributive red-black Jacobi relaxation have a specified convergence parameter zone of the added artificial pressure term.
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.
Energy Technology Data Exchange (ETDEWEB)
Finsterle, S.; Kowalsky, M.B.
2010-10-15
We propose a modification to the Levenberg-Marquardt minimization algorithm for a more robust and more efficient calibration of highly parameterized, strongly nonlinear models of multiphase flow through porous media. The new method combines the advantages of truncated singular value decomposition with those of the classical Levenberg-Marquardt algorithm, thus enabling a more robust solution of underdetermined inverse problems with complex relations between the parameters to be estimated and the observable state variables used for calibration. The truncation limit separating the solution space from the calibration null space is re-evaluated during the iterative calibration process. In between these re-evaluations, fewer forward simulations are required, compared to the standard approach, to calculate the approximate sensitivity matrix. Truncated singular values are used to calculate the Levenberg-Marquardt parameter updates, ensuring that safe small steps along the steepest-descent direction are taken for highly correlated parameters of low sensitivity, whereas efficient quasi-Gauss-Newton steps are taken for independent parameters with high impact. The performance of the proposed scheme is demonstrated for a synthetic data set representing infiltration into a partially saturated, heterogeneous soil, where hydrogeological, petrophysical, and geostatistical parameters are estimated based on the joint inversion of hydrological and geophysical data.
DEFF Research Database (Denmark)
Boiroux, Dimitri; Hagdrup, Morten; Mahmoudi, Zeinab
2016-01-01
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 pat...
Shoemaker, Christine; Wan, Ying
2016-04-01
Optimization of nonlinear water resources management issues which have a mixture of fixed (e.g. construction cost for a well) and variable (e.g. cost per gallon of water pumped) costs has been not well addressed because prior algorithms for the resulting nonlinear mixed integer problems have required many groundwater simulations (with different configurations of decision variable), especially when the solution space is multimodal. In particular heuristic methods like genetic algorithms have often been used in the water resources area, but they require so many groundwater simulations that only small systems have been solved. Hence there is a need to have a method that reduces the number of expensive groundwater simulations. A recently published algorithm for nonlinear mixed integer programming using surrogates was shown in this study to greatly reduce the computational effort for obtaining accurate answers to problems involving fixed costs for well construction as well as variable costs for pumping because of a substantial reduction in the number of groundwater simulations required to obtain an accurate answer. Results are presented for a US EPA hazardous waste site. The nonlinear mixed integer surrogate algorithm is general and can be used on other problems arising in hydrology with open source codes in Matlab and python ("pySOT" in Bitbucket).
DEFF Research Database (Denmark)
Kjems, Ulrik; Storther, Stephen C.; Anderson, Jon
1999-01-01
This paper addresses the problem of neuro-anatomical registration across individuals for functional [15O]water PET activation studies. A new algorithm for 3D non-linear structural registration (warping) of MR scans is presented. The method performs a hierarchically scaled search for a displacement...
DEFF Research Database (Denmark)
Kjems, Ulrik; Storther, Stephen C.; Anderson, Jon
1999-01-01
This paper addresses the problem of neuro-anatomical registration across individuals for functional [15O]water PET activation studies. A new algorithm for 3D non-linear structural registration (warping) of MR scans is presented. The method performs a hierarchically scaled search for a displacemen...
Pham, Mai Quyen; Ducros, Nicolas; Nicolas, Barbara
2017-03-01
Spectral computed tomography (CT) exploits the measurements obtained by a photon counting detector to reconstruct the chemical composition of an object. In particular, spectral CT has shown a very good ability to image K-edge contrast agent. Spectral CT is an inverse problem that can be addressed solving two subproblems, namely the basis material decomposition (BMD) problem and the tomographic reconstruction problem. In this work, we focus on the BMD problem, which is ill-posed and nonlinear. The BDM problem is classically either linearized, which enables reconstruction based on compressed sensing methods, or nonlinearly solved with no explicit regularization scheme. In a previous communication, we proposed a nonlinear regularized Gauss-Newton (GN) algorithm.1 However, this algorithm can only be applied to convex regularization functionals. In particular, the lp (p thorax phantom made of soft tissue, bone and gadolinium, which is scanned with a 90-kV x-ray tube and a 3-bin photon counting detector.
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).
Directory of Open Access Journals (Sweden)
K. Seshadri Sastry
2013-06-01
Full Text Available This paper presents Adaptive Population Sizing Genetic Algorithm (AGA assisted Maximum Likelihood (ML estimation of Orthogonal Frequency Division Multiplexing (OFDM symbols in the presence of Nonlinear Distortions. The proposed algorithm is simulated in MATLAB and compared with existing estimation algorithms such as iterative DAR, decision feedback clipping removal, iteration decoder, Genetic Algorithm (GA assisted ML estimation and theoretical ML estimation. Simulation results proved that the performance of the proposed AGA assisted ML estimation algorithm is superior compared with the existing estimation algorithms. Further the computational complexity of GA assisted ML estimation increases with increase in number of generations or/and size of population, in the proposed AGA assisted ML estimation algorithm the population size is adaptive and depends on the best fitness. The population size in GA assisted ML estimation is fixed and sufficiently higher size of population is taken to ensure good performance of the algorithm but in proposed AGA assisted ML estimation algorithm the size of population changes as per requirement in an adaptive manner thus reducing the complexity of the algorithm.
Sha, Daohang
2010-01-01
Back-propagation with gradient method is the most popular learning algorithm for feed-forward neural networks. However, it is critical to determine a proper fixed learning rate for the algorithm. In this paper, an optimized recursive algorithm is presented for online learning based on matrix operation and optimization methods analytically, which can avoid the trouble to select a proper learning rate for the gradient method. The proof of weak convergence of the proposed algorithm also is given. Although this approach is proposed for three-layer, feed-forward neural networks, it could be extended to multiple layer feed-forward neural networks. The effectiveness of the proposed algorithms applied to the identification of behavior of a two-input and two-output non-linear dynamic system is demonstrated by simulation experiments.
Mitchell, Lawrence; Müller, Eike Hermann
2016-12-01
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated (mixed) finite element discretisations on unstructured grids an efficient implementation can be very time consuming and requires the programmer to have in-depth knowledge of the mathematical theory, parallel computing and optimisation techniques on manycore CPUs. In this paper we show how the development of bespoke multigrid preconditioners can be simplified significantly by using a framework which allows the expression of the each component of the algorithm at the correct abstraction level. Our approach (1) allows the expression of the finite element problem in a language which is close to the mathematical formulation of the problem, (2) guarantees the automatic generation and efficient execution of parallel optimised low-level computer code and (3) is flexible enough to support different abstraction levels and give the programmer control over details of the preconditioner. We use the composable abstractions of the Firedrake/PyOP2 package to demonstrate the efficiency of this approach for the solution of strongly anisotropic PDEs in atmospheric modelling. The weak formulation of the PDE is expressed in Unified Form Language (UFL) and the lower PyOP2 abstraction layer allows the manual design of computational kernels for a bespoke geometric multigrid preconditioner. We compare the performance of this preconditioner to a single-level method and hypre's BoomerAMG algorithm. The Firedrake/PyOP2 code is inherently parallel and we present a detailed performance analysis for a single node (24 cores) on the ARCHER supercomputer. Our implementation utilises a significant fraction of the available memory bandwidth and shows very good weak scaling on up to 6,144 compute cores.
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.
Final Report on Subcontract B605152. Multigrid Methods for Systems of PDEs
Energy Technology Data Exchange (ETDEWEB)
Brannick, James [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Xu, Jinchao [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-07-07
The project team has continued with work on developing aggressive coarsening techniques for AMG methods. Of particular interest is the idea to use aggressive coarsening with polynomial smoothing. Using local Fourier analysis the optimal values for the parameters involved in defining the polynomial smoothers are determined automatically in a way to achieve fast convergence of cycles with aggressive coarsening. Numerical tests have the sharpness of the theoretical results. The methods are highly parallelizable and efficient multigrid algorithms on structured and semistructured grids in two and three spatial dimensions.
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Xiaoyan Lei
2016-01-01
Full Text Available A model for dynamic analysis of the vehicle-track nonlinear coupling system is established by the finite element method. The whole system is divided into two subsystems: the vehicle subsystem and the track subsystem. Coupling of the two subsystems is achieved by equilibrium conditions for wheel-to-rail nonlinear contact forces and geometrical compatibility conditions. To solve the nonlinear dynamics equations for the vehicle-track coupling system, a cross iteration algorithm and a relaxation technique are presented. Examples of vibration analysis of the vehicle and slab track coupling system induced by China’s high speed train CRH3 are given. In the computation, the influences of linear and nonlinear wheel-to-rail contact models and different train speeds are considered. It is found that the cross iteration algorithm and the relaxation technique have the following advantages: simple programming; fast convergence; shorter computation time; and greater accuracy. The analyzed dynamic responses for the vehicle and the track with the wheel-to-rail linear contact model are greater than those with the wheel-to-rail nonlinear contact model, where the increasing range of the displacement and the acceleration is about 10%, and the increasing range of the wheel-to-rail contact force is less than 5%.
Njafa, Jean-pierre Tchapet
2016-01-01
In this paper we present a model of Quantum Associative Memory (QAM) which can be a helpful tool for physicians without experience or laboratory facilities, for the diagnosis of four tropical diseases (malaria, typhoid fever, yellow fever and dengue) which have several similar symptoms. The memory can distinguish single infection from multi-infection. The two algorithms used for the Quantum Associative Memory are improve models of original linear algorithm made by Ventura for Quantum Associative Memory and the non-linear quantum search algorithm of Abrams and Lloyd. From the simulation results given, it appears that the efficiency of recognition is good when a particular symptom of a disease with the similar symptoms are inserted as linear algorithm is the main algorithm. The non-linear algorithm allows to confirm the diagnosis or to give some advices to the physician. So our QAM which have a graphical user interface for desktop and smartphone is a sensitive, low-cost diagnostic tools that enable rapid and ac...
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.
Energy Technology Data Exchange (ETDEWEB)
Kim, D.; Ghanem, R. [State Univ. of New York, Buffalo, NY (United States)
1994-12-31
Multigrid solution technique to solve a material nonlinear problem in a visual programming environment using the finite element method is discussed. The nonlinear equation of equilibrium is linearized to incremental form using Newton-Rapson technique, then multigrid solution technique is used to solve linear equations at each Newton-Rapson step. In the process, adaptive mesh refinement, which is based on the bisection of a pair of triangles, is used to form grid hierarchy for multigrid iteration. The solution process is implemented in a visual programming environment with distributed computing capability, which enables more intuitive understanding of solution process, and more effective use of resources.
Elenchezhiyan, M; Prakash, J
2015-09-01
In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme.
Designing A Nonlinear Integer Programming Model For A Cross-Dock By A Genetic Algorithm
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Bahareh Vaisi
2015-03-01
Full Text Available Abstract This paper presents a non-linear integer programming model for a cross-dock problem that considers the total transportation cost of inbound and outbound trucks from an origin to a destination and the total cost of assigning strip and stack doors to trucks based on their number of trips and the distance between doors in cross-dock. In previous studies these two cost-based problems are modeled separately however it is more realistic and practical to use both of them as an integrated cross-docking model. Additionally this model is solved for a randomly generated numerical example with three suppliers and two customers by the use of a genetic algorithm. By comparing two different parameter levels i.e. low and high numbers of populations the optimum solution is obtained considering a high level population size. A number of strip and stack doors are equal to a number of inbound and outbound trucks in the same sequence as 4 and 6 respectively. Finally the conclusion is presented.
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.
Multigrid methods for space fractional partial differential equations
Jiang, Yingjun; Xu, Xuejun
2015-12-01
We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means the convergence rates of the methods are independent of the mesh size and mesh level. Moreover, our theoretical analysis and convergence results do not require regularity assumptions of the model problems. Numerical results are given to support our theoretical findings.
A comparison of Eulerian and Lagrangian transport and non-linear reaction algorithms
Benson, David A.; Aquino, Tomás; Bolster, Diogo; Engdahl, Nicholas; Henri, Christopher V.; Fernàndez-Garcia, Daniel
2017-01-01
When laboratory-measured chemical reaction rates are used in simulations at the field-scale, the models typically overpredict the apparent reaction rates. The discrepancy is primarily due to poorer mixing of chemically distinct waters at the larger scale. As a result, realistic field-scale predictions require accurate simulation of the degree of mixing between fluids. The Lagrangian particle-tracking (PT) method is a now-standard way to simulate the transport of conservative or sorbing solutes. The method's main advantage is the absence of numerical dispersion (and its artificial mixing) when simulating advection. New algorithms allow particles of different species to interact in nonlinear (e.g., bimolecular) reactions. Therefore, the PT methods hold a promise of more accurate field-scale simulation of reactive transport because they eliminate the masking effects of spurious mixing due to advection errors inherent in grid-based methods. A hypothetical field-scale reaction scenario is constructed and run in PT and Eulerian (finite-volume/finite-difference) simulators. Grid-based advection schemes considered here include 1st- to 3rd-order spatially accurate total-variation-diminishing flux-limiting schemes, both of which are widely used in current transport/reaction codes. A homogeneous velocity field in which the Courant number is everywhere unity, so that the chosen Eulerian methods incur no error when simulating advection, shows that both the Eulerian and PT methods can achieve convergence in the L1 (integrated concentration) norm, but neither shows stricter pointwise convergence. In this specific case with a constant dispersion coefficient and bimolecular reaction A + B → P , the correct total amount of product is 0.221MA0, where MA0 is the original mass of reactant A. When the Courant number drops, the grid-based simulations can show remarkable errors due to spurious over- and under-mixing. In a heterogeneous velocity field (keeping the same constant and
A Critical Study of Agglomerated Multigrid Methods for Diffusion
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.
The mixed finite element multigrid method for stokes equations.
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 Q2-Q1 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.
An efficient algorithm for solving nonlinear system of differential equations and applications
Directory of Open Access Journals (Sweden)
Mustafa GÜLSU
2015-10-01
Full Text Available In this article, we apply Chebyshev collocation method to obtain the numerical solutions of nonlinear systems of differential equations. This method transforms the nonlinear systems of differential equation to nonlinear systems of algebraic equations. The convergence of the numerical method are given and their applicability is illustrated with some examples.
Dreano, D.
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.
Furuichi, M.; Nishiura, D.
2016-12-01
The complex dynamics of granular system is an essential part of natural processes such as crystal rich magma flow, accretion prism formation or tsunami sedimentation. Numerical modeling with Discrete Element Method (DEM) is an effective approach for understanding granular dynamics especially when the contact between particles induces strongly non-linear rheology (e.g. DEM-CFD simulation for magma reservoir [Bergantz et.al., Nature geo, 2015, Furuichi and Nishiura, G-cubed, 2014]). In Moving Lagrangian particle methods like DEM, a large number of particles is required to obtain an accurate solution. Therefore, an efficient parallelization of the code is important to handle huge particles system on HPC. However, since particles move around during the simulation, the workload between the different MPI processes becomes imbalance when using static sub-domains. To overcome this limitation, we present a new dynamic load balancing algorithms applicable to particle simulation methods such as DEM and Smoothed Particle Hydrodynamics (SPH) [Furuichi and Nishiura submitted to Comput. Phys. Comm.]. Our method utilizes flexible orthogonal domain decomposition in which the domain is divided into columns, each of which independently defines rectangle sub-domains by rows. We regard the difference of the executed time between neighbor logical processes as the residual of nonlinear problem of the domain change. The load balancing is attained by minimizing the residual within the framework of the iterative non-linear solver combined with the multi-grid level technique for the local relaxation. Scalability tests attest that the algorithm demonstrates close-to-optimal strong and weak scalability on the K-computer and the Earth Simulator. This result holds for even as well as uneven particle distribution, including different types of particles and heterogeneous computer architecture. We performed a DEM simulation with over 2 billion particles for demonstrating the proposed scheme. The
Challenges of Algebraic Multigrid across Multicore Architectures
Energy Technology Data Exchange (ETDEWEB)
Baker, A H; Gamblin, T; Schulz, M; Yang, U M
2010-04-12
Algebraic multigrid (AMG) is a popular solver for large-scale scientific computing and an essential component of many simulation codes. AMG has shown to be extremely efficient on distributed-memory architectures. However, when executed on modern multicore architectures, we face new challenges that can significantly deteriorate AMG's performance. We examine its performance and scalability on three disparate multicore architectures: a cluster with four AMD Opteron Quad-core processors per node (Hera), a Cray XT5 with two AMD Opteron Hex-core processors per node (Jaguar), and an IBM BlueGene/P system with a single Quad-core processor (Intrepid). We discuss our experiences on these platforms and present results using both an MPI-only and a hybrid MPI/OpenMP model. We also discuss a set of techniques that helped to overcome the associated problems, including thread and process pinning and correct memory associations.
Jafari, Masoumeh; Salimifard, Maryam; Dehghani, Maryam
2014-07-01
This paper presents an efficient method for identification of nonlinear Multi-Input Multi-Output (MIMO) systems in the presence of colored noises. The method studies the multivariable nonlinear Hammerstein and Wiener models, in which, the nonlinear memory-less block is approximated based on arbitrary vector-based basis functions. The linear time-invariant (LTI) block is modeled by an autoregressive moving average with exogenous (ARMAX) model which can effectively describe the moving average noises as well as the autoregressive and the exogenous dynamics. According to the multivariable nature of the system, a pseudo-linear-in-the-parameter model is obtained which includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. To overcome this problem, a Hierarchical Least Squares Iterative (HLSI) algorithm is used to simultaneously estimate the vector and the matrix of unknown parameters as well as the noises. The efficiency of the proposed identification approaches are investigated through three nonlinear MIMO case studies.
Directory of Open Access Journals (Sweden)
Fan Liang
2013-01-01
Full Text Available Off‐pump coronary artery bypass graft surgery outperforms the traditional on‐pump surgery because the assisted robotic tools can cancel the relative motion between the beating heart and the robotic tools, which reduces post‐surgery complications for patients. The challenge for the robot assisted tool when tracking the beating heart is the abrupt change caused by the nonlinear nature of heart motion and high precision surgery requirements. A characteristic analysis of 3D heart motion data through bi‐spectral analysis demonstrates the quadratic nonlinearity in heart motion. Therefore, it is necessary to introduce nonlinear heart motion prediction into the motion tracking control procedures. In this paper, the heart motion tracking problem is transformed into a heart motion model following problem by including the adaptive heart motion model into the controller. Moreover, the model following algorithm with the nonlinear heart motion model embedded inside provides more accurate future reference by the quadratic term of sinusoid series, which could enhance the tracking accuracy of sharp change point and approximate the motion with sufficient detail. The experiment results indicate that the proposed algorithm outperforms the linear prediction‐based model following controller in terms of tracking accuracy (root mean square.
Ilyas, Muhammad; Hong, Beomjin; Cho, Kuk; Baeg, Seung-Ho; Park, Sangdeok
2016-05-23
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.
Directory of Open Access Journals (Sweden)
Muhammad Ilyas
2016-05-01
Full Text Available 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.
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
A unified multigrid solver for the Navier-Stokes equations on mixed element meshes
Mavriplis, D. J.; Venkatakrishnan, V.
1995-01-01
A unified multigrid solution technique is presented for solving the Euler and Reynolds-averaged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms, and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the formulation of a complete solution technique which can handle structured grids, block structured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Navier-Stokes equations on tetrahedral elements, and the thin layer version of these equations on other types of elements, while using a single edge-based data-structure to construct the discretization over all element types. An agglomeration multigrid algorithm, which naturally handles meshes of any types of elements, is employed to accelerate convergence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tetrahedral elements into quadrilateral or prismatic elements is also described. The gains in computational efficiency afforded by the use of non-simplicial meshes over fully tetrahedral meshes are demonstrated through several examples.
Global Optimization Algorithm for Nonlinear Sum of Ratios Problems%非线性比式和问题的全局优化算法
Institute of Scientific and Technical Information of China (English)
焦红伟; 郭运瑞; 陈永强
2008-01-01
In this paper,a global optimization algorithm is proposed for nonlinear sum of ratios problem(P).The algorithm works by globally solving problem(P1)that is equivalent to problem(P),by utilizing linearization technique a linear relaxation programming of the(P1)is then obtained.The proposed algorithm is convergent to the global minimum of(P1)through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming.Numerical results indicate that the proposed algorithm is feasible and can be used to globally solve nonlinear sum of ratios problems(P).
Li, Xiao-Dong; Lv, Mang-Mang; Ho, John K. L.
2016-07-01
In this article, two adaptive iterative learning control (ILC) algorithms are presented for nonlinear continuous systems with non-parametric uncertainties. Unlike general ILC techniques, the proposed adaptive ILC algorithms allow that both the initial error at each iteration and the reference trajectory are iteration-varying in the ILC process, and can achieve non-repetitive trajectory tracking beyond a small initial time interval. Compared to the neural network or fuzzy system-based adaptive ILC schemes and the classical ILC methods, in which the number of iterative variables is generally larger than or equal to the number of control inputs, the first adaptive ILC algorithm proposed in this paper uses just two iterative variables, while the second even uses a single iterative variable provided that some bound information on system dynamics is known. As a result, the memory space in real-time ILC implementations is greatly reduced.
The Mixed Finite Element Multigrid Preconditioned MINRES Method for Stokes Equations
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Kizito Muzhinji
2016-01-01
Full Text Available The study considers the saddle point problem arising from the mixed finite element discretization of the steady state Stokes equations. The saddle point problem is an indefinite system of linear equations, a feature that degrades the performance of any iterative solver. The heart of the study is the construction of fast, robust and effective iterative solution methods for such systems. Specific attention is given to the preconditioned MINRES solver PMINRES which is carefully treated for the solution of the Stokes equations. The study concentrates on the block preconditioner applied to the MINRES to effectively solve the whole coupled system. We combine iterative techniques with the MINRES as preconditioner approximations to produce an efficient solver for indefinite system of equations. We consider different preconditioner approximations of the building blocks of the preconditioner and compare their effects in accelerating the MINRES iterative scheme. We give a detailed overview of the algorithmic aspects and the theoretical convergence analysis of our solver. We study the MINRES method with the following preconditioner approximations: diagonal, multigrid v-cycle, preconditioned conjugate gradient and Chebyshev semi iteration methods. A comparative analysis of the preconditioner approximations show that the multigrid method is a suitable accelerator for the MINRES method. The application of the preconditioner becomes mandatory as evidenced by poor performance of the MINRES as compared to PMINRES. We study the problem in a two dimensional setting using the Hood-Taylor Q2 − Q1 stable pair of finite elements. The incompressible flow iterative solution software(IFISS matlab toolbox is used to assemble the matrices. We present the numerical results to illustrate the efficiency and robustness of the MINRES scheme with the multigrid preconditioner.
Liu, Rengli; Wang, Yanfei
2016-04-01
An extended nonlinear chirp scaling (NLCS) algorithm is proposed to process data of highly squinted, high-resolution, missile-borne synthetic aperture radar (SAR) diving with a constant acceleration. Due to the complex diving movement, the traditional signal model and focusing algorithm are no longer suited for missile-borne SAR signal processing. Therefore, an accurate range equation is presented, named as the equivalent hyperbolic range model (EHRM), which is more accurate and concise compared with the conventional fourth-order polynomial range equation. Based on the EHRM, a two-dimensional point target reference spectrum is derived, and an extended NLCS algorithm for missile-borne SAR image formation is developed. In the algorithm, a linear range walk correction is used to significantly remove the range-azimuth cross coupling, and an azimuth NLCS processing is adopted to solve the azimuth space variant focusing problem. Moreover, the operations of the proposed algorithm are carried out without any interpolation, thus having small computational loads. Finally, the simulation results and real-data processing results validate the proposed focusing algorithm.
Energy Technology Data Exchange (ETDEWEB)
Banks, J.W., E-mail: banksj3@rpi.edu; Henshaw, W.D., E-mail: henshw@rpi.edu; Kapila, A.K., E-mail: kapila@rpi.edu; Schwendeman, D.W., E-mail: schwed@rpi.edu
2016-01-15
We describe an added-mass partitioned (AMP) algorithm for solving fluid–structure interaction (FSI) problems involving inviscid compressible fluids interacting with nonlinear solids that undergo large rotations and displacements. The computational approach is a mixed Eulerian–Lagrangian scheme that makes use of deforming composite grids (DCG) to treat large changes in the geometry in an accurate, flexible, and robust manner. The current work extends the AMP algorithm developed in Banks et al. [1] for linearly elasticity to the case of nonlinear solids. To ensure stability for the case of light solids, the new AMP algorithm embeds an approximate solution of a nonlinear fluid–solid Riemann (FSR) problem into the interface treatment. The solution to the FSR problem is derived and shown to be of a similar form to that derived for linear solids: the state on the interface being fundamentally an impedance-weighted average of the fluid and solid states. Numerical simulations demonstrate that the AMP algorithm is stable even for light solids when added-mass effects are large. The accuracy and stability of the AMP scheme is verified by comparison to an exact solution using the method of analytical solutions and to a semi-analytical solution that is obtained for a rotating solid disk immersed in a fluid. The scheme is applied to the simulation of a planar shock impacting a light elliptical-shaped solid, and comparisons are made between solutions of the FSI problem for a neo-Hookean solid, a linearly elastic solid, and a rigid solid. The ability of the approach to handle large deformations is demonstrated for a problem of a high-speed flow past a light, thin, and flexible solid beam.
(Approximate) Low-Mode Averaging with a new Multigrid Eigensolver
Bali, Gunnar; Frommer, Andreas; Kahl, Karsten; Kanamori, Issaku; Müller, Benjamin; Rottmann, Matthias; Simeth, Jakob
2015-01-01
We present a multigrid based eigensolver for computing low-modes of the Hermitian Wilson Dirac operator. For the non-Hermitian case multigrid methods have already replaced conventional Krylov subspace solvers in many lattice QCD computations. Since the $\\gamma_5$-preserving aggregation based interpolation used in our multigrid method is valid for both, the Hermitian and the non-Hermitian case, inversions of very ill-conditioned shifted systems with the Hermitian operator become feasible. This enables the use of multigrid within shift-and-invert type eigensolvers. We show numerical results from our MPI-C implementation of a Rayleigh quotient iteration with multigrid. For state-of-the-art lattice sizes and moderate numbers of desired low-modes we achieve speed-ups of an order of magnitude and more over PARPACK. We show results and develop strategies how to make use of our eigensolver for calculating disconnected contributions to hadronic quantities that are noisy and still computationally challenging. Here, we ...
Tysinger, Thomas Lee
1992-07-01
Efficient numerical procedures are developed for the solution of the Navier-Stokes equations. The Navier-Stokes equations are a system of conservation laws which govern the motion of compressible, viscous, heat-conducting fluids. A conservative finite volume formulation is used for spatial discretization of the governing equations, resulting in a system of ordinary differential equations. To advance the system in time, an Alternating Direction Implicit (ADI) procedure suitable for the Navier-Stokes equations is developed. The resulting implicit system is diagonalized to improve the computational efficiency of the scheme. Viscous contributions are added to the scheme implicitly in a way that enhances the stability, yet does not disturb the efficiency of the algorithm. Rapid convergence to a steady state solution is achieved with a recursive multigrid algorithm. The stability and efficiency of the scheme are demonstrated with simulations of flow over wing sections. Furthermore, the algorithm has been implemented within the framework of multiple-block structured grids in which the spatial domain is decomposed into multiple blocks and the solution is advanced in parallel on the different blocks. Generic utilities have been developed to implement such a scheme in distributed computing environments. The multiple-block algorithm is designed so that the explicit residual calculation is identical to that of the single-block scheme, and therefore converged solutions for both schemes must be the same. To accelerate convergence, horizontal, vertical, and asynchronous multigrid algorithms are tested. Significant speedups have been achieved in a multiprocessor environment, while convergence rates similar to those of the single-clock schemes are observed.
Mao, Heng; Zhao, Dazun
2009-03-16
A modified Levenberg-Marquardt (MLM) algorithm is proposed to substitute for modified G-S (MGS) algorithm in some situations of phase-diverse phase retrieval wavefront sensing (WFS), such as the obstructed pupil, in which the second derivative information is specifically employed to eliminate the local minimum stagnation. Experiments have been performed to validate MLM algorithm in WFS accuracy (less than lambda/30 RMS) referring to ZYGO interferometer results and in WFS repeatability (less than lambda/200 RMS), even the dynamic range is more than 7 lambda PV. Moreover, experiments have shown the MLM algorithm is superior to the MGS algorithm both in WFS accuracy and repeatability.
Time-domain Adaptive Compensation Algorithm for Distortion of Nonlinear Amplifiers
Ding, Yuanming; Sun, Lianming; Sano, Akira
A new time-domain adaptive predistortion scheme is proposed to compensate nonlinearity of high power amplifiers (HPA) in OFDM systems. A Hammerstein model is adopted to approximate the input-output nonlinear distortion of HPA by using complex power series followed by linear dynamical distortion. According to the Hammerstein model structure, the compensation input to HPA is adaptively given in an on-line manner so that the linearization from the predistorter input to the HPA output can be attained even if the nonlinear input-output relation of HPA is uncertain and changeable. The effectiveness of the proposed adaptive scheme is validated through numerical simulations.
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.
Sumin, M. I.
2015-06-01
A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.
Madsen, Niels K; Godtliebsen, Ian H; Christiansen, Ove
2017-04-07
Vibrational coupled-cluster (VCC) theory provides an accurate method for calculating vibrational spectra and properties of small to medium-sized molecules. Obtaining these properties requires the solution of the non-linear VCC equations which can in some cases be hard to converge depending on the molecule, the basis set, and the vibrational state in question. We present and compare a range of different algorithms for solving the VCC equations ranging from a full Newton-Raphson method to approximate quasi-Newton models using an array of different convergence-acceleration schemes. The convergence properties and computational cost of the algorithms are compared for the optimization of VCC states. This includes both simple ground-state problems and difficult excited states with strong non-linearities. Furthermore, the effects of using tensor-decomposed solution vectors and residuals are investigated and discussed. The results show that for standard ground-state calculations, the conjugate residual with optimal trial vectors algorithm has the shortest time-to-solution although the full Newton-Raphson method converges in fewer macro-iterations. Using decomposed tensors does not affect the observed convergence rates in our test calculations as long as the tensors are decomposed to sufficient accuracy.
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Wei Zhang
2016-06-01
Full Text Available 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.
Textbook Multigrid Efficiency for the Steady Euler Equations
Roberts, Thomas W.; Sidilkover, David; Swanson, R. C.
2004-01-01
A fast multigrid solver for the steady incompressible Euler equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Solvers for both unstructured triangular grids and structured quadrilateral grids have been written. Computations for channel flow and flow over a nonlifting airfoil have computed. Using Gauss-Seidel relaxation ordered in the flow direction, textbook multigrid convergence rates of nearly one order-of-magnitude residual reduction per multigrid cycle are achieved, independent of the grid spacing. This approach also may be applied to the compressible Euler equations and the incompressible Navier-Stokes equations.
Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation
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.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Bagheri, Saman; Nikkar, Ali [University of Tabriz, Tabriz (Iran, Islamic Republic of)
2014-11-15
This paper deals with the determination of approximate solutions for a model of column buckling using two efficient and powerful methods called He's variational approach and variational iteration algorithm-II. These methods are used to find analytical approximate solution of nonlinear dynamic equation of a model for the column buckling. First and second order approximate solutions of the equation of the system are achieved. To validate the solutions, the analytical results have been compared with those resulted from Runge-Kutta 4th order method. A good agreement of the approximate frequencies and periodic solutions with the numerical results and the exact solution shows that the present methods can be easily extended to other nonlinear oscillation problems in engineering. The accuracy and convenience of the proposed methods are also revealed in comparisons with the other solution techniques.
National Aeronautics and Space Administration — This paper presents a novel set of uncertainty measures to quantify the impact of input uncertainty on nonlinear prognosis systems. A Particle Filtering-based method...
Energy Technology Data Exchange (ETDEWEB)
Srinath Vadlamani; Scott Kruger; Travis Austin
2008-06-19
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.
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....
Directory of Open Access Journals (Sweden)
Malyj Wasyl
2005-08-01
Full Text Available Abstract Background Life processes are determined by the organism's genetic profile and multiple environmental variables. However the interaction between these factors is inherently non-linear 1. Microarray data is one representation of the nonlinear interactions among genes and genes and environmental factors. Still most microarray studies use linear methods for the interpretation of nonlinear data. In this study, we apply Isomap, a nonlinear method of dimensionality reduction, to analyze three independent large Affymetrix high-density oligonucleotide microarray data sets. Results Isomap discovered low-dimensional structures embedded in the Affymetrix microarray data sets. These structures correspond to and help to interpret biological phenomena present in the data. This analysis provides examples of temporal, spatial, and functional processes revealed by the Isomap algorithm. In a spinal cord injury data set, Isomap discovers the three main modalities of the experiment – location and severity of the injury and the time elapsed after the injury. In a multiple tissue data set, Isomap discovers a low-dimensional structure that corresponds to anatomical locations of the source tissues. This model is capable of describing low- and high-resolution differences in the same model, such as kidney-vs.-brain and differences between the nuclei of the amygdala, respectively. In a high-throughput drug screening data set, Isomap discovers the monocytic and granulocytic differentiation of myeloid cells and maps several chemical compounds on the two-dimensional model. Conclusion Visualization of Isomap models provides useful tools for exploratory analysis of microarray data sets. In most instances, Isomap models explain more of the variance present in the microarray data than PCA or MDS. Finally, Isomap is a promising new algorithm for class discovery and class prediction in high-density oligonucleotide data sets.
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
An angular multigrid method for computing mono-energetic particle beams in Flatland
Börgers, Christoph; MacLachlan, Scott
2010-04-01
Beams of microscopic particles penetrating scattering background matter play an important role in several applications. The parameter choices made here are motivated by the problem of electron-beam cancer therapy planning. Mathematically, a steady particle beam penetrating matter, or a configuration of several such beams, is modeled by a boundary value problem for a Boltzmann equation. Grid-based discretization of such a problem leads to a system of algebraic equations. This system is typically very large because of the large number of independent variables in the Boltzmann equation—six if no dimension-reducing assumptions other than time independence are made. If grid-based methods are to be practical for these problems, it is therefore necessary to develop very fast solvers for the discretized problems. For beams of mono-energetic particles interacting with a passive background, but not with each other, in two space dimensions, the first author proposed such a solver, based on angular domain decomposition, some time ago. Here, we propose and test an angular multigrid algorithm for the same model problem. Our numerical experiments show rapid, grid-independent convergence. For high-resolution calculations, our method is substantially more efficient than the angular domain decomposition method. In addition, unlike angular domain decomposition, the angular multigrid method works well even when the angular diffusion coefficient is fairly large.
AN INTERIOR TRUST REGION ALGORITHM FOR NONLINEAR MINIMIZATION WITH LINEAR CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
Jian-guo Liu
2002-01-01
An interior trust-region-based algorithm for linearly constrained minimization problems is proposed and analyzed. This algorithm is similar to trust region algorithms forunconstrained minimization: a trust region subproblem on a subspace is solved in eachiteration. We establish that the proposed algorithm has convergence properties analogousto those of the trust region algorithms for unconstrained minimization. Namely, every limitpoint of the generated sequence satisfies the Krush-Kuhn-Tucker (KKT) conditions andat least one limit point satisfies second order necessary optimality conditions. In adidition,if one limit point is a strong local minimizer and the Hessian is Lipschitz continuous in aneighborhood of that point, then the generated sequence converges globally to that pointin the rate of at least 2-step quadratic. We are mainly concerned with the theoretical properties of the algorithm in this paper. Implementation issues and adaptation to large-scaleproblems will be addressed in a future report.
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.
Institute of Scientific and Technical Information of China (English)
Xin LIU; Guo WEI; Jin-wei SUN; Dan LIU
2009-01-01
Least squares support vector machines (LS-SVMs) are modified support vector machines (SVMs) that involve equality constraints and work with a least squares cost function, which simplifies the optimization procedure. In this paper, a novel training algorithm based on total least squares (TLS) for an LS-SVM is presented and applied to muhifunctional sensor signal reconstruction. For three different nonlinearities of a multi functional sensor model, the reconstruction accuracies of input signals are 0.001 36%, 0.03184% and 0.504 80%, respectively. The experimental results demonstrate the higher reliability and accuracy of the proposed method for multi functional sensor signal reconstruction than the original LS-SVM training algorithm, and verify the feasibility and stability of the proposed method.
A Highly Functional Decision Paradigm Based on Nonlinear Adaptive Genetic Algorithm
1994-04-20
FEGA will still be evident. Table 1-1. Excitation Time for Different Sorting Algorithms Algorithm Type Excitation Time Bubble Sorting 1.13 x 109 hours...CARM Sorting 14.4 hours Conventional GA 2 - 3 seconds POC FEGA 0.3 - 0.5 seconds 2.0 HIGHLIGHTS OF PHASE I TECHNICAL OBJECTIVES AND RESULTS In Phase
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......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 absorption in optical media is proceeded conventionally through the iterative solution of nonlinear algebraic equations. Here, we study three approaches for the field update including simple noniterative explicit schemes. By comparing them to the analytical results for optical pulse propagation in long...
Pitschner, H F; Berkowitsch, A
2001-01-01
Symbolic dynamics as a non linear method and computation of the normalized algorithmic complexity (C alpha) was applied to basket-catheter mapping of atrial fibrillation (AF) in the right human atrium. The resulting different degrees of organisation of AF have been compared to conventional classification of Wells. Short time temporal and spatial distribution of the C alpha during AF and effects of propafenone on this distribution have been investigated in 30 patients. C alpha was calculated for a moving window. Generated C alpha was analyzed within 10 minutes before and after administration of propafenone. The inter-regional C alpha distribution was statistically analyzed. Inter-regional C alpha differences were found in all patients (p complexity areas according to individual patterns. A significant C alpha increase in cranio-caudal direction was confirmed inter-individually (p complexity.
Ahn, Joong-Bae; Lee, Joonlee
2016-08-01
A new multimodel ensemble (MME) method that uses a genetic algorithm (GA) is developed and applied to the prediction of winter surface air temperature (SAT) and precipitation. The GA based on the biological process of natural evolution is a nonlinear method which solves nonlinear optimization problems. Hindcast data of winter SAT and precipitation from the six coupled general circulation models participating in the seasonal MME prediction system of the Asia-Pacific Economic Conference Climate Center are used. Three MME methods using GA (MME/GAs) are examined in comparison with a simple composite MME strategy (MS0): MS1 which applies GA to single-model ensembles (SMEs), MS2 which applies GA to each ensemble member and then performs a simple composite method for MME, and MS3 which applies GA to both MME and SME. MS3 shows the highest predictability compared to MS0, MS1, and MS2 for both winter SAT and precipitation. These results indicate that biases of ensemble members of each model and model ensemble are more reduced with MS3 than with other MME/GAs and MS0. The predictability of the MME/GAs shows a greater improvement than that of MS0, particularly in higher-latitude land areas. The reason for the more improved increase of predictability over the land area, particularly in MS3, seems to be the fact that GA is more efficient in finding an optimum solution in a complex region where nonlinear physical properties are evident.
2015-04-24
Allgwer and A. Zheng, Nonlinear model predictive control vol. 26: Springer , 2000. [10] J. M. Park, D. W. Kim, Y. S. Yoon, H. J. Kim, and K. S. Yi...include modeling, simulation, and control of dynamic systems, with applications to energy systems, multibody dynamics, vehicle systems, and biomechanics
Assaf, Tareq; Rossiter, Jonathan M.; Porrill, John
2016-01-01
Electroactive polymer actuators are important for soft robotics, but can be difficult to control because of compliance, creep and nonlinearities. Because biological control mechanisms have evolved to deal with such problems, we investigated whether a control scheme based on the cerebellum would be useful for controlling a nonlinear dielectric elastomer actuator, a class of artificial muscle. The cerebellum was represented by the adaptive filter model, and acted in parallel with a brainstem, an approximate inverse plant model. The recurrent connections between the two allowed for direct use of sensory error to adjust motor commands. Accurate tracking of a displacement command in the actuator's nonlinear range was achieved by either semi-linear basis functions in the cerebellar model or semi-linear functions in the brainstem corresponding to recruitment in biological muscle. In addition, allowing transfer of training between cerebellum and brainstem as has been observed in the vestibulo-ocular reflex prevented the steady increase in cerebellar output otherwise required to deal with creep. The extensibility and relative simplicity of the cerebellar-based adaptive-inverse control scheme suggests that it is a plausible candidate for controlling this type of actuator. Moreover, its performance highlights important features of biological control, particularly nonlinear basis functions, recruitment and transfer of training. PMID:27655667
Geophysical modelling of 3D electromagnetic diffusion with multigrid
Mulder, W.A.
2008-01-01
The performance of a multigrid solver for time-harmonic electromagnetic problems in geophysical settings was investigated. With the low frequencies used in geophysical surveys for deeper targets, the light-speed waves in the earth can be neglected. Diffusion of induced currents is the dominant physi
Multigrid waveform relaxation for the time-fractional heat equation
F.J. Gaspar Lorenz (Franscisco); C. Rodrigo (Carmen)
2017-01-01
textabstractIn this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for which the coefficient matrix is dense.
Efficient Multigrid Methods based on Improved Coarse Grid Correction Techniques
Bin Zubair, H.
2009-01-01
Multigrid efficiency often suffers from inadequate coarse grid correction in different prototypic situations. We select a few problems, where coarse grid correction issues arise because of anisotropic coefficients, non-equidistant or non-uniform grid stretching, or inherent indefiniteness in the par
Multigrid and cyclic reduction applied to the Helmholtz equation
Brackenridge, Kenneth
1993-01-01
We consider the Helmholtz equation with a discontinuous complex parameter and inhomogeneous Dirichlet boundary conditions in a rectangular domain. A variant of the direct method of cyclic reduction (CR) is employed to facilitate the design of improved multigrid (MG) components, resulting in the method of CR-MG. We demonstrate the improved convergence properties of this method.
A novel multigrid based preconditioner for heterogeneous Helmholtz problems
Erlangga, Y.A.; Oosterlee, C.W.; Vuik, C.
2004-01-01
An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner
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.
Identification of Nonlinear Rational Systems Using A Prediction-Error Estimation Algorithm
1987-01-01
Identification of discrete-time noninear stochastic systems which can be represented by a rational input-output model is considered. A prediction-error parameter estimation algorithm is developed and a criterion is derived using results from the theory of hypothesis testing to determine the correct model structure. The identification of a simulated system and a heat exchanger are included to illustrate the algorithms.
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.
非结构网格的并行多重网格解算器%Parallel Multigrid Solver for Unstructured Grid
Institute of Scientific and Technical Information of China (English)
李宗哲; 王正华; 姚路; 曹维
2013-01-01
多重网格方法作为非结构网格的高效解算器，其串行与并行实现在时空上都具有优良特性。以控制方程离散过程为切入点，说明非结构网格在并行数值模拟的流程，指出多重网格方法主要用于求解时间推进格式产生的大规模代数系统方程，简述了算法实现的基本结构，分析了其高效性原理；其次，综述性地概括了几何多重网格与代数多种网格研究动态，并对其并行化的热点问题进行重点论述。同时，针对非结构网格的实际应用，总结了多重网格解算器采用的光滑算子；随后列举了非结构网格应用的部分开源项目软件，并简要说明了其应用功能；最后，指出并行多重网格解算器在非结构网格应用中的若干关键问题和未来的研究方向。%As an unstructured-grid high efficient solver, the multigrid algorithm, with its serial and parallel application, can achieve the optimal properties of being on time and having space complexity. To illustrate the numerical simulation process of an unstructured grid, this paper begins with the discretization of governing equations and points out that the multigrid algorithm is mainly used for solving large scale algebraic equation, which is derived from the time marching scheme. For the multigrid algorithm, the study briefly describes its basic structure and efficient principle. Secondly, the paper reviews research that trend about the geometric multigrid and algebraic multigrid and discusses the basic design principles and hot topics on parallelization. At the same time, for the practical application of unstructured grid, the paper summarizes and classifies many smoothers, followed by examples of open source software about unstructured grid industrial application. Finally, some applications and key problems in this field are highlighted, as well as the future progress of parallel multigrid solver on unstructured grid.
Nonlinear approximation method in Lagrangian relaxation-based algorithms for hydrothermal scheduling
Energy Technology Data Exchange (ETDEWEB)
Guan, X. [Pacific Gas and Electric, San Francisco, CA (United States); Luh, P.B.; Zhang, L. [Univ. of Connecticut, Storrs, CT (United States). Dept. of Electrical and Systems Engineering
1995-05-01
When the Lagrangian relaxation technique is used to solve hydrothermal scheduling problems, many subproblems have linear stage-wise cost functions. A well recognized difficulty is that the solutions to these subproblems may oscillate between maximum and minimum generations with slight changes of the multipliers. Furthermore, the subproblem solutions may become singular, i.e., they are un-determined when the linear coefficients become zero. This may result in large differences between subproblem solutions and the optimal primal schedule. In this paper, a nonlinear approximation method is presented which utilizes nonlinear functions, quadratic in this case, to approximate relevant linear cost functions. The analysis shows that the difficulty associated with solution oscillation is reduced, and singularity is avoided. Extensive testing based on Northeast Utilities data indicates that the method consistently generates better schedules than the standard Lagrangian relaxation method.
Zheng, Ziyi; Sun, Mingshan; Pavkovich, John; Star-Lack, Josh
2011-03-01
A challenge in using on-board cone beam computed tomography (CBCT) to image lung tumor motion prior to radiation therapy treatment is acquiring and reconstructing high quality 4D images in a sufficiently short time for practical use. For the 1 minute rotation times typical of Linacs, severe view aliasing artifacts, including streaks, are created if a conventional phase-correlated FDK reconstruction is performed. The McKinnon-Bates (MKB) algorithm provides an efficient means of reducing streaks from static tissue but can suffer from low SNR and other artifacts due to data truncation and noise. We have added truncation correction and bilateral nonlinear filtering to the MKB algorithm to reduce streaking and improve image quality. The modified MKB algorithm was implemented on a graphical processing unit (GPU) to maximize efficiency. Results show that a nearly 4x improvement in SNR is obtained compared to the conventional FDK phase-correlated reconstruction and that high quality 4D images with 0.4 second temporal resolution and 1 mm3 isotropic spatial resolution can be reconstructed in less than 20 seconds after data acquisition completes.
Energy Technology Data Exchange (ETDEWEB)
Lee, B C; Schulz, M; de Supinski, B R
2006-09-28
Increasing system and algorithmic complexity, combined with a growing number of tunable application parameters, pose significant challenges for analytical performance modeling. This report outlines a series of robust techniques that enable efficient parameter space exploration based on empirical statistical modeling. In particular, this report applies statistical techniques such as clustering, association, correlation analyses to understand the parameter space better. Results from these statistical techniques guide the construction of piecewise polynomial regression models. Residual and significance tests ensure the resulting model is unbiased and efficient. We demonstrate these techniques in R, a statistical computing environment, for predicting the performance of semicoarsening multigrid. 50 and 75 percent of predictions achieve error rates of 5.5 and 10.0 percent or less, respectively.
Fast Simulation of Nonlinear Circuits with an Algorithm of Partial Matrix Elimination (PME)
Institute of Scientific and Technical Information of China (English)
CAI Xingjian; MAO Junfa; YANG Xiaoping; LI Zhengfan
2001-01-01
In this paper a theorem is proven thatthe contribution of any linear circuit elements to theadmittance matrix [Y] in the modified nodal admit-tance (MNA) equation of circuit analysis is invariantwith time.Based on this theorem a fast time-domainalgorithm of partial matrix elimination (PME) is de-veloped for simulation of high-speed nonlinear circuitswith interconnects.In PME the matrix [Y] is ar-ranged to consist of two submatrices.The lower sub-matrix that contains entries from only linear circuit el-ements is partially triangulated by Gauss eliminationfor the first-time-step transient analysis.At the fol-lowing time steps of transient analysis,Gauss elimina-tion is needed only for the upper submatrix containingcontributions of nonlinear circuit devices.Efficiencyanalysis of PME is given in detail,showing that it canaccelerate circuit simulation by a factor of at least 2.5for linear or lightly nonlinear circuits without employ-ing any numerical approximation.Moreover,PME isuseful for circuits debugging.
Institute of Scientific and Technical Information of China (English)
宋丽娜; 王维国
2012-01-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
Song, Li-Na; Wang, Wei-Guo
2012-08-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
A parallel geometric multigrid method for finite elements on octree meshes
Energy Technology Data Exchange (ETDEWEB)
Sampath, Rahul S [ORNL; Biros, George [University of Texas, Austin
2010-01-01
In this article, we present a parallel geometric multigrid algorithm for solving variable-coefficient elliptic partial differential equations on the unit box (with Dirichlet or Neumann boundary conditions) using highly nonuniform, octree-based, conforming finite element discretizations. Our octrees are 2:1 balanced, that is, we allow no more than one octree-level difference between octants that share a face, edge, or vertex. We describe a parallel algorithm whose input is an arbitrary 2:1 balanced fine-grid octree and whose output is a set of coarser 2:1 balanced octrees that are used in the multigrid scheme. Also, we derive matrix-free schemes for the discretized finite element operators and the intergrid transfer operations. The overall scheme is second-order accurate for sufficiently smooth right-hand sides and material properties; its complexity for nearly uniform trees is {Omicron}(N/n{sub p} log N/n{sub p}) + {Omicron}(n{sub p} log n{sub p}), where N is the number of octree nodes and n{sub p} is the number of processors. Our implementation uses the Message Passing Interface standard. We present numerical experiments for the Laplace and Navier (linear elasticity) operators that demonstrate the scalability of our method. Our largest run was a highly nonuniform, 8-billion-unknown, elasticity calculation using 32,000 processors on the Teragrid system, 'Ranger,' at the Texas Advanced Computing Center. Our implementation is publically available in the Dendro library, which is built on top of the PETSc library from Argonne National Laboratory.
Implementation of FFT convolution and multigrid superposition models in the FOCUS RTP system
Miften, Moyed; Wiesmeyer, Mark; Monthofer, Suzanne; Krippner, Ken
2000-04-01
In radiotherapy treatment planning, convolution/superposition algorithms currently represent the best practical approach for accurate photon dose calculation in heterogeneous tissues. In this work, the implementation, accuracy and performance of the FFT convolution (FFTC) and multigrid superposition (MGS) algorithms are presented. The FFTC and MGS models use the same `TERMA' calculation and are commissioned using the same parameters. Both models use the same spectra, incorporate the same off-axis softening and base incident lateral fluence on the same measurements. In addition, corrections are explicitly applied to the polyenergetic and parallel kernel approximations, and electron contamination is modelled. Spectra generated by Monte Carlo (MC) modelling of treatment heads are used. Calculations using the MC spectra were in excellent agreement with measurements for many linear accelerator types. To speed up the calculations, a number of calculation techniques were implemented, including separate primary and scatter dose calculation, the FFT technique which assumes kernel invariance for the convolution calculation and a multigrid (MG) acceleration technique for the superposition calculation. Timing results show that the FFTC model is faster than MGS by a factor of 4 and 8 for small and large field sizes, respectively. Comparisons with measured data and BEAM MC results for a wide range of clinical beam setups show that (a) FFTC and MGS doses match measurements to better than 2% or 2 mm in homogeneous media; (b) MGS is more accurate than FFTC in lung phantoms where MGS doses are within 3% or 3 mm of BEAM results and (c) FFTC overestimates the dose in lung by a maximum of 9% compared to BEAM.
Fast Algorithm of Numerical Solutions for Strong Nonlinear Partial Differential Equations
Directory of Open Access Journals (Sweden)
Tongjing Liu
2014-07-01
Full Text Available Because of a high mobility ratio in the chemical and gas flooding for oil reservoirs, the problems of numerical dispersion and low calculation efficiency also exist in the common methods, such as IMPES and adaptive implicit methods. Therefore, the original calculation process, “one-step calculation for pressure and multistep calculation for saturation,” was improved by introducing a velocity item and using the fractional flow in a direction to calculate the saturation. Based on these developments, a new algorithm of numerical solution for “one-step calculation for pressure, one-step calculation for velocity, and multi-step calculation for fractional flow and saturation” was obtained, and the convergence condition for the calculation of saturation was also proposed. The simulation result of a typical theoretical model shows that the nonconvergence occurred for about 6,000 times in the conventional algorithm of IMPES, and a high fluctuation was observed in the calculation steps. However, the calculation step of the fast algorithm was stabilized for 0.5 d, indicating that the fast algorithm can avoid the nonconvergence caused by the saturation that was directly calculated by pressure. This has an important reference value in the numerical simulations of chemical and gas flooding for oil reservoirs.
Designing A Nonlinear Integer Programming Model For A Cross-Dock By A Genetic Algorithm
Bahareh Vaisi; Reza Tavakkoli-Moghaddam
2015-01-01
Abstract This paper presents a non-linear integer programming model for a cross-dock problem that considers the total transportation cost of inbound and outbound trucks from an origin to a destination and the total cost of assigning strip and stack doors to trucks based on their number of trips and the distance between doors in cross-dock. In previous studies these two cost-based problems are modeled separately however it is more realistic and practical to use both of them as an integrated cr...
An Improved Control Algorithm for High-order Nonlinear Systems with Unmodelled Dynamics
Institute of Scientific and Technical Information of China (English)
Na Duan; Fu-Nian Hu; Xin Yu
2009-01-01
In this paper, we consider a class of high-order nonlinear systems with unmodelled dynamics from the viewpoint of maintaining the desired control performance (e. g., asymptotical stability) and reducing the control effort. By introducing a new rescaling transformation, adopting an effective reduced-order observer, and choosing an ingenious Lyapunov function and appropriate design parameters, this paper designs an improved output-feedback controller. The output-feedback controller guarantees the globally asymptotical stability of the closed-loop system. Subsequently, taking a concrete system for an example, the smaller critical values for gain parameter and rescaling transformation parameter are obtained to effectively reduce the control effort.
Directory of Open Access Journals (Sweden)
Ching-Hung Lee
2011-01-01
Full Text Available This paper proposes a new type fuzzy neural systems, denoted IT2RFNS-A (interval type-2 recurrent fuzzy neural system with asymmetric membership function, for nonlinear systems identification and control. To enhance the performance and approximation ability, the triangular asymmetric fuzzy membership function (AFMF and TSK-type consequent part are adopted for IT2RFNS-A. The gradient information of the IT2RFNS-A is not easy to obtain due to the asymmetric membership functions and interval valued sets. The corresponding stable learning is derived by simultaneous perturbation stochastic approximation (SPSA algorithm which guarantees the convergence and stability of the closed-loop systems. Simulation and comparison results for the chaotic system identification and the control of Chua's chaotic circuit are shown to illustrate the feasibility and effectiveness of the proposed method.
Institute of Scientific and Technical Information of China (English)
ZHANG Ren; HONG Mei; SUN Zhao-bo; NIU Sheng-jie; ZHU Wei-jun; MIN Jin-zhong; WAN Qi-lin
2006-01-01
Aiming at the difficulty of accurately constructing the dynamic model of subtropical high, based on the potential height field time series over 500 hPa layer of T106 numerical forecast products, by using EOF(empirical orthogonal function) temporal-spatial separation technique, the disassembled EOF time coefficients series were regarded as dynamical model variables, and dynamic system retrieval idea as well as genetic algorithm were introduced to make dynamical model parameters optimization search, then, a reasonable non-linear dynamic model of EOF time-coefficients was established. By dynamic model integral and EOF temporal-spatial components assembly, a mid-/long-term forecast of subtropical high was carried out. The experimental results show that the forecast results of dynamic model are superior to that of general numerical model forecast results.A new modeling idea and forecast technique is presented for diagnosing and forecasting such complicated weathers as subtropical high.
Directory of Open Access Journals (Sweden)
P. S. Hiremath
2008-01-01
recognition in the framework of symbolic data analysis. Classical KDA extracts features, which are single-valued in nature to represent face images. These single-valued variables may not be able to capture variation of each feature in all the images of same subject; this leads to loss of information. The symbolic KDA algorithm extracts most discriminating nonlinear interval-type features which optimally discriminate among the classes represented in the training set. The proposed method has been successfully tested for face recognition using two databases, ORL database and Yale face database. The effectiveness of the proposed method is shown in terms of comparative performance against popular face recognition methods such as kernel Eigenface method and kernel Fisherface method. Experimental results show that symbolic KDA yields improved recognition rate.
Xu, Liangfei; Hu, Junming; Cheng, Siliang; Fang, Chuan; Li, Jianqiu; Ouyang, Minggao; Lehnert, Werner
2017-07-01
A scheme for designing a second-order sliding-mode (SOSM) observer that estimates critical internal states on the cathode side of a polymer electrolyte membrane (PEM) fuel cell system is presented. A nonlinear, isothermal dynamic model for the cathode side and a membrane electrolyte assembly are first described. A nonlinear observer topology based on an SOSM algorithm is then introduced, and equations for the SOSM observer deduced. Online calculation of the inverse matrix produces numerical errors, so a modified matrix is introduced to eliminate the negative effects of these on the observer. The simulation results indicate that the SOSM observer performs well for the gas partial pressures and air stoichiometry. The estimation results follow the simulated values in the model with relative errors within ± 2% at stable status. Large errors occur during the fast dynamic processes (system parameters. The partial pressures are more sensitive than the air stoichiometry to system parameters. Finally, the order of effects of parameter uncertainties on the estimation results is outlined and analyzed.
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.
Sheta, B.; M. Elhabiby; Sheimy, N.
2012-01-01
A robust scale and rotation invariant image matching algorithm is vital for the Visual Based Navigation (VBN) of aerial vehicles, where matches between an existing geo-referenced database images and the real-time captured images are used to georeference (i.e. six transformation parameters - three rotation and three translation) the real-time captured image from the UAV through the collinearity equations. The georeferencing information is then used in aiding the INS integration Kalman filter a...
An improved algorithm for anisotropic nonlinear diffusion for denoising cryo-tomograms.
Fernández, José Jesús; Li, Sam
2003-01-01
Cryo-electron tomography is an imaging technique with an unique potential for visualizing large complex biological specimens. It ensures preservation of the biological material but the resulting cryotomograms are extremely noisy. Sophisticated denoising techniques are thus essential for allowing the visualization and interpretation of the information contained in the cryotomograms. Here a software tool based on anisotropic nonlinear diffusion is described for filtering cryotomograms. The approach reduces local noise and meanwhile enhances both curvilinear and planar structures. In the program a novel solution of the partial differential equation has been implemented, which allows a reliable estimation of derivatives and, furthermore, reduces computation time and memory requirements. Several criteria have been included to automatically select the optimal stopping time. The behaviour of the denoising approach is tested for visualizing filamentous structures in cryotomograms.
El-Ajou, Ahmad; Arqub, Omar Abu; Momani, Shaher
2015-07-01
In this paper, explicit and approximate solutions of the nonlinear fractional KdV-Burgers equation with time-space-fractional derivatives are presented and discussed. The solutions of our equation are calculated in the form of rabidly convergent series with easily computable components. The utilized method is a numerical technique based on the generalized Taylor series formula which constructs an analytical solution in the form of a convergent series. Five illustrative applications are given to demonstrate the effectiveness and the leverage of the present method. Graphical results and series formulas are utilized and discussed quantitatively to illustrate the solution. The results reveal that the method is very effective and simple in determination of solution of the fractional KdV-Burgers equation.
A nonlinear fuzzy assisted image reconstruction algorithm for electrical capacitance tomography.
Deabes, W A; Abdelrahman, M A
2010-01-01
A nonlinear method based on a Fuzzy Inference System (FIS) to improve the images obtained from Electrical Capacitance Tomography (ECT) is proposed. Estimation of the molten metal characteristic in the Lost Foam Casting (LFC) process is a novel application in the area of the tomography process. The convergence rate of iterative image reconstruction techniques is dependent on the accuracy of the first image. The possibility of the existence of metal in the first image is computed by the proposed fuzzy system. This first image is passed to an iterative image reconstruction technique to get more precise images and to speed up the convergence rate. The proposed technique is able to detect the position of the metal on the periphery of the imaging area by using just eight capacitive sensors. The final results demonstrate the advantage of using the FIS compared to the performance of the iterative back projection image reconstruction technique.
Balkaya, Çağlayan; Ekinci, Yunus Levent; Göktürkler, Gökhan; Turan, Seçil
2017-01-01
3D non-linear inversion of total field magnetic anomalies caused by vertical-sided prismatic bodies has been achieved by differential evolution (DE), which is one of the population-based evolutionary algorithms. We have demonstrated the efficiency of the algorithm on both synthetic and field magnetic anomalies by estimating horizontal distances from the origin in both north and east directions, depths to the top and bottom of the bodies, inclination and declination angles of the magnetization, and intensity of magnetization of the causative bodies. In the synthetic anomaly case, we have considered both noise-free and noisy data sets due to two vertical-sided prismatic bodies in a non-magnetic medium. For the field case, airborne magnetic anomalies originated from intrusive granitoids at the eastern part of the Biga Peninsula (NW Turkey) which is composed of various kinds of sedimentary, metamorphic and igneous rocks, have been inverted and interpreted. Since the granitoids are the outcropped rocks in the field, the estimations for the top depths of two prisms representing the magnetic bodies were excluded during inversion studies. Estimated bottom depths are in good agreement with the ones obtained by a different approach based on 3D modelling of pseudogravity anomalies. Accuracy of the estimated parameters from both cases has been also investigated via probability density functions. Based on the tests in the present study, it can be concluded that DE is a useful tool for the parameter estimation of source bodies using magnetic anomalies.
Segmented Domain Decomposition Multigrid For 3-D Turbomachinery Flows
Celestina, M. L.; Adamczyk, J. J.; Rubin, S. G.
2001-01-01
A Segmented Domain Decomposition Multigrid (SDDMG) procedure was developed for three-dimensional viscous flow problems as they apply to turbomachinery flows. The procedure divides the computational domain into a coarse mesh comprised of uniformly spaced cells. To resolve smaller length scales such as the viscous layer near a surface, segments of the coarse mesh are subdivided into a finer mesh. This is repeated until adequate resolution of the smallest relevant length scale is obtained. Multigrid is used to communicate information between the different grid levels. To test the procedure, simulation results will be presented for a compressor and turbine cascade. These simulations are intended to show the ability of the present method to generate grid independent solutions. Comparisons with data will also be presented. These comparisons will further demonstrate the usefulness of the present work for they allow an estimate of the accuracy of the flow modeling equations independent of error attributed to numerical discretization.
Efficient relaxed-Jacobi smoothers for multigrid on parallel computers
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.
Analysis of extrapolation cascadic multigrid method(EXCMG)
Institute of Scientific and Technical Information of China (English)
2008-01-01
Based on an asymptotic expansion of finite element,a new extrapolation formula and extrapolation cascadic multigrid method(EXCMG)are proposed,in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid.In the case of triple grids,the error of the new initial value is analyzed in detail.A larger scale computation is completed in PC.
FINAL REPORT: Multigrid for Systems and Time-Dependent PDEs
Energy Technology Data Exchange (ETDEWEB)
Jones, J. E. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-08-02
This report has two sections. The first section is the motivation for looking at differing discretizations on coarse grids for solving a parabolic equation using multigrid in time. The second section contains selected numerical results from the many experiments conducted. The most interesting result is that for explicit fine grid discretizations, the best coarse discretization (i.e. smallest convergence rates) is a weighting between implicit and explicit methods.
Yang, Ji Seung; Cai, Li
2013-01-01
The main purpose of this study is to improve estimation efficiency in obtaining full-information maximum likelihood (FIML) estimates of contextual effects in the framework of a nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM; Cai, 2008, 2010a, 2010b). Results indicate that the MH-RM…
Ender, I A; Flegontova, E Yu; Gerasimenko, A B
2016-01-01
An algorithm for sequential calculation of non-isotropic matrix elements of the collision integral which are necessary for the solution of the non-linear Boltzmann equation by moment method is proposed. Isotropic matrix elements that we believe are known, are starting ones. The procedure is valid for any interaction law and any mass ratio of the colliding particles.
Matveev, A. D.
2016-11-01
To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.
A general nonlinear inverse transport algorithm using forward and adjoint flux computations
Energy Technology Data Exchange (ETDEWEB)
Norton, S.J. [Oak Ridge National Lab., TN (United States)
1997-04-01
Iterative approaches to the nonlinear inverse transport problem are described, which give rise to the structure that best predicts a set of transport observations. Such methods are based on minimizing a global error functional measuring the discrepancy between predicted and observed transport data. Required for this minimization is the functional gradient (Frechet derivative) of the global error evaluated with respect to a set of unknown material parameters (specifying boundary locations, scattering cross sections, etc.) which are to be determined. It is shown how this functional gradient is obtained from numerical solutions to the forward and adjoint transport problems computed once per iteration. This approach is not only far more efficient, but also more accurate, than a finite-difference method for computing the gradient of the global error. The general technique can be applied to inverse-transport problems of all descriptions, provided only that solutions to the forward and adjoint problems can be found numerically. As an illustration, two inverse problems are treated: the reconstruction of an anisotropic scattering function in a one-dimensional homogeneous slab and the two-dimensional imaging of a spatially-varying scattering cross section.
AN UNSTRUCTURED FINITE-VOLUME ALGORITHM FOR NONLINEAR TWO-DIMENSIOAL SHALLOW WATER EQUATION
Institute of Scientific and Technical Information of China (English)
WANG Zhi-li; GENG Yan-fen; JIN Sheng
2005-01-01
An unstructured finite-volume numerical algorithm was presented for solution of the two-dimensional shallow water equations, based on triangular or arbitrary quadrilateral meshes. The Roe type approximate Riemann solver was used to the system. A second-order TVD scheme with the van Leer limiter was used in the space discretization and a two-step Runge-Kutta approach was used in the time discretization. An upwind, as opposed to a pointwise, treatment of the slope source terms was adopted and the semi-implicit treatment was used for the friction source terms. Verification for two-dimension dam-break problems are carried out by comparing the present results with others and very good agreement is shown.
Zhang, Huaguang; Wei, Qinglai; Luo, Yanhong
2008-08-01
In this paper, we aim to solve the infinite-time optimal tracking control problem for a class of discrete-time nonlinear systems using the greedy heuristic dynamic programming (HDP) iteration algorithm. A new type of performance index is defined because the existing performance indexes are very difficult in solving this kind of tracking problem, if not impossible. Via system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then, the greedy HDP iteration algorithm is introduced to deal with the regulation problem with rigorous convergence analysis. Three neural networks are used to approximate the performance index, compute the optimal control policy, and model the nonlinear system for facilitating the implementation of the greedy HDP iteration algorithm. An example is given to demonstrate the validity of the proposed optimal tracking control scheme.
Samareh, Hossein; Khoshrou, Seyed Hassan; Shahriar, Kourosh; Ebadzadeh, Mohammad Mehdi; Eslami, Mohammad
2017-09-01
When particle's wave velocity resulting from mining blasts exceeds a certain level, then the intensity of produced vibrations incur damages to the structures around the blasting regions. Development of mathematical models for predicting the peak particle velocity (PPV) based on the properties of the wave emission environment is an appropriate method for better designing of blasting parameters, since the probability of incurred damages can considerably be mitigated by controlling the intensity of vibrations at the building sites. In this research, first out of 11 blasting and geo-mechanical parameters of rock masses, four parameters which had the greatest influence on the vibrational wave velocities were specified using regression analysis. Thereafter, some models were developed for predicting the PPV by nonlinear regression analysis (NLRA) and artificial neural network (ANN) with correlation coefficients of 0.854 and 0.662, respectively. Afterward, the coefficients associated with the parameters in the NLRA model were optimized using optimization particle swarm-genetic algorithm. The values of PPV were estimated for 18 testing dataset in order to evaluate the accuracy of the prediction and performance of the developed models. By calculating statistical indices for the test recorded maps, it was found that the optimized model can predict the PPV with a lower error than the other two models. Furthermore, considering the correlation coefficient (0.75) between the values of the PPV measured and predicted by the optimized nonlinear model, it was found that this model possesses a more desirable performance for predicting the PPV than the other two models.
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.
Standard and Economical Cascadic Multigrid Methods for the Mortar Finite Element Methods
Institute of Scientific and Technical Information of China (English)
Xuejun Xu; Wenbin Chen
2009-01-01
In this paper, standard and economical cascadic multigrid methods are con-sidered for solving the algebraic systems resulting from the mortar finite element meth-ods. Both cascadic multigrid methods do not need full elliptic regularity, so they can be used to tackle more general elliptic problems. Numerical experiments are reported to support our theory.
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.
Multigrid for high dimensional elliptic partial differential equations on non-equidistant grids
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
Multigrid for high dimensional elliptic partial differential equations on non-equidistant grids
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 pr
Nonlinear External Kink Computing with NIMROD
Bunkers, K. J.; Sovinec, C. R.
2016-10-01
Vertical displacement events (VDEs) during disruptions often include non-axisymmetric activity, including external kink modes, which are driven unstable as contact with the wall eats into the q-profile. The NIMROD code is being applied to study external-kink-unstable tokamak profiles in toroidal and cylindrical geometries. Simulations with external kinks show the plasma swallowing a vacuum bubble, similar to. NIMROD reproduces external kinks in both geometries, using an outer vacuum region (modeled as a plasma with a large resistivity), but as the boundary between the vacuum and plasma regions becomes more 3D, the resistivity becomes a 3D function, and it becomes more difficult for algebraic solves to converge. To help allow non-axisymmetric, nonlinear VDE calculations to proceed without restrictively small time-steps, several computational algorithms have been tested. Flexible GMRES, using a Fourier and real space representation for the toroidal angle has shown improvements. Off-diagonal preconditioning and a multigrid approach were tested and showed little improvement. A least squares finite element method (LSQFEM) has also helped improve the algebraic solve. This effort is supported by the U.S. Dept. of Energy, Award Numbers DE-FG02-06ER54850 and DE-FC02-08ER54975.
Directory of Open Access Journals (Sweden)
Mohammad Ali Afshari
2012-10-01
Full Text Available The aim of this paper is to present mathematical models optimizing all materials flows in supply chain. In this research a fuzzy multi-objective nonlinear mixed- integer programming model with piecewise linear membership function is applied to design a multi echelon supply chain network (SCN by considering total transportation costs and capacities of all echelons with fuzzy objectives. The model that is proposed in this study has 4 fuzzy functions. The first function is minimizing the total transportation costs between all echelons (suppliers, factories, distribution centers (DCs and customers. The second one is minimizing holding and ordering cost on DCs. The third objective is minimizing the unnecessary and unused capacity of factories and DCs via decreasing variance of transported amounts between echelons. The forth is minimizing the number of total vehicles that ship the materials and products along with SCN. For solving such a problem, as nodes increases in SCN, the traditional method does not have ability to solve large scale problem. So, we applied a Meta heuristic method called Genetic Algorithm. The numerical example is real world applied and compared the results with each other demonstrate the feasibility of applying the proposed model to given problem, and also its advantages are discussed.
Roozegar, Mehdi; Mahjoob, Mohammad J.; Ayati, Moosa
2017-05-01
This paper deals with adaptive estimation of the unknown parameters and states of a pendulum-driven spherical robot (PDSR), which is a nonlinear in parameters (NLP) chaotic system with parametric uncertainties. Firstly, the mathematical model of the robot is deduced by applying the Newton-Euler methodology for a system of rigid bodies. Then, based on the speed gradient (SG) algorithm, the states and unknown parameters of the robot are estimated online for different step length gains and initial conditions. The estimated parameters are updated adaptively according to the error between estimated and true state values. Since the errors of the estimated states and parameters as well as the convergence rates depend significantly on the value of step length gain, this gain should be chosen optimally. Hence, a heuristic fuzzy logic controller is employed to adjust the gain adaptively. Simulation results indicate that the proposed approach is highly encouraging for identification of this NLP chaotic system even if the initial conditions change and the uncertainties increase; therefore, it is reliable to be implemented on a real robot.
Directory of Open Access Journals (Sweden)
Yulong Ying
2015-01-01
Full Text Available In the lifespan of a gas turbine engine, abrupt faults and performance degradation of its gas-path components may happen; however the performance degradation is not easily foreseeable when the level of degradation is small. Gas path analysis (GPA method has been widely applied to monitor gas turbine engine health status as it can easily obtain the magnitudes of the detected component faults. However, when the number of components within engine is large or/and the measurement noise level is high, the smearing effect may be strong and the degraded components may not be recognized. In order to improve diagnostic effect, a nonlinear steady-state model based gas turbine health status estimation approach with improved particle swarm optimization algorithm (PSO-GPA has been proposed in this study. The proposed approach has been tested in ten test cases where the degradation of a model three-shaft marine engine has been analyzed. These case studies have shown that the approach can accurately search and isolate the degraded components and further quantify the degradation for major gas-path components. Compared with the typical GPA method, the approach has shown better measurement noise immunity and diagnostic accuracy.
An efficient flexible-order model for 3D nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bingham, Harry B.; Lindberg, Ole
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...
Directory of Open Access Journals (Sweden)
Gisela C V Ramadas
Full Text Available This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.
Ramadas, Gisela C V; Rocha, Ana Maria A C; Fernandes, Edite M G P
2015-01-01
This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.
Rapidly converging multigrid reconstruction of cone-beam tomographic data
Myers, Glenn R.; Kingston, Andrew M.; Latham, Shane J.; Recur, Benoit; Li, Thomas; Turner, Michael L.; Beeching, Levi; Sheppard, Adrian P.
2016-10-01
In the context of large-angle cone-beam tomography (CBCT), we present a practical iterative reconstruction (IR) scheme designed for rapid convergence as required for large datasets. The robustness of the reconstruction is provided by the "space-filling" source trajectory along which the experimental data is collected. The speed of convergence is achieved by leveraging the highly isotropic nature of this trajectory to design an approximate deconvolution filter that serves as a pre-conditioner in a multi-grid scheme. We demonstrate this IR scheme for CBCT and compare convergence to that of more traditional techniques.
An improved convergence analysis of smoothed aggregation algebraic multigrid
Energy Technology Data Exchange (ETDEWEB)
Brezina, Marian [Univ. of Colorado, Boulder, CO (United States). Dept. of Applied Mathematics; Vaněk, Petr [University of West Bohemia (Czech Republic). Dept. of Mathematics; Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
2011-03-02
We present an improved analysis of the smoothed aggregation (SA) alge- braic multigrid method (AMG) extending the original proof in [SA] and its modification in [Va08]. The new result imposes fewer restrictions on the aggregates that makes it eas- ier to verify in practice. Also, we extend a result in [Van] that allows us to use aggressive coarsening at all levels due to the special properties of the polynomial smoother, that we use and analyze, and thus provide a multilevel convergence estimate with bounds independent of the coarsening ratio.
An improved convergence analysis of smoothed aggregation algebraic multigrid
Energy Technology Data Exchange (ETDEWEB)
Brezina, Marian [Univ. of Colorado, Boulder, CO (United States). Dept. of Applied Mathematics; Vaněk, Petr [University of West Bohemia (Czech Republic). Dept. of Mathematics; Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
2011-03-02
We present an improved analysis of the smoothed aggregation (SA) alge- braic multigrid method (AMG) extending the original proof in [SA] and its modification in [Va08]. The new result imposes fewer restrictions on the aggregates that makes it eas- ier to verify in practice. Also, we extend a result in [Van] that allows us to use aggressive coarsening at all levels due to the special properties of the polynomial smoother, that we use and analyze, and thus provide a multilevel convergence estimate with bounds independent of the coarsening ratio.
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.
Energy Technology Data Exchange (ETDEWEB)
Brezina, M; Manteuffel, T; McCormick, S; Ruge, J; Sanders, G; Vassilevski, P S
2007-05-31
Consider the linear system Ax = b, where A is a large, sparse, real, symmetric, and positive definite matrix and b is a known vector. Solving this system for unknown vector x using a smoothed aggregation multigrid (SA) algorithm requires a characterization of the algebraically smooth error, meaning error that is poorly attenuated by the algorithm's relaxation process. For relaxation processes that are typically used in practice, algebraically smooth error corresponds to the near-nullspace of A. Therefore, having a good approximation to a minimal eigenvector is useful to characterize the algebraically smooth error when forming a linear SA solver. This paper discusses the details of a generalized eigensolver based on smoothed aggregation (GES-SA) that is designed to produce an approximation to a minimal eigenvector of A. GES-SA might be very useful as a standalone eigensolver for applications that desire an approximate minimal eigenvector, but the primary aim here is for GES-SA to produce an initial algebraically smooth component that may be used to either create a black-box SA solver or initiate the adaptive SA ({alpha}SA) process.
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.
Directory of Open Access Journals (Sweden)
James E Skinner
2008-04-01
Full Text Available James E Skinner, Jerry M Anchin, Daniel N WeissVicor Technologies, Inc., Bangor, PA, USAAbstract: Heart rate variability (HRV reflects both cardiac autonomic function and risk of arrhythmic death (AD. Reduced indices of HRV based on linear stochastic models are independent risk factors for AD in post-myocardial infarct cohorts. Indices based on nonlinear deterministic models have a significantly higher sensitivity and specificity for predicting AD in retrospective data. A need exists for nonlinear analytic software easily used by a medical technician. In the current study, an automated nonlinear algorithm, the time-dependent point correlation dimension (PD2i, was evaluated. The electrocardiogram (ECG data were provided through an National Institutes of Health-sponsored internet archive (PhysioBank and consisted of all 22 malignant arrhythmia ECG files (VF/VT and 22 randomly selected arrhythmia files as the controls. The results were blindly calculated by automated software (Vicor 2.0, Vicor Technologies, Inc., Boca Raton, FL and showed all analyzable VF/VT files had PD2i < 1.4 and all analyzable controls had PD2i > 1.4. Five VF/VT and six controls were excluded because surrogate testing showed the RR-intervals to contain noise, possibly resulting from the low digitization rate of the ECGs. The sensitivity was 100%, specificity 85%, relative risk > 100; p < 0.01, power > 90%. Thus, automated heartbeat analysis by the time-dependent nonlinear PD2i-algorithm can accurately stratify risk of AD in public data made available for competitive testing of algorithms.Keywords: heart rate variability, sudden death, ventricular arrhythmias, nonlinear, chaos
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.
多约束非线性背包问题的一种有效算法%An efficient algorithm for multi-dimensional nonlinear knapsack problems
Institute of Scientific and Technical Information of China (English)
陈娟; 孙小玲; 郭慧娟
2006-01-01
Multi-dimensional nonlinear knapsack problem is a bounded nonlinear integer programming problem that maximizes a separable nondecreasing function subject to multiple separable nondecreasing constraints. This problem is often encountered in resource allocation, industrial planning and computer network. In this paper, a new convergent Lagrangian dual method was proposed for solving this problem. Cutting plane method was used to solve the dual problem and to compute the Lagrangian bounds of the primal problem. In order to eliminate the duality gap and thus to guarantee the convergence of the algorithm, domain cut technique was employed to remove certain integer boxes and partition the revised domain to a union of integer boxes. Extensive computational results show that the proposed method is efficient for solving large-scale multi-dimensional nonlinear knapsack problems. Our numerical results also indicate that the cutting plane method significantly outperforms the subgradient method as a dual search procedure.
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/.
Tweed Relaxation: a new multigrid smoother for stretched structured grids
Bewley, Thomas; Mashayekhi, Alireza
2012-11-01
In DNS/LES of the NSE using a fractional step method, one must accurately solve a Poisson equation for the pressure update at each timestep. This step often represents a significant fraction of the overall computational burden and, when Fourier methods are unavailable, geometric multigrid methods are a preferred choice. When working on an unstretched Cartesian grid, the red-black Gauss-Seidel method is the most efficient multigrid smoother available. When working on a Cartesian grid that is stretched in 1 coordinate direction to provide grid clustering near a wall, zebra relaxation, on sets of lines perpendicular to the wall, is most efficient. When working on a structured grid that is stretched in 2 or 3 coordinate directions, however, one is forced to alternate the directions that the zebra relaxation is applied in order to pass information quickly across all regions of grid clustering. A new relaxation method is introduced which is shown to significantly outperform such alternating direction line smoothers. This new method is implicit along sets of lines that branch and form 90° corners, like the stripes at the shoulder of a tweed shirt, to stay everywhere perpendicular to the nearest wall, thus passing information quickly across all regions of grid clustering.
Comparative Study on Some Nonlinear Filtering Algorithms%几种非线性滤波算法的比较研究
Institute of Scientific and Technical Information of China (English)
王庆欣; 史连艳
2011-01-01
针对组合导航等非线性系统,扩展卡尔曼滤波算法(EKF)在初值不准确时存在滤波发散的现象,故提出U-卡尔曼滤波(UKF);粒子滤波算法(PF)适合于强非线性、非高斯噪声系统,但同时存在退化现象,故提出2种改进算法.前人的工作多集中在单一算法的研究,而在此是将上述各种算法应用到同一典型非线性系统,通过应用Matlab进行仿真实验得出具体滤渡效果数据,综合对比分析了各算法的优缺点,得出一些有用的结论,为组合导航系统中非线性滤波算法的选择提供了参考.%For the nonlinear systems such as integrated navigation systems, since the extended Kalman filtering ( EKF) has a dispersing phenomenon when the initial state value is inaccurate, the unscented Kalman filiering ( UKF) is proposed,and although particle filtering (PF) is suitable for any nonlinear non-Gaussian systems, it has a degeneracy phenomenon, then two kinds of improved filtering algorithms are put forward. Scientific researchers focused on single filtering before. The filtering algorithms mentioned above are adopted in a same typical model of nonlinear system in this paper. The detailed data of the filtering algorithms were obtained by emulational experiments with Matlab. Some useful conclusios were acquired after the contrast and analysis of their advantages and disadvantages. A reference is offered in choosing a suitable nonlinearfiltering algorithm for integrated navigation systems.
2010-01-01
Back-propagation with gradient method is the most popular learning algorithm for feed-forward neural networks. However, it is critical to determine a proper fixed learning rate for the algorithm. In this paper, an optimized recursive algorithm is presented for online learning based on matrix operation and optimization methods analytically, which can avoid the trouble to select a proper learning rate for the gradient method. The proof of weak convergence of the proposed algorithm also is given...
CASCADIC MULTIGRID METHOD FOR THE MORTAR ELEMENT METHOD FOR P1 NONCONFORMING ELEMENT
Institute of Scientific and Technical Information of China (English)
Chun-jia Bi; Dan-hui Hong
2005-01-01
In this paper, we consider the cascadic multigrid method for the mortar P1 nonconforming element which is used to solve the Poisson equation and prove that the cascadic conjugate gradient method is accurate with optimal complexity.
Multi-grid Beam and Warming scheme for the simulation of unsteady ...
African Journals Online (AJOL)
2010-03-08
Mar 8, 2010 ... cal methods, the implicit finite-difference method and finite element method ... a few iterations, but after that these methods will be converged slowly. Multi-grid ...... VENUTELLI M (2002) Stability and accuracy of weighted four-.
Calogero, Francesco
2016-10-01
Recently a simple differential algorithm to compute all the zeros of a generic polynomial was introduced. In this paper an analogous, but finite-difference, algorithm is introduced and discussed. At the end of the paper a minor generalization of the differential algorithm is also mentioned.
Multi-Grid and Resolution Full-Wave Tomography and Moment Tensor Inversion (Postprint)
2012-06-04
number of discrete nodes in numerical methods, we adapt a multigrid/multilevel method ( Briggs , 1987) to solve the wave propagation and inversion...Monitoring Technologies 186 Approved for public release; distribution is unlimited. Antoun, T., D. Harris, T. Lay, S.C. Myers , M.E. Pasyanos, P...The current limits of resolution for surface wave tomography in North America, Eos Trans AGU, 81, F897. Briggs , W.L. (1987). A multigrid Tutorial
非线性自适应拥塞控制算法研究%Study of Non-Linear Adaptive Congestion Control Algorithm
Institute of Scientific and Technical Information of China (English)
范训礼; 郑锋; Lin GUAN
2011-01-01
研究丢弃概率的变化率与队列长度稳定性间的关系,分析ARED算法及REM算法的丢弃概率计算函数,采用非线性化函数计算丢弃概率,提出一种非线性自适应拥塞控制算法(NLACCA),根据队列长度与目标队列长度中值的偏离程度动态地调整丢弃概率的变化率,从而减小队列长度波动,提高算法稳定性.在NS-2上进行的大量实验结果表明,该算法具有队列长度抖动性小、平均时延低、丢包数少等特点.%This paper studies the relationship between the changing rate of drop probability and the queue stability, and specifically researches computing function of dropping probability of Adaptive Random Early Detection(ARED) algorithm and Random Exponent Marking(REM) algorithm respectively. As a result, a Non-Linear Adaptive Congestion Control Algorithm(NLACCA) is proposed. Based on the Active Queue Management(AQM) scheme, which provides a non-linear adaptation to the dropping probability function of the ARED, NLACCA enables the dropping probability gradient to vary along with the deviation that is between the instantaneous queue length and the target queue length. NLACCA can not only reduce the jitter of the target queue length, but also improve the stability of the algorithm. Simulation results demonstrate that the NLAC CA algorithm outperforms in most scenarios, such as the jitter of queue length, delay, and packets dropped.
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.
Institute of Scientific and Technical Information of China (English)
童小娇; 周叔子
2003-01-01
This paper presents a trust region two-phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.
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.
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.
Directory of Open Access Journals (Sweden)
Jun Wang
2015-01-01
Full Text Available 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.
Institute of Scientific and Technical Information of China (English)
王赟松; 刘钦龙; 高卫中
2004-01-01
标准BP神经网络算法收敛速度慢是限制其广泛应用的主要原因.为此,以标准BP算法为基础,应用最小二乘法理论,提出了一种收敛速度快的BP算法--NLMSBP算法.仿真结果表明,和标准BP算法及其它改进形式比较,NLMSBP算法收敛速度大大提高,稳定性并未降低,这为BP神经网络应用于实时性要求高的场合提供了算法基础.该算法缺点是计算量大,所需计算机内存大,不适于大型网络的计算.%That standard backpropagation(BP) algorithm for training neural networks converges slowly is the main reason why it cannot be used widely in practical applications. Therefore, a new kind of BP algorithm, called the NLMSBP algorithm for short, is put forward in this paper by using solutions for a nonlinear least mean square problem. The experimental results have proved that the algorithm converges very fast and has good stability compared with the standard BP algorithm and the other modifications. It is suitable for training the network with a few thousands of weights and offsets and high training precision demand. If the computer memory is enough, the superiority of the algorithm over the others is very notable. Indeed, it is worth popularizing.
Implementation and Optimization of miniGMG - a Compact Geometric Multigrid Benchmark
Energy Technology Data Exchange (ETDEWEB)
Williams, Samuel; Kalamkar, Dhiraj; Singh, Amik; Deshpande, Anand M.; Straalen, Brian Van; Smelyanskiy, Mikhail; Almgren, Ann; Dubey, Pradeep; Shalf, John; Oliker, Leonid
2012-12-01
Multigrid methods are widely used to accelerate the convergence of iterative solvers for linear systems used in a number of different application areas. In this report, we describe miniGMG, our compact geometric multigrid benchmark designed to proxy the multigrid solves found in AMR applications. We explore optimization techniques for geometric multigrid on existing and emerging multicore systems including the Opteron-based Cray XE6, Intel Sandy Bridge and Nehalem-based Infiniband clusters, as well as manycore-based architectures including NVIDIA's Fermi and Kepler GPUs and Intel's Knights Corner (KNC) co-processor. This report examines a variety of novel techniques including communication-aggregation, threaded wavefront-based DRAM communication-avoiding, dynamic threading decisions, SIMDization, and fusion of operators. We quantify performance through each phase of the V-cycle for both single-node and distributed-memory experiments and provide detailed analysis for each class of optimization. Results show our optimizations yield significant speedups across a variety of subdomain sizes while simultaneously demonstrating the potential of multi- and manycore processors to dramatically accelerate single-node performance. However, our analysis also indicates that improvements in networks and communication will be essential to reap the potential of manycore processors in large-scale multigrid calculations.
A new multi-grid type MSGC with pad readout
Takahashi, H; Yano, K; Fukuda, D; Nakazawa, M; Hasegawa, K
2001-01-01
Recently, a new multi-grid type MSGC has been proposed. Between the anode and the cathode, additional grid strips are placed in this new type of MSGC. Gaps between these strips are chosen to be around 10 mu m which assure efficient removal of surface charges which even do not need the lower surface resistivity and bare glass can be used up to 10 sup 6 cps/mm sup 2. Another feature of the MSGC is its high gain capability. Owing to the existence of other strips of lower potentials, the field strength around the opposing grid to the anode strip is not so high as conventional small gap detectors. Furthermore, the contribution of the surface streamer is greatly suppressed because the electric field parallel to the surface is screened by the intermediate grid electrodes. However, the existence of additional electrodes also screens all the electric field upper than the substrate and we cannot observe induced signals from backside of the substrate. To overcome the difficulty, we propose another signal readout method ...
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.
Chen, Guangye
2015-01-01
For decades, the Vlasov-Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. Here, we explore a fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space-time-centered, employing particle sub-cycling and orbit-averaging. The algorithm conserves total energy, local charge, canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large time steps and cell sizes, which are determined by accuracy consid...
Ramcharan, A. M.; Kemanian, A.; Richard, T.
2013-12-01
The largest terrestrial carbon pool is soil, storing more carbon than present in above ground biomass (Jobbagy and Jackson, 2000). In this context, soil organic carbon has gained attention as a managed sink for atmospheric CO2 emissions. The variety of models that describe soil carbon cycling reflects the relentless effort to characterize the complex nature of soil and the carbon within it. Previous works have laid out the range of mathematical approaches to soil carbon cycling but few have compared model structure performance in diverse agricultural scenarios. As interest in increasing the temporal and spatial scale of models grows, assessing the performance of different model structures is essential to drawing reasonable conclusions from model outputs. This research will address this challenge using the Evolutionary Algorithm Borg-MOEA to optimize the functionality of carbon models in a multi-objective approach to parameter estimation. Model structure performance will be assessed through analysis of multi-objective trade-offs using experimental data from twenty long-term carbon experiments across the globe. Preliminary results show a successful test of this proof of concept using a non-linear soil carbon model structure. Soil carbon dynamics were based on the amount of carbon inputs to the soil and the degree of organic matter saturation of the soil. The degree of organic matter saturation of the soil was correlated with the soil clay content. Six parameters of the non-linear soil organic carbon model were successfully optimized to steady-state conditions using Borg-MOEA and datasets from five agricultural locations in the United States. Given that more than 50% of models rely on linear soil carbon decomposition dynamics, a linear model structure was also optimized and compared to the non-linear case. Results indicate linear dynamics had a significantly lower optimization performance. Results show promise in using the Evolutionary Algorithm Borg-MOEA to assess
Gao, Hao; Phan, Lan; Lin, Yuting
2012-09-01
A graphics processing unit-based parallel multigrid solver for a radiative transfer equation with vacuum boundary condition or reflection boundary condition is presented for heterogeneous media with complex geometry based on two-dimensional triangular meshes or three-dimensional tetrahedral meshes. The computational complexity of this parallel solver is linearly proportional to the degrees of freedom in both angular and spatial variables, while the full multigrid method is utilized to minimize the number of iterations. The overall gain of speed is roughly 30 to 300 fold with respect to our prior multigrid solver, which depends on the underlying regime and the parallelization. The numerical validations are presented with the MATLAB codes at https://sites.google.com/site/rtefastsolver/.
Chen, G.; Chacón, L.
2015-12-01
For decades, the Vlasov-Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. Here, we explore a fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space-time-centered, employing particle sub-cycling and orbit-averaging. The algorithm conserves total energy, local charge, canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D-3V.
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.
Métodos multigrid em malhas nao-aninhadas aplicados a problemas elásticos
Bittencourt, Marco Lucio; Feijóo, Raúl A.
1998-01-01
Neste trabalho apresentam-se conceitos de métodos multigrid aplicados a problemas elásticos lineares. Consideram-se exemplos bi e tridimensionais com malhas nao-estruturadase nao-aninhadas. Tradicionalmente, os métodos multigrid t6m sido utilizados com malhas aninhadas devido a maior simplicidade dos operadores de transferencia. No entanto, para modelar problemas de engenharia, a aplicaqáo de malhas nao-estruturadas é mais conveniente. Comparaqóes com métodos diretos e iterativos sao ap...
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.
Nonlinear Predictive Control Algorithm for Variable Pitch Controller of Wind Turbine%风机变桨距非线性预测控制算法
Institute of Scientific and Technical Information of China (English)
雷涛; 贾利民
2011-01-01
Pitch-Controlled technique is one of the significant control techniques to MW level large variable speed pitch-controlled wind turbines, and the output power can be maintained close to the rated output power by pitch controlling. Due to the strong nonlinear characteristics of the blades, using the conventional PID controller is always hard to choose the parameters and lack of self-tuning capability. This paper proposes a design method of pitch-controlled nonlinear prediction controller based on genetic algorithms. A restricted nonlinear prediction control algorithm based on intelligent searching is designed for the nonlinear control objects based on the prediction control strategy of prediction model, rolling optimization and feedback verification. This algorithm has well restricted prediction control characteristics to the nonlinear objects referring to the results of the simulation. Compared to the conventional PID controller, this method has the advantages of fast responding, small overshoot and good anti-disturbance capability, which can also reduce the design work of controller parameters significantly by rolling local optimization. The results of the simulation demonstrate the effective of the approach proposed in this paper.%变桨控制技术是MW级大型变速变桨风力发电机组的核心控制技术之一,通过变桨控制可以保证风电机组输出功率恒定在额定功率附近.由于风轮的强非线性特性,采用常规的PID控制器往往面临参数难以设计以及参数缺乏自整定能力的问题.提出了基于遗传算法的变桨距非线性预测控制器设计方法,根据优化和反馈校正的预测控制思想,针对风轮非线性控制对象设计了一种基于智能搜索方法的带约束的非线性预测控制算法进行仿真.仿真结果表明算法对非线性对象控制中具有很好的约束预测控制性能.与传统PI算法相比,具有响应快速、超调小、抗干扰能力好的
Uilhoorn, F. E.
2016-10-01
In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.
模型不确定非线性Markov跳变系统的滤波算法%Filter algorithm for nonlinear Markov jump systems with uncertain models
Institute of Scientific and Technical Information of China (English)
赵顺毅; 刘飞
2012-01-01
Considering the state estimation problem for the nonlinear Markov jump system with uncertain model, a novel filtering algorithm is proposed. Compared with the traditional interacting multiple particle filter method, in this method, a term of filtering error at previous time instant is introduced to increase the effect of the particles which are true but with small weights due to the inaccuracy model to improve the estimation performance in the filtering process. Simulation results show the effectiveness of this method in handling with the state estimation problem for the nonlinear Markov jump systems with uncertain model parameter.%针对模型不确定非线性Markov跳变系统,提出一种新的滤波算法.相比于传统交互多模型粒子滤波,该方法通过引入前一时刻的滤波误差来增强原先由于不精确模型而造成权值较小的真实粒子在滤波过程中的作用,以此来改善算法的估计性能.仿真结果表明,该方法在处理含不确定模型参数的非线性Markov跳变系统状态估计问题时具有较好的性能.
Zhong, Jian; Dong, Gang; Sun, Yimei; Zhang, Zhaoyang; Wu, Yuqin
2016-11-01
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. Project supported by the National Natural Science Foundation of China (Grant Nos. 41230421 and 41605075) and the National Basic Research Program of China (Grant No. 2013CB430101).
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.
Wang, Xiangyu; Li, Shihua; Chen, Michael Z Q
2017-07-27
This paper is devoted to solving the output consensus problem of leader-follower higher-order nonlinear multiagent systems subject to mismatched disturbances. The disturbances are allowed to be in higher-order forms. First, by constructing a generalized proportional-integral observer for each follower, estimates of the disturbances and their derivatives are obtained. At the same time, a distributed observer is also developed for the followers to estimate the leader state information. Second, based on the estimates of the disturbances and the leader state, together with the backstepping technique, a feedforward-feedback composite consensus control scheme is proposed. The designed distributed protocols guarantee asymptotic output consensus for the agents. Simulation results validate the effectiveness of the proposed composite control scheme.
Chen, Guangye
2013-01-01
A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen, Chacon, Barnes, J. Comput. Phys. 230 (2011) 7018). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation of Maxwell's equations, which avoids radiative aliasing noise issues by ordering out the light wave. An implicit, orbit-averaged time-space-centered finite difference scheme is applied to both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. Several 1D numer...
Non-linear Manifold Learning Algorithm Based on Intensity of Points%基于点密集度的非线性流形学习算法
Institute of Scientific and Technical Information of China (English)
黄淑萍
2012-01-01
This paper presents a non-linear manifold learning algorithm based on intensity of sample points. It proposes an effective intensity parameter of sample points, which constraints the low-dimensional embedding of uneven data well. There is a better embedding result than LLE. The experimental results on the artificial and face datasets show that the new algorithm yields a better embedding and classification result.%提出一种样本点密集度的非线性流形学习算法．该算法提出了一个有效的数据点密集参数，能够很好地对非均匀数据的低维嵌入进行约束，其嵌效结果明显优于LLE算法．在人工和人脸数据集上的实验结果表明，新算法产生了较好的嵌入及分类结果．
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.
A Simulation Research of Nonlinear Lowry Model Based on Genetic Algorithm%基于遗传算法的非线性Lowry模型模拟研究
Institute of Scientific and Technical Information of China (English)
周彬学; 戴特奇; 梁进社; 张华
2011-01-01
Under the principle of genetic algorithm, by using the genetic algorithm toolbox, after proving the applicability of genetic algorithm on a numerical example of 3 zones, 3-section economy of nonlinear Lowry model, the authors use this model to perform a simulated experiment on 9 zones, 3-section economy under a fan-shaped urban framework. The results show that, at first, if the residential charm of every district is at the same degree, traffic factor will play a very important role in residential structure of urban area; secondly, the district at the best traffic location owns the highest population density. Because of the limitation of land and maximization of economic goal, this type of district is the first choice to the industry which have high added value. This article shows a good explanatory ability of nonlinear Lowry model and lays a good foundation for the practical simulated research of urban.%利用遗传算法思想，借助以MATLAB语言为基础的遗传算法工具箱，在验证遗传算法在三区域、三部门模拟运算适用性之后，用非线性Lowry模型对扇形城市空间结构下的九区域、三部门进行模拟实验。结果表明：在各区域居住魅力相同的情况下，交通因素对城市居住空间结构变化起到至关重要的作用；交通区位最好的区域也是人口密度最大的区域，因为用地的有限性和地区产值的最大化追求，使这些区域也是高附加值产业首选之地。研究结果展示了非线性Lowry模型良好的解释能力，为该模型推向具体城市模拟研究打下良好基础，提高了其实用性。
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.
Development of a multigrid finite difference solver for benchmark permeability analysis
Loendersloot, Richard; Grouve, Wouter J.B.; Akkerman, Remko; Boer, de André; Michaud, V.
2010-01-01
A finite difference solver, dedicated to flow around fibre architectures is currently being developed. The complexity of the internal geometry of textile reinforcements results in extreme computation times, or inaccurate solutions. A compromise between the two is found by implementing a multigrid al
Yosui, Kuniaki; Iwashita, Takeshi; Mori, Michiya; Kobayashi, Eiichi
Finite element analyses of electromagnetic field are commonly used for designing of various electronic devices. The scale of the analyses becomes larger and larger, therefore, a fast linear solver is needed to solve linear equations arising from the finite element method. Since a multigrid solver is the fastest linear solver for these problems, parallelization of a multigrid solver is a quite useful approach. From the viewpoint of industrial applications, an effective usage of a small-scale PC cluster is important due to initial cost for introducing parallel computers. In this paper, a distributed parallel multigrid solver for a small-scale PC cluster is developed. In high frequency electromagnetic field analyses, a special block Gauss-Seidel smoother is used for the multigrid solver instead of general smoothers such as Gauss-Seidel smoother or Jacobi smoother in order to improve a convergence rate. The block multicolor ordering technique is applied to parallelize the smoother. A numerical exsample shows that a 3.7-fold speed-up in computational time and a 3.0-fold increase in the scale of the analysis were attained when the number of CPU was increased from one to five.
Multigrid method based on a space-time approach with standard coarsening for parabolic problems
S.R. Franco (Sebastião Romero); F.J. Gaspar Lorenz (Franscisco); M.A. Villela Pinto (Marcio Augusto); C. Rodrigo (Carmen)
2018-01-01
textabstractIn this work, a space-time multigrid method which uses standard coarsening in both temporal and spatial domains and combines the use of different smoothers is proposed for the solution of the heat equation in one and two space dimensions. In particular, an adaptive smoothing strategy,
Sheikh, A.H.
2014-01-01
The Helmholtz equation is the simplest possible model for the wave propagation. Perhaps this is the reason, despite denying traditional iterative methods like Krylov sub-space methods, Multigrids, etcetera, numerical solution of the Helmholtz equation has been an interesting and abundant problem to
Multigrid with FFT smoother for a simplified 2D frictional contact problem
Zhao, J.; Vollebregt, E.A.H.; Oosterlee, C.W.
2014-01-01
This paper aims to develop a fast multigrid (MG) solver for a Fredholm integral equation of the first kind, arising from the 2D elastic frictional contact problem. After discretization on a rectangular contact area, the integral equation gives rise to a linear system with the coefficient matrix bein
Smoke simulation for fire engineering using a multigrid method on graphics hardware
DEFF Research Database (Denmark)
Glimberg, Stefan; Erleben, Kenny; Bennetsen, Jens
2009-01-01
We present a GPU-based Computational Fluid Dynamics solver for the purpose of fire engineering. We apply a multigrid method to the Jacobi solver when solving the Poisson pressure equation, supporting internal boundaries. Boundaries are handled on the coarse levels, ensuring that boundaries will n...
Eigensystem analysis of classical relaxation techniques with applications to multigrid analysis
Lomax, Harvard; Maksymiuk, Catherine
1987-01-01
Classical relaxation techniques are related to numerical methods for solution of ordinary differential equations. Eigensystems for Point-Jacobi, Gauss-Seidel, and SOR methods are presented. Solution techniques such as eigenvector annihilation, eigensystem mixing, and multigrid methods are examined with regard to the eigenstructure.
Phase retrieval using nonlinear diversity.
Lu, Chien-Hung; Barsi, Christopher; Williams, Matthew O; Kutz, J Nathan; Fleischer, Jason W
2013-04-01
We extend the Gerchberg-Saxton algorithm to phase retrieval in a nonlinear system. Using a tunable photorefractive crystal, we experimentally demonstrate the noninterferometric technique by reconstructing an unknown phase object from optical intensity measurements taken at different nonlinear strengths.
Lehtonen, J V; Denessiouk, K; May, A C; Johnson, M S
1999-02-15
We have developed a generic tool for the automatic identification of regions of local structural similarity in unrelated proteins having different folds, as well as for defining more global similarities that result from homologous protein structures. The computer program GENFIT has evolved from the genetic algorithm-based three-dimensional protein structure comparison program GA_FIT. GENFIT, however, can locate and superimpose regions of local structural homology regardless of their position in a pair of structures, the fold topology, or the chain direction. Furthermore, it is possible to restrict the search to a volume centered about a region of interest (e.g., catalytic site, ligand-binding site) in two protein structures. We present a number of examples to illustrate the function of the program, which is a parallel processing implementation designed for distribution to multiple machines over a local network or to run on a single multiprocessor computer.
Multigrid Methods for Mortar-Type Nonconforming Quadrilateral Element%Mortar型非协调四边形元多重网格方法
Institute of Scientific and Technical Information of China (English)
王锋; 徐为
2008-01-01
Muhigrid algorithms for mortar-type nonconforming quadrilateral element were discussed. An intergrid transfer operator were proposed for the nonested mortar element spaces. It was proved that the W-cycle and variable V-cycle mul-tigrid methods were both optimal. And the numerical experiments confirmed our results.%讨论了Mortar型四边形元的多重网格方法.针对非嵌套的Mortar元空间,提出了一种网格转移算子.并证明了W循环和可变的V循环多重网格方法是最优的.数值实验验证了我们的理论结果.
Improvement Particle Filtering Algorithm for Nonlinear Non-Gaussian models%非线性非高斯模型的改进粒子滤波算法
Institute of Scientific and Technical Information of China (English)
周航; 冯新喜; 王蓉
2012-01-01
An improved particle filter algorithm is proposed for the highly non-linear passive location and tracking system in which the common tracking filters often faile to catch and keep tracking of the emitter. Firstly, the algorithm uses limite gaussian mixture model to approximate the posterior density of states. Secondly, in order to solve the problem in which the stochastic observation noise influence the accuracy of particle weights, an improved based on averaging likelihood functions with diverse proportion is proposed. According to x2 testing, the new method combines multi-observations to compute the likelihood functions of each particle and then average them with single observation computes the likelihood functions of each particle to update particle weights. The method not only reduces the influence of the stochastic observation noise to particle weight but also improves real-time. Finally, the traditional process of particle filter resampling is replaced by the aitken-de-terministic annealing expectation maximization ( A-DAEM) algorithm, avoiding to a local maximum and reducing the effects cause by sampling depletion. Simulation results show that the algorithm outperforms the one based on PF-ALDP and the other based on EM-GMPF in tracking accuracy and stability. Therefore it is more suitable to the nonlinear state estimation.%针对被动定位跟踪系统非线性强、传统跟踪滤波方法收敛速度慢且容易发散的问题,给出了一种用于纯方位目标跟踪的改进粒子滤波算法.该算法首先用有限的高斯混合模型来近似后验状态密度；其次针对随机噪声对粒子权值准确性的影响,给出了改进的变权平均似然函数.根据X2检验,对每个粒子权值的更新,采取由多次观测值计算粒子似然函数并对其求变权平均和单一观测值求似然函数相结合的方式进行,既减小随机观测噪声对权值的影响也提高了算法实时性；最后利用基于退火机制的Aitken
基于直接学习法的一种新预失真器%Novel Adaptive Nonlinear Predistorter Based on the Direct Learning Algorithm
Institute of Scientific and Technical Information of China (English)
徐琪; 段哲明
2012-01-01
为了克服宽带信号经过记忆放大器的非线性失真,针对有记忆非线性功放的多项式模型,提出了一种新的基于直接学习法的自适应算法.该算法采用无记忆预失真器的级联扩展,具有横向滤波器结构,与记忆多项式有相似的线性化效果.并且针对信号噪声对自适应算法的扰动和收敛速度慢等缺点,采用归一化LMS算法加以改进.在非线性功放的记忆多项式模型下,通过宽带信号验证了基于直接学习法的记忆型预失真器算法的有效性.%A novel adaptive direct learning algorithm for power amplifier with memory effects is proposed to compensate the nonlinear distortion introduced by HPAs. The cascade extension of the memoryless predistorter and the structure of finite ?impulse ?response filter significantly can get the close performs compare to memory polynomial method. The Normalize LMS algorithm is proposed to the disturb of signal noise and convergence speed problems. Under power amplifier' s memory polynomial model, simulation result show that the predistorter has the excellent 昿erformance when the wideband signal pass it.
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
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
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.
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.
Institute of Scientific and Technical Information of China (English)
周泽民; 曾新吾; 龚昌超; 田章福; 孙海洋
2013-01-01
针对调制气流声源存在较强的谐波畸变，将声源系统等效为 Hammerstein 非线性模型，利用该模型下的预失真技术对声源进行非线性补偿研究。根据辨识的 Hammerstein 模型中静态非线性部分带有直流分量的特点，给出了考虑直流分量补偿的预失真算法，并用数值仿真验证了算法的准确性和直流分量补偿的必要性。在非线性补偿实验中，根据单频信号辨识得到 Hammerstein 模型参数，采用 NFxPEM算法求得对应的预失真 Wiener 模型参数和预失真波形。实验结果表明，与直接发射相比，补偿发射后声波的功率谱中谐波能量有所下降，而基频能量有小幅度的上升，说明了研究思路的正确性。%Aimed at the harmonic distortion problem in the air-modulated speaker(AMS),the AMS behavioral model was represented by a Hammerstein structure,and the research on predistortion of AMS based on this model was made.As the DC offset exists in the nonlinearity of the Hammerstein model,a predistortion algorithm considering the DC offset compensation was developed.The validity of the algorithm and the necessity of the DC offset compensation were verified by computer simulation.In the experiment,a single sinusoidal excitation signal was first used to identify the Hammerstein model.Then,using the identified system parameters,the NFxPEMalgorithm was performed to obtain the parameters of Wiener predistorter and to predistort the excitation signal.From the experiment results,it is found that our approach is effective in reducing the harmonic power with a relatively small upgrade in the fundamental frequency power.
MGGHAT: Elliptic PDE software with adaptive refinement, multigrid and high order finite elements
Mitchell, William F.
1993-01-01
MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations in two dimensional polygonal domains. This program is now available for public use. It is a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Window display, and a posteriori through output files that can be used as GNUPLOT input. In this paper, we describe the methods used by MGGHAT, define the problem domain for which it is appropriate, illustrate use of the program, show numerical and graphical examples, and explain how to obtain the software.
Adaptive Aggregation Based Domain Decomposition Multigrid for the Lattice Wilson Dirac Operator
Frommer, Andreas; Krieg, Stefan; Leder, Björn; Rottmann, Matthias
2013-01-01
In lattice QCD computations a substantial amount of work is spent in solving discretized versions of the Dirac equation. Conventional Krylov solvers show critical slowing down for large system sizes and physically interesting parameter regions. We present a domain decomposition adaptive algebraic multigrid method used as a precondtioner to solve the "clover improved" Wilson discretization of the Dirac equation. This approach combines and improves two approaches, namely domain decomposition and adaptive algebraic multigrid, that have been used seperately in lattice QCD before. We show in extensive numerical test conducted with a parallel production code implementation that considerable speed-up over conventional Krylov subspace methods, domain decomposition methods and other hierarchical approaches for realistic system sizes can be achieved.
Application of multi-grid method on the simulation of incremental forging processes
Ramadan, Mohamad; Khaled, Mahmoud; Fourment, Lionel
2016-10-01
Numerical simulation becomes essential in manufacturing large part by incremental forging processes. It is a splendid tool allowing to show physical phenomena however behind the scenes, an expensive bill should be paid, that is the computational time. That is why many techniques are developed to decrease the computational time of numerical simulation. Multi-Grid method is a numerical procedure that permits to reduce computational time of numerical calculation by performing the resolution of the system of equations on several mesh of decreasing size which allows to smooth faster the low frequency of the solution as well as its high frequency. In this paper a Multi-Grid method is applied to cogging process in the software Forge 3. The study is carried out using increasing number of degrees of freedom. The results shows that calculation time is divide by two for a mesh of 39,000 nodes. The method is promising especially if coupled with Multi-Mesh method.
A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids
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.
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.
An automatic multigrid method for the solution of sparse linear systems
Shapira, Yair; Israeli, Moshe; Sidi, Avram
1993-01-01
An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.
CASCADIC MULTIGRID METHODS FOR MORTAR WILSON FINITE ELEMENT METHODS ON PLANAR LINEAR ELASTICITY
Institute of Scientific and Technical Information of China (English)
陈文斌; 汪艳秋
2003-01-01
Cascadic multigrid technique for mortar Wilson finite element method ofhomogeneous boundary value planar linear elasticity is described and analyzed. Firstthe mortar Wilson finite element method for planar linear elasticity will be analyzed,and the error estimate under L2 and H1 norm is optimal. Then a cascadic multigridmethod for the mortar finite element discrete problem is described. Suitable grid trans-fer operator and smoother are developed which lead to an optimal cascadic multigridmethod. Finally, the computational results are presented.
A new extrapolation cascadic multigrid method for three dimensional elliptic boundary value problems
Pan, Kejia; He, Dongdong; Hu, Hongling; Ren, Zhengyong
2017-09-01
In this paper, we develop a new extrapolation cascadic multigrid method, which makes it possible to solve three dimensional elliptic boundary value problems with over 100 million unknowns on a desktop computer in half a minute. First, by combining Richardson extrapolation and quadratic finite element (FE) interpolation for the numerical solutions on two-level of grids (current and previous grids), we provide a quite good initial guess for the iterative solution on the next finer grid, which is a third-order approximation to the FE solution. And the resulting large linear system from the FE discretization is then solved by the Jacobi-preconditioned conjugate gradient (JCG) method with the obtained initial guess. Additionally, instead of performing a fixed number of iterations as used in existing cascadic multigrid methods, a relative residual tolerance is introduced in the JCG solver, which enables us to obtain conveniently the numerical solution with the desired accuracy. Moreover, a simple method based on the midpoint extrapolation formula is proposed to achieve higher-order accuracy on the finest grid cheaply and directly. Test results from four examples including two smooth problems with both constant and variable coefficients, an H3-regular problem as well as an anisotropic problem are reported to show that the proposed method has much better efficiency compared to the classical V-cycle and W-cycle multigrid methods. Finally, we present the reason why our method is highly efficient for solving these elliptic problems.
Application of a Multigrid Method to a Mass-Consistent Diagnostic Wind Model.
Wang, Yansen; Williamson, Chatt; Garvey, Dennis; Chang, Sam; Cogan, James
2005-07-01
A multigrid numerical method has been applied to a three-dimensional, high-resolution diagnostic model for flow over complex terrain using a mass-consistent approach. The theoretical background for the model is based on a variational analysis using mass conservation as a constraint. The model was designed for diagnostic wind simulation at the microscale in complex terrain and in urban areas. The numerical implementation takes advantage of a multigrid method that greatly improves the computation speed. Three preliminary test cases for the model's numerical efficiency and its accuracy are given. The model results are compared with an analytical solution for flow over a hemisphere. Flow over a bell-shaped hill is computed to demonstrate that the numerical method is applicable in the case of parameterized lee vortices. A simulation of the mean wind field in an urban domain has also been carried out and compared with observational data. The comparison indicated that the multigrid method takes only 3%-5% of the time that is required by the traditional Gauss-Seidel method.
1980-10-01
superior to projected SOR and modified block SOR (see TalbIs 5.3 and 6.3, and Section 4). 3. For high accuracy solutions of the discrete LCP, one should use...of variational inequalities. Math. Computation, 28(1974), pp. 963-971. R. GLOWINSKI. La methode de relaxation. Rendiconti di Matematica , 14 (1971
MAPCUMBA : a fast iterative multi-grid map-making algorithm for CMB experiments
Doré, O; Teyssier, R.; Bouchet, F. R.; Vibert, D.; Prunet, S.
2001-01-01
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 to 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 ...
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
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.
NEURON-CONTROL OF NONLINEAR SYSTEMS USING GENETIC ALGORITHMS%采用遗传网络算法实现非线性系统的神经网络控制
Institute of Scientific and Technical Information of China (English)
赵小兵; 赵贤燮
2002-01-01
In this thesis,we present a genetic algorithm neuron-control scheme for nonlinear systems.Our method is different from those using supervised learning algorithms,such as the backpropagation(BP) algorithm,that needs training information in each step.The contributions of this thesis are the new approach to constructing neural network architecture and its training.These improvements include: Optimizing connection weights and Optimizing network topology.%提出一种对于非线性系统遗传算法的神经网络控制模型,并给出了新的神经网络训练模型.该模型的主要优点是,优化网络连接权重,优化网络拓扑结构.
Nonlinear least squares estimation based on multiple genetic algorithms%基于多群体遗传算法的非线性最小二乘估计
Institute of Scientific and Technical Information of China (English)
刘德玲; 马志强
2011-01-01
Conventional Newton-like algorithms, widely used for parameter estimation of nonlinear models,are sensitive to initial values while simple genetic algorithms are liable to fall into local optimization. This paper proposes a multiple genetic algorithm. It searches the solution with several genetic algorithms and can adjust the parameter domain dynamically according to the optimum solution found by each genetic algorithm with several iterations, for which it can avoid running into local optimization,increase the performance and liability that the solution found is the global optimum solution. Experimental results show that the proposed algorithm is an effective approach of parameter estimations of nonlinear systems.%由于非线性模型参数估计理论广泛使用的传统牛顿类算法对初值的敏感性,以及简单遗传算法易陷入局部最优的问题,提出了一种多群体遗传算法,它采用多个群体执行遗传算法搜索解,并且能根据各个群体在较少迭代次数中找到的最优解动态调整参数域,提高了遗传算法的性能及搜索到的解是全局最优解的可靠性.实验结果表明:新的算法是一种有效的非线性系统模型参数估计方法.
A nonlinear poroelastic model for the periodontal ligament
Favino, Marco; Bourauel, Christoph; Krause, Rolf
2016-05-01
A coupled elastic-poroelastic model for the simulation of the PDL and the adjacent tooth is presented. A poroelastic constitutive material model for the periodontal ligament (PDL) is derived. The solid phase is modeled by means of a Fung material law, accounting for large displacements and strains. Numerical solutions are performed by means of a multigrid Newton method to solve the arising large nonlinear system. Finally, by means of numerical experiments, the biomechanical response of the PDL is studied. In particular, the effect of the hydraulic conductivity and of the mechanical parameters of a Fung potential is investigated in two realistic applications.
Institute of Scientific and Technical Information of China (English)
王秋平; 左玲; 康顺
2011-01-01
为解决非线性部分状态卡尔曼滤波算法中由于线性化误差所导致的滤波精度下降问题,提出采用UT变换方法计算系统状态误差方差,及基于新息自适应调整系统噪声方差,进而构成一种新的非线性自适应部分状态卡尔曼滤波算法,并总结出详细算法结构.同时,将此方法应用到非线性测量光电跟踪系统中,并与U卡尔曼滤波和非线性部分状态卡尔曼滤波进行性能对比.仿真实验结果证明,将UT变换和基于新息自适应调整系统噪声方差方法引入部分状态卡尔曼滤波是有效的,而且其性能明显优于U卡尔曼滤波和非线性部分状态卡尔曼滤波.%In order to solve the problem of accuracy decline caused by the linearization error in nonlinear reduced state Kalman filter, a new nonlinear adaptive reduced state Kalman filter algorithm is provided by using UT transformation to calculate the covariance of the system state error and modify adaptively the system noise covariance based on innovation,and the algorithm structure is summarized in detail. Then, the algorithm is applied in nonlinear measurement electro-optical tracking system and the performances of nonlinear adaptive reduced state Kalman filter were compared with unscented Kalman filter and nonlinear reduced state Kalman filter. The Matlab simulation results show that applying UT transformation and modifying adaptively the system noise covariance based on innovation in reduced state Kalman filter is valid, and the performance outperforms those of the unscented Kalman filter and nonlinear reduced state Kalman filter.
Institute of Scientific and Technical Information of China (English)
李德启; 刘传领
2011-01-01
The structure of high dimensional images with high recognition rate of Viti Levu down the key link, and some of the traditional algorithm to reduce the dimensions of the image processing has yielded some results, but exposed the shortcomings of their own. In order to achieve the high ideals of nonlinear effects of image recognition, dimension reduction in the traditional algorithm analysis and refinement of their advantages, put forward an improved algorithm for nonlinear dimensionality reduction to solve the shortcomings of the traditional algorithm. Respectively, in the ORL and CMU PIE database, the simulation experiment on the image to show that the algorithm for high-dimensional image pattern recognition viability.%对高维非线性结构的图像进行降维是提高识别率的关键环节,而一些传统的算法在对图像进行降维处理过程中虽然取得了一定的成效,但也暴露了它们各自的缺陷.为了达到对高维非线性图像识别的理想效果,在对传统的降维算法分析并对其优势进行提炼的基础上,提出了一种改进的非线性降维算法,解决了传统算法的缺陷,并分别在ORL和CMU PIE数据库图像上进行了仿真实验,从而验证了该算法对高维非线性图像在模式识别上的可行性.
Institute of Scientific and Technical Information of China (English)
程莹; 刘明波
2001-01-01
针对无功优化计算中离散变量和连续变量共存问题，提出用直接非线性原—对偶内点法内嵌罚函数的新算法。通过对几个不同规模试验系统计算分析，并与Tabu搜索法求得的结果比较，证明了该方法是有效的，而且在计算速度、收敛性和优化精度上都优于Tabu搜索法。这使内点法在解决非线性混合整数规划无功优化的有效性和实用性方面更进了一步。%A new algorithm for reactive power optimization problem involving both discrete and continuous variables is presented, which incorporating a penalty function into the nonlinear primal-dual interior point algorithm. By comparing with Tabu search method, the numerical results of several test systems show that the proposed method is effective, and is superior to Tabu search method on side of computation speed, convergence and optimization accuracy. The effectiveness and practicality of the interior point algorithm in solving nonlinear mixed integer programming model of reactive power optimization is improved.
Beck, Christian; E, Weinan; Jentzen, Arnulf
2017-01-01
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio. Moreover, such PDEs are often fully nonlinear due to the need to incorporate certain nonlinear phenomena in the model such as default risks, ...
Liu, C.; Liu, Z.
1993-01-01
The fourth-order finite-difference scheme with fully implicit time-marching presently used to computationally study the spatial instability of planar Poiseuille flow incorporates a novel treatment for outflow boundary conditions that renders the buffer area as short as one wavelength. A semicoarsening multigrid method accelerates convergence for the implicit scheme at each time step; a line-distributive relaxation is developed as a robust fast solver that is efficient for anisotropic grids. Computational cost is no greater than that of explicit schemes, and excellent agreement with linear theory is obtained.
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.
A New Algorithm for Total Variation Based Image Denoising
Institute of Scientific and Technical Information of China (English)
Yi-ping XU
2012-01-01
We propose a new algorithm for the total variation based on image denoising problem.The split Bregman method is used to convert an unconstrained minimization denoising problem to a linear system in the outer iteration.An algebraic multi-grid method is applied to solve the linear system in the inner iteration.Furthermore,Krylov subspace acceleration is adopted to improve convergence in the outer iteration.Numerical experiments demonstrate that this algorithm is efficient even for images with large signal-to-noise ratio.
A multi-level solution algorithm for steady-state Markov chains
Horton, Graham; Leutenegger, Scott T.
1993-01-01
A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.
Institute of Scientific and Technical Information of China (English)
袁晓; 利洁婷; 王世其
2011-01-01
本文针对某公司电力容量扩展问题，采用一元线性回归模型拟合未来10年的需求量，再建立0—1非线性整数规划模型，并将该模型的0—1变量连续化处理，采用遗传算法中的GENOCOP算法求解。%In this paper,the next 10- year demand of a company for power capacity is fitted by monadic linear regression model. A model for 0 - 1 nonlinear integer programming is built, and the 0 - 1 variables of the model are disposed continuously. It is solved by the GENOCOP algorithm of genetic algorithm.
Institute of Scientific and Technical Information of China (English)
宁方立; 董梁; 张文治; 王康
2012-01-01
In order to expand the engineering application area of nonlinear standing waves in acoustic resonators, a new numerical algorithm is proposed for simulating nonlinear standing waves in resonators. It also can be used to overcome the shortages of the existing numerical methods, which restrict the solution to the nonlinear standing waves in cylindrical resonators and exponential resonators. The numerical algorithm is constructed based on the Navier-Stokes equations in the resonators with variable cross-section for an unsteady compressible thermoviscous fluid without truncation, and the space conservation law. The numerical algorithm-finite volume method for solving the nonlinear standing waves in acoustic resonators by piston driving is built based on the semi-implicit method for pressure-linked equations-consistent algorithm and staggered grid technique. Simulations for solving the nonlinear standing waves in cylindrical resonators, exponential resonators and conical resonators are carried out. By comparison with the existing experimental results and numerical simulation results, the accuracy of the developed finite volume algorithm is verified. Some new physical results are obtained, including unsteady velocity, density and temperature. The shock-like pressure wave shapes are found in cylindrical resonators, simultaneously, and the results show that the sharp velocity spikes appear in the cylindrical resonators. High amplitude acoustic pressures are generated in exponential resonators and conical resonators. Shock-like pressure waves and the sharp velocity spikes are not found. The strong dependence of the physical properties of nonlinear standing waves on resonator shape is demonstrated through the simulative results.%为了扩展谐振管内非线性驻波在工程中的应用，以及克服现有数值计算方法仅局限于求解直圆柱形和指数形谐振管内非线性驻波的问题．根据变截面的非稳态可压缩热黏性流体Navier-Stokes方
Mathematical and algorithmic issues in multiphysics coupling.
Energy Technology Data Exchange (ETDEWEB)
Gai, Xiuli (University of Texas at Austin, Austin, TX); Stone, Charles Michael; Wheeler, Mary Fanett (University of Texas at Austin, Austin, TX)
2004-06-01
The modeling of fluid/structure interaction is of growing importance in both energy and environmental applications. Because of the inherent complexity, these problems must be simulated on parallel machines in order to achieve high resolution. The purpose of this research was to investigate techniques for coupling flow and geomechanics in porous media that are suitable for parallel computation. In particular, our main objective was to develop an iterative technique which can be as accurate as a fully coupled model but which allows for robust and efficient coupling of existing complex models (software). A parallel linear elastic module was developed which was coupled to a three phase three-component black oil model in IPARS (Integrated Parallel Accurate Reservoir Simulator). An iterative de-coupling technique was introduced at each time step. The resulting nonlinear iteration involved solving for displacements and flow sequentially. Rock compressibility was used in the flow model to account for the effect of deformation on the pore volume. Convergence was achieved when the mass balance for each component satisfied a given tolerance. This approach was validated by comparison with a fully coupled approach implemented in the British PetroledAmoco ACRES simulator. Another objective of this work was to develop an efficient parallel solver for the elasticity equations. A preconditioned conjugate gradient solver was implemented to solve the algebraic system arising from tensor product linear Galerkin approximations for the displacements. Three preconditioners were developed: LSOR (line successive over-relaxation), block Jacobi, and agglomeration multi-grid. The latter approach involved coarsening the 3D system to 2D and using LSOR as a smoother that is followed by applying geometric multi-grid with SOR (successive over-relaxation) as a smoother. Preliminary tests on a 64-node Beowulf cluster at CSM indicate that the agglomeration multi-grid approach is robust and efficient.
Mathematical and algorithmic issues in multiphysics coupling.
Energy Technology Data Exchange (ETDEWEB)
Gai, Xiuli (University of Texas at Austin, Austin, TX); Stone, Charles Michael; Wheeler, Mary Fanett (University of Texas at Austin, Austin, TX)
2004-06-01
The modeling of fluid/structure interaction is of growing importance in both energy and environmental applications. Because of the inherent complexity, these problems must be simulated on parallel machines in order to achieve high resolution. The purpose of this research was to investigate techniques for coupling flow and geomechanics in porous media that are suitable for parallel computation. In particular, our main objective was to develop an iterative technique which can be as accurate as a fully coupled model but which allows for robust and efficient coupling of existing complex models (software). A parallel linear elastic module was developed which was coupled to a three phase three-component black oil model in IPARS (Integrated Parallel Accurate Reservoir Simulator). An iterative de-coupling technique was introduced at each time step. The resulting nonlinear iteration involved solving for displacements and flow sequentially. Rock compressibility was used in the flow model to account for the effect of deformation on the pore volume. Convergence was achieved when the mass balance for each component satisfied a given tolerance. This approach was validated by comparison with a fully coupled approach implemented in the British PetroledAmoco ACRES simulator. Another objective of this work was to develop an efficient parallel solver for the elasticity equations. A preconditioned conjugate gradient solver was implemented to solve the algebraic system arising from tensor product linear Galerkin approximations for the displacements. Three preconditioners were developed: LSOR (line successive over-relaxation), block Jacobi, and agglomeration multi-grid. The latter approach involved coarsening the 3D system to 2D and using LSOR as a smoother that is followed by applying geometric multi-grid with SOR (successive over-relaxation) as a smoother. Preliminary tests on a 64-node Beowulf cluster at CSM indicate that the agglomeration multi-grid approach is robust and efficient.
Institute of Scientific and Technical Information of China (English)
陈岁生; 卢建刚; 楼晓春
2012-01-01
New localization algorithms for wireless sensor networks which combine multidimensional scal-ing-map (MDS-MAP) and nonlinear filtering were studied to improve the localization accuracy of sensor nodes. According to the nonlinear relationship between the sensor node distances and the node localized coordinates, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) were applied to refine the localized coordinates obtained by the MDS-MAP algorithm. The localization accuracies of these three different localization algorithms, MDS-MAP, MDS-EKF (combination of MDS-MAP and EKF) and MDS-UKF (combination of MDS-MAP and UKF), were compared. Experimental results show that the implementation of nonlinear filtering algorithms (EKF and UKF) can improve the localization accuracy. Under the same conditions, the MDS-UKF localization algorithm achieves the best accuracy and its generated network topology is the closest to the actual network topology.%为提高传感器网络节点的定位精度,对MDS-MAP结合非线性滤波方法的多种传感器网络定位算法进行研究.根据传感器节点间距离与节点定位坐标之间存在的非线性关系,在MDS-MAP定位算法的基础上,引入扩展卡尔曼滤波(EKF)求精算法和不敏卡尔曼滤波(UKF)求精算法,对MDS- MAP求得的节点坐标进行求精.对MDS-MAP定位算法、MDS-MAP和EKF相结合的定位算法(MDS-EKF)、MDS-MAP和UKF相结合的定位算法(MDS-UKF)的定位精度进行比较.实验结果表明:EKF和UKF等非线性滤波方法的应用可以提高定位精度,在相同条件下MDS-UKF定位算法的定位精度更高并且其生成的网络拓扑图最接近于实际网络拓扑图.
Energy Technology Data Exchange (ETDEWEB)
Miettinen, A.; Siikonen, T.
1997-12-31
An implementation of a multigrid technique to solve the pressure correction equation of incompressible flow is described. Two methods, full approximation storage (FAS) and multigrid (MG), were investigated and compared with a single level (SL) iteration technique. Only simple V-cycles were used. The solutions of the equations were always iterated by using the Gauss-Seidel method (GS). The grid of the test problem was 64 x 64, and the problem itself was a pressure correction problem of Driven Cavity Flow at Re=400. The CPU time needed to achieve the machine accuracy of the computer (Indigo 2 Workstation) was measured. The best achieved ratio between MG-GS and SL-GS was 1/145. When using a combination of the FAS technique and fixed V-cycles it was impossible to attain the machine accuracy. To reach the machine accuracy the FAS technique needs sensitive solution cycles, which makes the solver vulnerable. Thus it is recommended to use the MG technique, which can be easily developed after FAS implementation. (orig.) 9 refs.