Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator

International Nuclear Information System (INIS)

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

2010-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Gjesdal, Thor

1997-12-31

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

A parallel version of a multigrid algorithm for isotropic transport equations

International Nuclear Information System (INIS)

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

1994-01-01

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

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

Science.gov (United States)

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

1997-08-01

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

Multigrid methods in structural mechanics

Science.gov (United States)

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

1986-01-01

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

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.

Unweighted least squares phase unwrapping by means of multigrid techniques

Science.gov (United States)

Pritt, Mark D.

1995-11-01

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

Optimal multigrid algorithms for the massive Gaussian model and path integrals

International Nuclear Information System (INIS)

Brandt, A.; Galun, M.

1996-01-01

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

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.

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

Science.gov (United States)

Dinar, N.

1978-01-01

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

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

Science.gov (United States)

1980-10-01

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

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

NARCIS (Netherlands)

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

2012-01-01

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

Progress with multigrid schemes for hypersonic flow problems

International Nuclear Information System (INIS)

Radespiel, R.; Swanson, R.C.

1995-01-01

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

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

Science.gov (United States)

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

2003-02-01

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

Self-correcting Multigrid Solver

International Nuclear Information System (INIS)

Lewandowski, Jerome L.V.

2004-01-01

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

Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

International Nuclear Information System (INIS)

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

2010-01-01

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

Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

International Nuclear Information System (INIS)

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

2013-01-01

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

Extending the applicability of multigrid methods

International Nuclear Information System (INIS)

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

2006-01-01

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

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

International Nuclear Information System (INIS)

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

1986-11-01

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

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

KAUST Repository

Bonito, Andrea

2012-09-01

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

Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

KAUST Repository

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

2010-01-01

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

Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

KAUST Repository

Adams, Mark F.

2010-09-01

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

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

KAUST Repository

Bonito, Andrea; Pasciak, Joseph E.

2013-01-01

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

Segmental Refinement: A Multigrid Technique for Data Locality

KAUST Repository

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

2016-01-01

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

Segmental Refinement: A Multigrid Technique for Data Locality

KAUST Repository

Adams, Mark F.

2016-08-04

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

Multigrid

CERN Document Server

Trottenberg, Ulrich; Schuller, Anton

2000-01-01

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

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

Science.gov (United States)

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

2018-04-01

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

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.

Multigrid treatment of implicit continuum diffusion

Science.gov (United States)

Francisquez, Manaure; Zhu, Ben; Rogers, Barrett

2017-10-01

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

Multigrid Methods for the Computation of Propagators in Gauge Fields

Science.gov (United States)

Kalkreuter, Thomas

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

New multigrid solver advances in TOPS

International Nuclear Information System (INIS)

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

2005-01-01

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

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

International Nuclear Information System (INIS)

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

1987-01-01

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

Preisach hysteresis model for non-linear 2D heat diffusion

International Nuclear Information System (INIS)

Jancskar, Ildiko; Ivanyi, Amalia

2006-01-01

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

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

International Nuclear Information System (INIS)

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

1998-01-01

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

Efficient multigrid computation of steady hypersonic flows

NARCIS (Netherlands)

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

1991-01-01

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

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

Science.gov (United States)

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

1999-01-01

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

Multigrid for Staggered Lattice Fermions

Energy Technology Data Exchange (ETDEWEB)

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

2018-01-23

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

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

Science.gov (United States)

Kifonidis, K.; Müller, E.

2012-08-01

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

Multigrid methods for the computation of propagators in gauge fields

International Nuclear Information System (INIS)

Kalkreuter, T.

1992-11-01

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

Investigations on application of multigrid method to MHD equilibrium analysis

International Nuclear Information System (INIS)

Ikuno, Soichiro

2000-01-01

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

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

International Nuclear Information System (INIS)

Kalkreuter, T.

1991-09-01

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

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.

Analysis and development of stochastic multigrid methods in lattice field theory

International Nuclear Information System (INIS)

Grabenstein, M.

1994-01-01

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

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

International Nuclear Information System (INIS)

Lewandowski, J.L.V.

2003-01-01

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

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

International Nuclear Information System (INIS)

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

2003-01-01

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

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

Science.gov (United States)

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

2003-07-01

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

Multigrid Computation of Stratified Flow over Two-Dimensional Obstacles

Science.gov (United States)

Paisley, M. F.

1997-09-01

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

Multigrid methods III

CERN Document Server

Trottenberg, U; Third European Conference on Multigrid Methods

1991-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

NONE

1995-12-31

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

Multicloud: Multigrid convergence with a meshless operator

International Nuclear Information System (INIS)

Katz, Aaron; Jameson, Antony

2009-01-01

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

Multigrid and defect correction for the steady Navier-Stokes equations

NARCIS (Netherlands)

Koren, B.

1990-01-01

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

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

International Nuclear Information System (INIS)

Edwards, J.R.

1996-01-01

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

Multigrid methods for fully implicit oil reservoir simulation

Energy Technology Data Exchange (ETDEWEB)

Molenaar, J.

1995-12-31

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

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

Science.gov (United States)

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

1993-01-01

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

Nonlinear multigrid solvers exploiting AMGe coarse spaces with approximation properties

DEFF Research Database (Denmark)

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

2017-01-01

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

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

Science.gov (United States)

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

2001-07-01

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

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

Science.gov (United States)

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

2001-08-01

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

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

Science.gov (United States)

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

2017-07-01

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

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

NARCIS (Netherlands)

Koren, B.

1991-01-01

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

Toward robust scalable algebraic multigrid solvers

International Nuclear Information System (INIS)

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

2010-01-01

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

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.

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.

Algorithms For Integrating Nonlinear Differential Equations

Science.gov (United States)

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

1994-01-01

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

The multigrid preconditioned conjugate gradient method

Science.gov (United States)

Tatebe, Osamu

1993-01-01

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

Conjugate gradient coupled with multigrid for an indefinite problem

Science.gov (United States)

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

1984-01-01

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

An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems

Science.gov (United States)

Deng, Qingping

1996-01-01

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

Improved algorithm for solving nonlinear parabolized stability equations

International Nuclear Information System (INIS)

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

2016-01-01

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

Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library

Energy Technology Data Exchange (ETDEWEB)

2017-10-24

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

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

NARCIS (Netherlands)

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

2005-01-01

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

Improved algorithm for solving nonlinear parabolized stability equations

Science.gov (United States)

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

2016-08-01

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

Multi-grid and ICCG for problems with interfaces

International Nuclear Information System (INIS)

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

1980-01-01

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

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.

Achieving Textbook Multigrid Efficiency for Hydrostatic Ice Sheet Flow

KAUST Repository

Brown, Jed; Smith, Barry; Ahmadia, Aron

2013-01-01

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

Achieving Textbook Multigrid Efficiency for Hydrostatic Ice Sheet Flow

KAUST Repository

Brown, Jed

2013-03-12

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-06-30

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

Algorithms for non-linear M-estimation

DEFF Research Database (Denmark)

Madsen, Kaj; Edlund, O; Ekblom, H

1997-01-01

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

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

Directory of Open Access Journals (Sweden)

Fabio Henrique Pereira

2009-01-01

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

A Parallel Algebraic Multigrid Solver on Graphics Processing Units

KAUST Repository

Haase, Gundolf

2010-01-01

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

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

African Journals Online (AJOL)

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

Totally parallel multilevel algorithms

Science.gov (United States)

Frederickson, Paul O.

1988-01-01

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

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

Science.gov (United States)

Zhang, H.; Tian, X.

2017-12-01

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

Applications and algorithms for mixed integer nonlinear programming

International Nuclear Information System (INIS)

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

2009-01-01

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

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

International Nuclear Information System (INIS)

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

2013-01-01

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

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

Science.gov (United States)

Lavery, N.; Taylor, C.

1999-07-01

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

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

International Nuclear Information System (INIS)

Grassi, G.

2006-01-01

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

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.

Nonlinear Multigrid for Reservoir Simulation

DEFF Research Database (Denmark)

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

2016-01-01

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

Layout optimization with algebraic multigrid methods

Science.gov (United States)

Regler, Hans; Ruede, Ulrich

1993-01-01

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

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

Directory of Open Access Journals (Sweden)

A.D. Matveev

2016-12-01

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

A Critical Study of Agglomerated Multigrid Methods for Diffusion

Science.gov (United States)

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

2011-01-01

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

Combined algorithms in nonlinear problems of magnetostatics

International Nuclear Information System (INIS)

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

1988-01-01

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

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

International Nuclear Information System (INIS)

Manteuffel, T.

1994-12-01

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

Concise quantum associative memories with nonlinear search algorithm

International Nuclear Information System (INIS)

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

2016-01-01

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

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

International Nuclear Information System (INIS)

Belliard, M.; Grandotto, M.

2003-01-01

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

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.

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

KAUST Repository

Chen, Yujia

2015-01-01

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

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

Science.gov (United States)

Brædstrup, Christian; Egholm, David

2013-04-01

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

The Mixed Finite Element Multigrid Method for Stokes Equations

Science.gov (United States)

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

2015-01-01

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

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

Science.gov (United States)

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

2005-01-01

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

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.

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

NARCIS (Netherlands)

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

2017-01-01

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

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

International Nuclear Information System (INIS)

Barbie, L.

2013-01-01

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

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.

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.

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

Science.gov (United States)

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

2017-03-01

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

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

International Nuclear Information System (INIS)

Baker, K.L.

2005-01-01

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

New preconditioned conjugate gradient algorithms for nonlinear unconstrained optimization problems

International Nuclear Information System (INIS)

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

1997-01-01

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

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.

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.

Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation

KAUST Repository

Chen, Meng-Huo

2015-09-13

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

Nonlinear model predictive control theory and algorithms

CERN Document Server

Grüne, Lars

2017-01-01

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

Multigrid Methods for EHL Problems

Science.gov (United States)

Nurgat, Elyas; Berzins, Martin

1996-01-01

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

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

International Nuclear Information System (INIS)

Du, Hongchu

2015-01-01

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

A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem

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Mio Horai

2016-01-01

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

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

Science.gov (United States)

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

2017-01-01

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

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

Science.gov (United States)

Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger

2016-11-01

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

Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

Science.gov (United States)

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

2018-01-01

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

Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

Directory of Open Access Journals (Sweden)

Azmat Ullah

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

Iterative Nonlinear Tikhonov Algorithm with Constraints for Electromagnetic Tomography

Science.gov (United States)

Xu, Feng; Deshpande, Manohar

2012-01-01

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

Sparse Nonlinear Electromagnetic Imaging Accelerated With Projected Steepest Descent Algorithm

KAUST Repository

Desmal, Abdulla

2017-04-03

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

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

Science.gov (United States)

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

2017-09-01

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

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

KAUST Repository

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

2012-01-01

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

Flaw characterization through nonlinear ultrasonics and wavelet cross-correlation algorithms

Science.gov (United States)

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

2018-04-01

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

Multiscale Monte Carlo algorithms in statistical mechanics and quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Lauwers, P G

1990-12-01

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

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

Directory of Open Access Journals (Sweden)

Agarwal RaviP

2009-01-01

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

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.

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

Directory of Open Access Journals (Sweden)

Kelin Zhuang

2017-01-01

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

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

Science.gov (United States)

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

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

Multigrid solution of diffusion equations on distributed memory multiprocessor systems

International Nuclear Information System (INIS)

Finnemann, H.

1988-01-01

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

Experiences using multigrid for geothermal simulation

Energy Technology Data Exchange (ETDEWEB)

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

1995-03-01

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

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

Science.gov (United States)

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

2017-10-01

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

An efficient flexible-order model for 3D nonlinear water waves

Science.gov (United States)

Engsig-Karup, A. P.; Bingham, H. B.; Lindberg, O.

2009-04-01

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.

An efficient flexible-order model for 3D nonlinear water waves

International Nuclear Information System (INIS)

Engsig-Karup, A.P.; Bingham, H.B.; Lindberg, O.

2009-01-01

The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature

A quasi-Newton algorithm for large-scale nonlinear equations

Directory of Open Access Journals (Sweden)

Linghua Huang

2017-02-01

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

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

Science.gov (United States)

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

2018-03-01

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

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

Science.gov (United States)

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

2017-11-07

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

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

Directory of Open Access Journals (Sweden)

Tianzhu Yi

2017-11-01

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

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

International Nuclear Information System (INIS)

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

1977-01-01

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

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

Science.gov (United States)

Bouchard, M

2001-01-01

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

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

International Nuclear Information System (INIS)

Vadlamani, Srinath; Kruger, Scott; Austin, Travis

2008-01-01

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

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

Directory of Open Access Journals (Sweden)

Koh Kim Jie

2017-01-01

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

Accelerating Lattice QCD Multigrid on GPUs Using Fine-Grained Parallelization

Energy Technology Data Exchange (ETDEWEB)

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

2016-12-22

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

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

International Nuclear Information System (INIS)

McCormick, Stephen F.

2016-01-01

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

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/.

Neural multigrid for gauge theories and other disordered systems

International Nuclear Information System (INIS)

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

1992-09-01

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

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

Science.gov (United States)

Telban, Robert J.

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

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

NARCIS (Netherlands)

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

2006-01-01

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

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.

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

Science.gov (United States)

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

1992-01-01

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

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.

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

NARCIS (Netherlands)

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

2008-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-08-14

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

The multigrid method for reactor calculations

International Nuclear Information System (INIS)

Douglas, S.R.

1991-07-01

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

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

Science.gov (United States)

Mizutani, Eiji; Demmel, James W

2003-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-04-02

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

An efficient control algorithm for nonlinear systems

International Nuclear Information System (INIS)

Sinha, S.

1990-12-01

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

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

Directory of Open Access Journals (Sweden)

Y. W. Sun

2013-08-01

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

Genetic algorithms applied to nonlinear and complex domains

International Nuclear Information System (INIS)

Barash, D; Woodin, A E

1999-01-01

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

Algorithms of estimation for nonlinear systems a differential and algebraic viewpoint

CERN Document Server

Martínez-Guerra, Rafael

2017-01-01

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

Multigrid methods for S/sub N/ problems

International Nuclear Information System (INIS)

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

1987-01-01

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

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

KAUST Repository

Domínguez, Luis F.

2012-06-25

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

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

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

NARCIS (Netherlands)

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

2017-01-01

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

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

International Nuclear Information System (INIS)

Li, X.; Sokal, A.D.

1991-01-01

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

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

Directory of Open Access Journals (Sweden)

Hui Huang

2017-01-01

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

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

Directory of Open Access Journals (Sweden)

Ronghui Zhang

2017-05-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-12-20

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

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.

On multigrid-CG for efficient topology optimization

DEFF Research Database (Denmark)

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

2014-01-01

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

A chaos-based evolutionary algorithm for general nonlinear programming problems

International Nuclear Information System (INIS)

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

2016-01-01

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

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

Science.gov (United States)

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

2008-03-01

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

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

International Nuclear Information System (INIS)

Huang, Xiaobiao; Safranek, James

2014-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2014-09-01

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

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

International Nuclear Information System (INIS)

Mesgarani, H; Parmour, P; Aghazadeh, N

2010-01-01

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

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

Directory of Open Access Journals (Sweden)

Dah-Jing Jwo

2013-05-01

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

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

Directory of Open Access Journals (Sweden)

S. I. Samsudin

2014-01-01

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

Morphing Wing Structural Optimization Using Opposite-Based Population-Based Incremental Learning and Multigrid Ground Elements

Directory of Open Access Journals (Sweden)

S. Sleesongsom

2015-01-01

Full Text Available This paper has twin aims. Firstly, a multigrid design approach for optimization of an unconventional morphing wing is proposed. The structural design problem is assigned to optimize wing mass, lift effectiveness, and buckling factor subject to structural safety requirements. Design variables consist of partial topology, nodal positions, and component sizes of a wing internal structure. Such a design process can be accomplished by using multiple resolutions of ground elements, which is called a multigrid approach. Secondly, an opposite-based multiobjective population-based incremental learning (OMPBIL is proposed for comparison with the original multiobjective population-based incremental learning (MPBIL. Multiobjective design problems with single-grid and multigrid design variables are then posed and tackled by OMPBIL and MPBIL. The results show that using OMPBIL in combination with a multigrid design approach is the best design strategy. OMPBIL is superior to MPBIL since the former provides better population diversity. Aeroelastic trim for an elastic morphing wing is also presented.

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

Science.gov (United States)

Hu, Yi-Chung

2014-01-01

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

Advanced Algebraic Multigrid Solvers for Subsurface Flow Simulation

KAUST Repository

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

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

Qiang Zhang

2017-09-01

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

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

International Nuclear Information System (INIS)

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

2007-01-01

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

Genetic algorithms applied to nonlinear and complex domains; TOPICAL

International Nuclear Information System (INIS)

Barash, D; Woodin, A E

1999-01-01

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

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

DEFF Research Database (Denmark)

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

2015-01-01

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

Bonus algorithm for large scale stochastic nonlinear programming problems

CERN Document Server

Diwekar, Urmila

2015-01-01

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

Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

Science.gov (United States)

Atkins, H. L.; Helenbrook, B. T.

2005-01-01

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

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

KAUST Repository

Fsheikh, Ahmed H.

2013-01-01

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

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

Institute of Scientific and Technical Information of China (English)

WANG; Shunjin; ZHANG; Hua

2006-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1993-12-31

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

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

International Nuclear Information System (INIS)

Gutbrod, F.

1992-12-01

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

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

International Nuclear Information System (INIS)

Gu Lizhen; Bao Weizhu

1992-01-01

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

A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition

OpenAIRE

De Sterck, Hans

2011-01-01

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

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

Directory of Open Access Journals (Sweden)

Felix Fritzen

2018-02-01

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

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

Science.gov (United States)

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

2018-01-01

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

Efficient relaxed-Jacobi smoothers for multigrid on parallel computers

Science.gov (United States)

Yang, Xiang; Mittal, Rajat

2017-03-01

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

Analysis of multigrid methods on massively parallel computers: Architectural implications

Science.gov (United States)

Matheson, Lesley R.; Tarjan, Robert E.

1993-01-01

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

Fast algorithms for transport models. Final report

International Nuclear Information System (INIS)

Manteuffel, T.A.

1994-01-01

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

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

Science.gov (United States)

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

2018-06-01

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

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

International Nuclear Information System (INIS)

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

1991-07-01

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

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.

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.

Data Reduction Algorithm Using Nonnegative Matrix Factorization with Nonlinear Constraints

Science.gov (United States)

Sembiring, Pasukat

2017-12-01

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

A Line Search Multilevel Truncated Newton Algorithm for Computing the Optical Flow

Directory of Open Access Journals (Sweden)

Lluís Garrido

2015-06-01

Full Text Available We describe the implementation details and give the experimental results of three optimization algorithms for dense optical flow computation. In particular, using a line search strategy, we evaluate the performance of the unilevel truncated Newton method (LSTN, a multiresolution truncated Newton (MR/LSTN and a full multigrid truncated Newton (FMG/LSTN. We use three image sequences and four models of optical flow for performance evaluation. The FMG/LSTN algorithm is shown to lead to better optical flow estimation with less computational work than both the LSTN and MR/LSTN algorithms.

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

Directory of Open Access Journals (Sweden)

Er Gao

2012-01-01

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

Algorithms for adaptive nonlinear pattern recognition

Science.gov (United States)

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

2011-09-01

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

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.

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

International Nuclear Information System (INIS)

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

1995-07-01

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

Multigrid time-accurate integration of Navier-Stokes equations

Science.gov (United States)

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

1993-01-01

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

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

Institute of Scientific and Technical Information of China (English)

2008-01-01

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

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

Science.gov (United States)

Hano, Mitsuo; Hotta, Masashi

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

Primal-Dual Interior Point Multigrid Method for Topology Optimization

Czech Academy of Sciences Publication Activity Database

Kočvara, Michal; Mohammed, S.

2016-01-01

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

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

Science.gov (United States)

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

2017-04-01

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

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

Science.gov (United States)

Xia, Youshen; Kamel, Mohamed S

2007-06-01

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

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

Science.gov (United States)

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

2012-05-01

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

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

Science.gov (United States)

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

2017-12-01

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

Efficiency Analysis of the Parallel Implementation of the SIMPLE Algorithm on Multiprocessor Computers

Science.gov (United States)

Lashkin, S. V.; Kozelkov, A. S.; Yalozo, A. V.; Gerasimov, V. Yu.; Zelensky, D. K.

2017-12-01

This paper describes the details of the parallel implementation of the SIMPLE algorithm for numerical solution of the Navier-Stokes system of equations on arbitrary unstructured grids. The iteration schemes for the serial and parallel versions of the SIMPLE algorithm are implemented. In the description of the parallel implementation, special attention is paid to computational data exchange among processors under the condition of the grid model decomposition using fictitious cells. We discuss the specific features for the storage of distributed matrices and implementation of vector-matrix operations in parallel mode. It is shown that the proposed way of matrix storage reduces the number of interprocessor exchanges. A series of numerical experiments illustrates the effect of the multigrid SLAE solver tuning on the general efficiency of the algorithm; the tuning involves the types of the cycles used (V, W, and F), the number of iterations of a smoothing operator, and the number of cells for coarsening. Two ways (direct and indirect) of efficiency evaluation for parallelization of the numerical algorithm are demonstrated. The paper presents the results of solving some internal and external flow problems with the evaluation of parallelization efficiency by two algorithms. It is shown that the proposed parallel implementation enables efficient computations for the problems on a thousand processors. Based on the results obtained, some general recommendations are made for the optimal tuning of the multigrid solver, as well as for selecting the optimal number of cells per processor.

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

Science.gov (United States)

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

2016-01-01

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

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

Directory of Open Access Journals (Sweden)

H. Vazquez-Leal

2014-01-01

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

A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids

Science.gov (United States)

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

2001-01-01

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

A conservative Fourier pseudospectral algorithm for a coupled nonlinear Schrödinger system

International Nuclear Information System (INIS)

Cai Jia-Xiang; Wang Yu-Shun

2013-01-01

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

An algorithm for nonlinear thermal analysis of fuel bearing pads

International Nuclear Information System (INIS)

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

1983-01-01

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

Nonlinear acceleration of transport criticality problems

International Nuclear Information System (INIS)

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

2011-01-01

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

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

International Nuclear Information System (INIS)

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

1998-01-01

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

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.

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

International Nuclear Information System (INIS)

Sockol, Peter M.

2003-01-01

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

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

NARCIS (Netherlands)

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

2002-01-01

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

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

Data.gov (United States)

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

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

Science.gov (United States)

Kazemi, Mahdi; Arefi, Mohammad Mehdi

2017-03-01

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

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

Science.gov (United States)

Milic, Vladimir; Kasac, Josip; Novakovic, Branko

2015-10-01

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

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

International Nuclear Information System (INIS)

Normolle, D.P.

1993-01-01

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

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

Science.gov (United States)

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

2018-01-01

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

Conservative multigrid methods for Cahn-Hilliard fluids

International Nuclear Information System (INIS)

Kim, Junseok; Kang, Kyungkeun; Lowengrub, John

2004-01-01

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

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

NARCIS (Netherlands)

Koren, B.; Leer, van B.

1995-01-01

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

Nonlinear evolution of f(R) cosmologies. I. Methodology

International Nuclear Information System (INIS)

Oyaizu, Hiroaki

2008-01-01

We introduce the method and the implementation of a cosmological simulation of a class of metric-variation f(R) models that accelerate the cosmological expansion without a cosmological constant and evade solar-system bounds of small-field deviations to general relativity. Such simulations are shown to reduce to solving a nonlinear Poisson equation for the scalar degree of freedom introduced by the f(R) modifications. We detail the method to efficiently solve the nonlinear Poisson equation by using a Newton-Gauss-Seidel relaxation scheme coupled with the multigrid method to accelerate the convergence. The simulations are shown to satisfy tests comparing the simulated outcome to analytical solutions for simple situations, and the dynamics of the simulations are tested with orbital and Zeldovich collapse tests. Finally, we present several static and dynamical simulations using realistic cosmological parameters to highlight the differences between standard physics and f(R) physics. In general, we find that the f(R) modifications result in stronger gravitational attraction that enhances the dark matter power spectrum by ∼20% for large but observationally allowed f(R) modifications. A more detailed study of the nonlinear f(R) effects on the power spectrum are presented in a companion paper.

Compiler generation and autotuning of communication-avoiding operators for geometric multigrid

Energy Technology Data Exchange (ETDEWEB)

Basu, Protonu [Univ. of Utah, Salt Lake City, UT (United States); Venkat, Anand [Univ. of Utah, Salt Lake City, UT (United States); Hall, Mary [Univ. of Utah, Salt Lake City, UT (United States); Williams, Samuel [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Van Straalen, Brian [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Oliker, Leonid [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

2014-04-17

This paper describes a compiler approach to introducing communication-avoiding optimizations in geometric multigrid (GMG), one of the most popular methods for solving partial differential equations. Communication-avoiding optimizations reduce vertical communication through the memory hierarchy and horizontal communication across processes or threads, usually at the expense of introducing redundant computation. We focus on applying these optimizations to the smooth operator, which successively reduces the error and accounts for the largest fraction of the GMG execution time. Our compiler technology applies both novel and known transformations to derive an implementation comparable to manually-tuned code. To make the approach portable, an underlying autotuning system explores the tradeoff between reduced communication and increased computation, as well as tradeoffs in threading schemes, to automatically identify the best implementation for a particular architecture and at each computation phase. Results show that we are able to quadruple the performance of the smooth operation on the finest grids while attaining performance within 94% of manually-tuned code. Overall we improve the overall multigrid solve time by 2.5× without sacrificing programer productivity.

Cellular Automaton Modeling of Dendritic Growth Using a Multi-grid Method

International Nuclear Information System (INIS)

Natsume, Y; Ohsasa, K

2015-01-01

A two-dimensional cellular automaton model with a multi-grid method was developed to simulate dendritic growth. In the present model, we used a triple-grid system for temperature, solute concentration and solid fraction fields as a new approach of the multi-grid method. In order to evaluate the validity of the present model, we carried out simulations of single dendritic growth, secondary dendrite arm growth, multi-columnar dendritic growth and multi-equiaxed dendritic growth. From the results of the grid dependency from the simulation of single dendritic growth, we confirmed that the larger grid can be used in the simulation and that the computational time can be reduced dramatically. In the simulation of secondary dendrite arm growth, the results from the present model were in good agreement with the experimental data and the simulated results from a phase-field model. Thus, the present model can quantitatively simulate dendritic growth. From the simulated results of multi-columnar and multi-equiaxed dendrites, we confirmed that the present model can perform simulations under practical solidification conditions. (paper)

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

Czech Academy of Sciences Publication Activity Database

Kočvara, Michal; Mohammed, S.

2016-01-01

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

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

Science.gov (United States)

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

2017-12-01

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

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

International Nuclear Information System (INIS)

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

2012-01-01

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

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

Directory of Open Access Journals (Sweden)

Zongyan Li

2016-01-01

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

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2017-07-09

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

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

OpenAIRE

Gao, Er; Song, Songhe; Zhang, Xinjian

2012-01-01

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

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

Science.gov (United States)

Codd, A. L.; Gross, L.

2018-03-01

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

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

Science.gov (United States)

Bandyopadhyay, Saptarshi

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

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

NARCIS (Netherlands)

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

2018-01-01

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

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

DEFF Research Database (Denmark)

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

2013-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1999-08-01

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

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

Directory of Open Access Journals (Sweden)

Zhong Jin

2012-01-01

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

Identification of time-varying nonlinear systems using differential evolution algorithm

DEFF Research Database (Denmark)

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

2013-01-01

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

Fast algorithms for chiral fermions in 2 dimensions

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Hyka (Xhako Dafina

2018-01-01

Full Text Available In lattice QCD simulations the formulation of the theory in lattice should be chiral in order that symmetry breaking happens dynamically from interactions. In order to guarantee this symmetry on the lattice one uses overlap and domain wall fermions. On the other hand high computational cost of lattice QCD simulations with overlap or domain wall fermions remains a major obstacle of research in the field of elementary particles. We have developed the preconditioned GMRESR algorithm as fast inverting algorithm for chiral fermions in U(1 lattice gauge theory. In this algorithm we used the geometric multigrid idea along the extra dimension.The main result of this work is that the preconditioned GMRESR is capable to accelerate the convergence 2 to 12 times faster than the other optimal algorithms (SHUMR for different coupling constant and lattice 32x32. Also, in this paper we tested it for larger lattice size 64x64. From the results of simulations we can see that our algorithm is faster than SHUMR. This is a very promising result that this algorithm can be adapted also in 4 dimension.

Scalable multi-grid preconditioning techniques for the even-parity S_N solver in UNIC

International Nuclear Information System (INIS)

Mahadevan, Vijay S.; Smith, Michael A.

2011-01-01

The Even-parity neutron transport equation with FE-S_N discretization is solved traditionally using SOR preconditioned CG method at the lowest level of iterations in order to compute the criticality in reactor analysis problems. The use of high order isoparametric finite elements prohibits the formation of the discrete operator explicitly due to memory constraints in peta scale architectures. Hence, a h-p multi-grid preconditioner based on linear tessellation of the higher order mesh is introduced here for the space-angle system and compared against SOR and Algebraic MG black-box solvers. The performance and scalability of the multi-grid scheme was determined for two test problems and found to be competitive in terms of both computational time and memory requirements. The implementation of this preconditioner in an even-parity solver like UNIC from ANL can further enable high fidelity calculations in a scalable manner on peta flop machines. (author)

A Trust-region-based Sequential Quadratic Programming Algorithm

DEFF Research Database (Denmark)

Henriksen, Lars Christian; Poulsen, Niels Kjølstad

This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints.......This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....

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

Science.gov (United States)

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

2006-01-01

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

Multigrid techniques with non-standard coarsening and group relaxation methods

International Nuclear Information System (INIS)

Danaee, A.

1989-06-01

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

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

International Nuclear Information System (INIS)

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

2006-01-01

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

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

Science.gov (United States)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

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

CERN Document Server

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

2003-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2013-11-07

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

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

Directory of Open Access Journals (Sweden)

Marwa Jouini

2017-01-01

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

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.

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

Science.gov (United States)

Wang, Xiaogang; Chen, Wen; Chen, Xudong

2014-09-22

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

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

Directory of Open Access Journals (Sweden)

Afnizanfaizal Abdullah

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

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

Science.gov (United States)

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

2013-01-01

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

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

KAUST Repository

Dreano, Denis

2017-04-05

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

Modeling of frequency-domain scalar wave equation with the average-derivative optimal scheme based on a multigrid-preconditioned iterative solver

Science.gov (United States)

Cao, Jian; Chen, Jing-Bo; Dai, Meng-Xue

2018-01-01

An efficient finite-difference frequency-domain modeling of seismic wave propagation relies on the discrete schemes and appropriate solving methods. The average-derivative optimal scheme for the scalar wave modeling is advantageous in terms of the storage saving for the system of linear equations and the flexibility for arbitrary directional sampling intervals. However, using a LU-decomposition-based direct solver to solve its resulting system of linear equations is very costly for both memory and computational requirements. To address this issue, we consider establishing a multigrid-preconditioned BI-CGSTAB iterative solver fit for the average-derivative optimal scheme. The choice of preconditioning matrix and its corresponding multigrid components is made with the help of Fourier spectral analysis and local mode analysis, respectively, which is important for the convergence. Furthermore, we find that for the computation with unequal directional sampling interval, the anisotropic smoothing in the multigrid precondition may affect the convergence rate of this iterative solver. Successful numerical applications of this iterative solver for the homogenous and heterogeneous models in 2D and 3D are presented where the significant reduction of computer memory and the improvement of computational efficiency are demonstrated by comparison with the direct solver. In the numerical experiments, we also show that the unequal directional sampling interval will weaken the advantage of this multigrid-preconditioned iterative solver in the computing speed or, even worse, could reduce its accuracy in some cases, which implies the need for a reasonable control of directional sampling interval in the discretization.

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

Science.gov (United States)

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

2015-11-01

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

Angular Multigrid Preconditioner for Krylov-Based Solution Techniques Applied to the Sn Equations with Highly Forward-Peaked Scattering

Science.gov (United States)

Turcksin, Bruno; Ragusa, Jean C.; Morel, Jim E.

2012-01-01

It is well known that the diffusion synthetic acceleration (DSA) methods for the Sn equations become ineffective in the Fokker-Planck forward-peaked scattering limit. In response to this deficiency, Morel and Manteuffel (1991) developed an angular multigrid method for the 1-D Sn equations. This method is very effective, costing roughly twice as much as DSA per source iteration, and yielding a maximum spectral radius of approximately 0.6 in the Fokker-Planck limit. Pautz, Adams, and Morel (PAM) (1999) later generalized the angular multigrid to 2-D, but it was found that the method was unstable with sufficiently forward-peaked mappings between the angular grids. The method was stabilized via a filtering technique based on diffusion operators, but this filtering also degraded the effectiveness of the overall scheme. The spectral radius was not bounded away from unity in the Fokker-Planck limit, although the method remained more effective than DSA. The purpose of this article is to recast the multidimensional PAM angular multigrid method without the filtering as an Sn preconditioner and use it in conjunction with the Generalized Minimal RESidual (GMRES) Krylov method. The approach ensures stability and our computational results demonstrate that it is also significantly more efficient than an analogous DSA-preconditioned Krylov method.

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

Directory of Open Access Journals (Sweden)

A. Averbuch

1994-01-01

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

FINAL REPORT (MILESTONE DATE 9/30/11) FOR SUBCONTRACT NO. B594099 NUMERICAL METHODS FOR LARGE-SCALE DATA FACTORIZATION

Energy Technology Data Exchange (ETDEWEB)

De Sterck, H

2011-10-18

The following work has been performed by PI Hans De Sterck and graduate student Manda Winlaw for the required tasks 1-5 (as listed in the Statement of Work). Graduate student Manda Winlaw has visited LLNL January 31-March 11, 2011 and May 23-August 19, 2010, working with Van Henson and Mike O'Hara on non-negative matrix factorizations (NMF). She has investigated the dense subgraph clustering algorithm from 'Finding Dense Subgraphs for Sparse Undirected, Directed, and Bipartite Graphs' by Chen and Saad, testing this method on several term-document matrices and adapting it to cluster based on the rank of the subgraphs instead of the density. Manda Winlaw was awarded a first prize in the annual LLNL summer student poster competition for a poster on her NMF research. PI Hans De Sterck has developed a new adaptive algebraic multigrid algorithm for computing a few dominant or minimal singular triplets of sparse rectangular matrices. This work builds on adaptive algebraic multigrid methods that were further developed by the PI and collaborators (including Sanders and Henson) for Markov chains. The method also combines and extends existing multigrid algorithms for the symmetric eigenproblem. The PI has visited LLNL February 22-25, 2011, and has given a CASC seminar 'Algebraic Multigrid for the Singular Value Problem' on this work on February 23, 2011. During his visit, he has discussed this work and related topics with Van Henson, Geoffrey Sanders, Panayot Vassilevski, and others. He has tested the algorithm on PDE matrices and on a term-document matrix, with promising initial results. Manda Winlaw has also started to work, with O'Hara, on estimating probability distributions over undirected graph edges. The goal is to estimate probabilistic models from sets of undirected graph edges for the purpose of prediction, anomaly detection and support to supervised learning. Graduate student Manda Winlaw is writing a paper on the results obtained with

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

DEFF Research Database (Denmark)

Delbary, Fabrice; Knudsen, Kim

2014-01-01

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

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

Science.gov (United States)

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

2016-06-17

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

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

Science.gov (United States)

Cavaglieri, Daniele; Bewley, Thomas; Mashayek, Ali

2015-11-01

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

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

International Nuclear Information System (INIS)

Kotiluoto, P.

2007-05-01

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

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

Science.gov (United States)

Wu, Huai-Ning; Luo, Biao

2012-12-01

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

{sup 10}B multi-grid proportional gas counters for large area thermal neutron detectors

Energy Technology Data Exchange (ETDEWEB)

Andersen, K. [ESS, P.O. Box 176, SE-221 00 Lund (Sweden); Bigault, T. [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); Birch, J. [Linköping University, SE-581, 83 Linköping (Sweden); Buffet, J. C.; Correa, J. [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); Hall-Wilton, R. [ESS, P.O. Box 176, SE-221 00 Lund (Sweden); Hultman, L. [Linköping University, SE-581, 83 Linköping (Sweden); Höglund, C. [ESS, P.O. Box 176, SE-221 00 Lund (Sweden); Linköping University, SE-581, 83 Linköping (Sweden); Guérard, B., E-mail: guerard@ill.fr [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); Jensen, J. [Linköping University, SE-581, 83 Linköping (Sweden); Khaplanov, A. [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); ESS, P.O. Box 176, SE-221 00 Lund (Sweden); Kirstein, O. [Linköping University, SE-581, 83 Linköping (Sweden); Piscitelli, F.; Van Esch, P. [ILL, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9 (France); Vettier, C. [ESS, P.O. Box 176, SE-221 00 Lund (Sweden)

2013-08-21

{sup 3}He was a popular material in neutrons detectors until its availability dropped drastically in 2008. The development of techniques based on alternative convertors is now of high priority for neutron research institutes. Thin films of {sup 10}B or {sup 10}B{sub 4}C have been used in gas proportional counters to detect neutrons, but until now, only for small or medium sensitive area. We present here the multi-grid design, introduced at the ILL and developed in collaboration with ESS for LAN (large area neutron) detectors. Typically thirty {sup 10}B{sub 4}C films of 1 μm thickness are used to convert neutrons into ionizing particles which are subsequently detected in a proportional gas counter. The principle and the fabrication of the multi-grid are described and some preliminary results obtained with a prototype of 200 cm×8 cm are reported; a detection efficiency of 48% has been measured at 2.5 Å with a monochromatic neutron beam line, showing the good potential of this new technique.

On the multi-level solution algorithm for Markov chains

Energy Technology Data Exchange (ETDEWEB)

Horton, G. [Univ. of Erlangen, Nuernberg (Germany)

1996-12-31

We discuss the recently introduced multi-level algorithm for the steady-state solution of Markov chains. The method is based on the aggregation principle, which is well established in the literature. Recursive application of the aggregation yields a multi-level method which has been shown experimentally to give results significantly faster than the methods currently in use. The algorithm can be reformulated as an algebraic multigrid scheme of Galerkin-full approximation type. The uniqueness of the scheme stems from its solution-dependent prolongation operator which permits significant computational savings in the evaluation of certain terms. This paper describes the modeling of computer systems to derive information on performance, measured typically as job throughput or component utilization, and availability, defined as the proportion of time a system is able to perform a certain function in the presence of component failures and possibly also repairs.

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

Science.gov (United States)

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

2018-01-01

The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled Uzawa smoother is employed as an efficient numerical technique for the linear discrete system obtained by finite volumes on staggered grids. A specialty in our modeling approach is that at the interface of the fluid and poroelastic medium, two unknowns from the different subsystems are defined at the same grid point. We propose a special discretization at and near the points on the interface, which combines the approximation of the governing equations and the considered interface conditions. In the decoupled Uzawa smoother, Local Fourier Analysis (LFA) helps us to select optimal values of the relaxation parameter appearing. To implement the monolithic multigrid method, grid partitioning is used to deal with the interface updates when communication is required between two subdomains. Numerical experiments show that the proposed numerical method has an excellent convergence rate. The efficiency and robustness of the method are confirmed in numerical experiments with typically small realistic values of the physical coefficients.

Genetic design of interpolated non-linear controllers for linear plants

International Nuclear Information System (INIS)

Ajlouni, N.

2000-01-01

The techniques of genetic algorithms are proposed as a means of designing non-linear PID control systems. It is shown that the use of genetic algorithms for this purpose results in highly effective non-linear PID control systems. These results are illustrated by using genetic algorithms to design a non-linear PID control system and contrasting the results with an optimally tuned linear PID controller. (author)

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

KAUST Repository

Elsheikh, A. H.

2013-12-01

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

Algorithms for computational fluid dynamics n parallel processors

International Nuclear Information System (INIS)

Van de Velde, E.F.

1986-01-01

A study of parallel algorithms for the numerical solution of partial differential equations arising in computational fluid dynamics is presented. The actual implementation on parallel processors of shared and nonshared memory design is discussed. The performance of these algorithms is analyzed in terms of machine efficiency, communication time, bottlenecks and software development costs. For elliptic equations, a parallel preconditioned conjugate gradient method is described, which has been used to solve pressure equations discretized with high order finite elements on irregular grids. A parallel full multigrid method and a parallel fast Poisson solver are also presented. Hyperbolic conservation laws were discretized with parallel versions of finite difference methods like the Lax-Wendroff scheme and with the Random Choice method. Techniques are developed for comparing the behavior of an algorithm on different architectures as a function of problem size and local computational effort. Effective use of these advanced architecture machines requires the use of machine dependent programming. It is shown that the portability problems can be minimized by introducing high level operations on vectors and matrices structured into program libraries

Final Report of Optimization Algorithms for Hierarchical Problems, with Applications to Nanoporous Materials

Energy Technology Data Exchange (ETDEWEB)

Nash, Stephen G.

2013-11-11

The research focuses on the modeling and optimization of nanoporous materials. In systems with hierarchical structure that we consider, the physics changes as the scale of the problem is reduced and it can be important to account for physics at the fine level to obtain accurate approximations at coarser levels. For example, nanoporous materials hold promise for energy production and storage. A significant issue is the fabrication of channels within these materials to allow rapid diffusion through the material. One goal of our research is to apply optimization methods to the design of nanoporous materials. Such problems are large and challenging, with hierarchical structure that we believe can be exploited, and with a large range of important scales, down to atomistic. This requires research on large-scale optimization for systems that exhibit different physics at different scales, and the development of algorithms applicable to designing nanoporous materials for many important applications in energy production, storage, distribution, and use. Our research has two major research thrusts. The first is hierarchical modeling. We plan to develop and study hierarchical optimization models for nanoporous materials. The models have hierarchical structure, and attempt to balance the conflicting aims of model fidelity and computational tractability. In addition, we analyze the general hierarchical model, as well as the specific application models, to determine their properties, particularly those properties that are relevant to the hierarchical optimization algorithms. The second thrust was to develop, analyze, and implement a class of hierarchical optimization algorithms, and apply them to the hierarchical models we have developed. We adapted and extended the optimization-based multigrid algorithms of Lewis and Nash to the optimization models exemplified by the hierarchical optimization model. This class of multigrid algorithms has been shown to be a powerful tool for

Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design

Energy Technology Data Exchange (ETDEWEB)

Liao, Ben-Shan; Bai, Zhaojun; /UC, Davis; Lee, Lie-Quan; Ko, Kwok; /SLAC

2006-09-28

A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.

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

Science.gov (United States)

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

2013-06-01

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

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

Science.gov (United States)

Xu, Yunjun; Remeikas, Charles; Pham, Khanh

2014-03-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2007-06-13

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

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.

A Design of a Hybrid Non-Linear Control Algorithm

Directory of Open Access Journals (Sweden)

Farinaz Behrooz

2017-11-01

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

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

Directory of Open Access Journals (Sweden)

Akemi Gálvez

2013-01-01

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

Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

Directory of Open Access Journals (Sweden)

Y. N. Pavlov

2015-01-01

Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

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.

Ranking scientific publications: the effect of nonlinearity

Science.gov (United States)

Yao, Liyang; Wei, Tian; Zeng, An; Fan, Ying; di, Zengru

2014-10-01

Ranking the significance of scientific publications is a long-standing challenge. The network-based analysis is a natural and common approach for evaluating the scientific credit of papers. Although the number of citations has been widely used as a metric to rank papers, recently some iterative processes such as the well-known PageRank algorithm have been applied to the citation networks to address this problem. In this paper, we introduce nonlinearity to the PageRank algorithm when aggregating resources from different nodes to further enhance the effect of important papers. The validation of our method is performed on the data of American Physical Society (APS) journals. The results indicate that the nonlinearity improves the performance of the PageRank algorithm in terms of ranking effectiveness, as well as robustness against malicious manipulations. Although the nonlinearity analysis is based on the PageRank algorithm, it can be easily extended to other iterative ranking algorithms and similar improvements are expected.

Ranking scientific publications: the effect of nonlinearity.

Science.gov (United States)

Yao, Liyang; Wei, Tian; Zeng, An; Fan, Ying; Di, Zengru

2014-10-17

Ranking the significance of scientific publications is a long-standing challenge. The network-based analysis is a natural and common approach for evaluating the scientific credit of papers. Although the number of citations has been widely used as a metric to rank papers, recently some iterative processes such as the well-known PageRank algorithm have been applied to the citation networks to address this problem. In this paper, we introduce nonlinearity to the PageRank algorithm when aggregating resources from different nodes to further enhance the effect of important papers. The validation of our method is performed on the data of American Physical Society (APS) journals. The results indicate that the nonlinearity improves the performance of the PageRank algorithm in terms of ranking effectiveness, as well as robustness against malicious manipulations. Although the nonlinearity analysis is based on the PageRank algorithm, it can be easily extended to other iterative ranking algorithms and similar improvements are expected.

Multigrid preconditioned conjugate-gradient method for large-scale wave-front reconstruction.

Science.gov (United States)

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

2002-09-01

We introduce a multigrid preconditioned conjugate-gradient (MGCG) iterative scheme for computing open-loop wave-front reconstructors for extreme adaptive optics systems. We present numerical simulations for a 17-m class telescope with n = 48756 sensor measurement grid points within the aperture, which indicate that our MGCG method has a rapid convergence rate for a wide range of subaperture average slope measurement signal-to-noise ratios. The total computational cost is of order n log n. Hence our scheme provides for fast wave-front simulation and control in large-scale adaptive optics systems.

A matrix-free implicit unstructured multigrid finite volume method for simulating structural dynamics and fluid structure interaction

Science.gov (United States)

Lv, X.; Zhao, Y.; Huang, X. Y.; Xia, G. H.; Su, X. H.

2007-07-01

A new three-dimensional (3D) matrix-free implicit unstructured multigrid finite volume (FV) solver for structural dynamics is presented in this paper. The solver is first validated using classical 2D and 3D cantilever problems. It is shown that very accurate predictions of the fundamental natural frequencies of the problems can be obtained by the solver with fast convergence rates. This method has been integrated into our existing FV compressible solver [X. Lv, Y. Zhao, et al., An efficient parallel/unstructured-multigrid preconditioned implicit method for simulating 3d unsteady compressible flows with moving objects, Journal of Computational Physics 215(2) (2006) 661-690] based on the immersed membrane method (IMM) [X. Lv, Y. Zhao, et al., as mentioned above]. Results for the interaction between the fluid and an immersed fixed-free cantilever are also presented to demonstrate the potential of this integrated fluid-structure interaction approach.

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

Science.gov (United States)

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

2016-03-01

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

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

Directory of Open Access Journals (Sweden)

Chung-Ta Li

2014-01-01

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

SPP propagation in nonlinear glass-metal interface

KAUST Repository

Sagor, Rakibul Hasan

2011-12-01

The non-linear propagation of Surface-Plasmon-Polaritons (SPP) in single interface of metal and chalcogenide glass (ChG) is considered. A time domain simulation algorithm is developed using the Finite Difference Time Domain (FDTD) method. The general polarization algorithm incorporated in the auxiliary differential equation (ADE) is used to model frequency-dependent dispersion relation and third-order nonlinearity of ChG. The main objective is to observe the nonlinear behavior of SPP propagation and study the dynamics of the whole structure. © 2011 IEEE.

Finding all solutions of nonlinear equations using the dual simplex method

Science.gov (United States)

Yamamura, Kiyotaka; Fujioka, Tsuyoshi

2003-03-01

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations using the dual simplex method. In this letter, an improved version of the LP test algorithm is proposed. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time.

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

Energy Technology Data Exchange (ETDEWEB)

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

1976-08-01

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

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

Directory of Open Access Journals (Sweden)

Chenlu Miao

2016-01-01

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

Nonlinear convergence active vibration absorber for single and multiple frequency vibration control

Science.gov (United States)

Wang, Xi; Yang, Bintang; Guo, Shufeng; Zhao, Wenqiang

2017-12-01

This paper presents a nonlinear convergence algorithm for active dynamic undamped vibration absorber (ADUVA). The damping of absorber is ignored in this algorithm to strengthen the vibration suppressing effect and simplify the algorithm at the same time. The simulation and experimental results indicate that this nonlinear convergence ADUVA can help significantly suppress vibration caused by excitation of both single and multiple frequency. The proposed nonlinear algorithm is composed of equivalent dynamic modeling equations and frequency estimator. Both the single and multiple frequency ADUVA are mathematically imitated by the same mechanical structure with a mass body and a voice coil motor (VCM). The nonlinear convergence estimator is applied to simultaneously satisfy the requirements of fast convergence rate and small steady state frequency error, which are incompatible for linear convergence estimator. The convergence of the nonlinear algorithm is mathematically proofed, and its non-divergent characteristic is theoretically guaranteed. The vibration suppressing experiments demonstrate that the nonlinear ADUVA can accelerate the convergence rate of vibration suppressing and achieve more decrement of oscillation attenuation than the linear ADUVA.

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

Science.gov (United States)

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

2014-04-01

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

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

Science.gov (United States)

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

2012-05-10

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

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

Science.gov (United States)

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

1992-01-01

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

Algorithm 896: LSA: Algorithms for Large-Scale Optimization

Czech Academy of Sciences Publication Activity Database

Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan

2009-01-01

Roč. 36, č. 3 (2009), 16-1-16-29 ISSN 0098-3500 R&D Pro jects: GA AV ČR IAA1030405; GA ČR GP201/06/P397 Institutional research plan: CEZ:AV0Z10300504 Keywords : algorithms * design * large-scale optimization * large-scale nonsmooth optimization * large-scale nonlinear least squares * large-scale nonlinear minimax * large-scale systems of nonlinear equations * sparse pro blems * partially separable pro blems * limited-memory methods * discrete Newton methods * quasi-Newton methods * primal interior-point methods Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.904, year: 2009

Comparison of multihardware parallel implementations for a phase unwrapping algorithm

Science.gov (United States)

Hernandez-Lopez, Francisco Javier; Rivera, Mariano; Salazar-Garibay, Adan; Legarda-Sáenz, Ricardo

2018-04-01

Phase unwrapping is an important problem in the areas of optical metrology, synthetic aperture radar (SAR) image analysis, and magnetic resonance imaging (MRI) analysis. These images are becoming larger in size and, particularly, the availability and need for processing of SAR and MRI data have increased significantly with the acquisition of remote sensing data and the popularization of magnetic resonators in clinical diagnosis. Therefore, it is important to develop faster and accurate phase unwrapping algorithms. We propose a parallel multigrid algorithm of a phase unwrapping method named accumulation of residual maps, which builds on a serial algorithm that consists of the minimization of a cost function; minimization achieved by means of a serial Gauss-Seidel kind algorithm. Our algorithm also optimizes the original cost function, but unlike the original work, our algorithm is a parallel Jacobi class with alternated minimizations. This strategy is known as the chessboard type, where red pixels can be updated in parallel at same iteration since they are independent. Similarly, black pixels can be updated in parallel in an alternating iteration. We present parallel implementations of our algorithm for different parallel multicore architecture such as CPU-multicore, Xeon Phi coprocessor, and Nvidia graphics processing unit. In all the cases, we obtain a superior performance of our parallel algorithm when compared with the original serial version. In addition, we present a detailed comparative performance of the developed parallel versions.

FILMPAR: A parallel algorithm designed for the efficient and accurate computation of thin film flow on functional surfaces containing micro-structure

Science.gov (United States)

Lee, Y. C.; Thompson, H. M.; Gaskell, P. H.

2009-12-01

FILMPAR is a highly efficient and portable parallel multigrid algorithm for solving a discretised form of the lubrication approximation to three-dimensional, gravity-driven, continuous thin film free-surface flow over substrates containing micro-scale topography. While generally applicable to problems involving heterogeneous and distributed features, for illustrative purposes the algorithm is benchmarked on a distributed memory IBM BlueGene/P computing platform for the case of flow over a single trench topography, enabling direct comparison with complementary experimental data and existing serial multigrid solutions. Parallel performance is assessed as a function of the number of processors employed and shown to lead to super-linear behaviour for the production of mesh-independent solutions. In addition, the approach is used to solve for the case of flow over a complex inter-connected topographical feature and a description provided of how FILMPAR could be adapted relatively simply to solve for a wider class of related thin film flow problems. Program summaryProgram title: FILMPAR Catalogue identifier: AEEL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 530 421 No. of bytes in distributed program, including test data, etc.: 1 960 313 Distribution format: tar.gz Programming language: C++ and MPI Computer: Desktop, server Operating system: Unix/Linux Mac OS X Has the code been vectorised or parallelised?: Yes. Tested with up to 128 processors RAM: 512 MBytes Classification: 12 External routines: GNU C/C++, MPI Nature of problem: Thin film flows over functional substrates containing well-defined single and complex topographical features are of enormous significance, having a wide variety of engineering

Numerical study of propagation properties of surface plasmon polaritons in nonlinear media

KAUST Repository

Sagor, Rakibul Hasan

2016-03-29

We present a time-domain algorithm for simulating nonlinear propagation of surface plasmon polaritons (SPPs) in chalcogenide glass. Due to the high non-linearity property and strong dispersion and confinement chalcogenide glasses are widely known as ultrafast nonlinear materials. We have used the finite difference time domain (FDTD) method to develop the simulation algorithm for the current analysis. We have modeled the frequency dependent dispersion properties and third order nonlinearity property of chalcogenide glass utilizing the general polarization algorithm merged in the auxiliary differential equation (ADE) method. The propagation dynamics of the whole structure with and without third order nonlinearity property of chalcogenide glass have been simulated and the effect of nonlinearity on the propagation properties of SPP has been investigated. © 2016 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.

Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion

International Nuclear Information System (INIS)

Mousseau, V.A.; Knoll, D.A.; Rider, W.J.

2000-01-01

An algorithm is presented for the solution of the time dependent reaction-diffusion systems which arise in non-equilibrium radiation diffusion applications. This system of nonlinear equations is solved by coupling three numerical methods, Jacobian-free Newton-Krylov, operator splitting, and multigrid linear solvers. An inexact Newton's method is used to solve the system of nonlinear equations. Since building the Jacobian matrix for problems of interest can be challenging, the authors employ a Jacobian-free implementation of Newton's method, where the action of the Jacobian matrix on a vector is approximated by a first order Taylor series expansion. Preconditioned generalized minimal residual (PGMRES) is the Krylov method used to solve the linear systems that come from the iterations of Newton's method. The preconditioner in this solution method is constructed using a physics-based divide and conquer approach, often referred to as operator splitting. This solution procedure inverts the scalar elliptic systems that make up the preconditioner using simple multigrid methods. The preconditioner also addresses the strong coupling between equations with local 2 x 2 block solves. The intra-cell coupling is applied after the inter-cell coupling has already been addressed by the elliptic solves. Results are presented using this solution procedure that demonstrate its efficiency while incurring minimal memory requirements

Implementation of software-based sensor linearization algorithms on low-cost microcontrollers.

Science.gov (United States)

Erdem, Hamit

2010-10-01

Nonlinear sensors and microcontrollers are used in many embedded system designs. As the input-output characteristic of most sensors is nonlinear in nature, obtaining data from a nonlinear sensor by using an integer microcontroller has always been a design challenge. This paper discusses the implementation of six software-based sensor linearization algorithms for low-cost microcontrollers. The comparative study of the linearization algorithms is performed by using a nonlinear optical distance-measuring sensor. The performance of the algorithms is examined with respect to memory space usage, linearization accuracy and algorithm execution time. The implementation and comparison results can be used for selection of a linearization algorithm based on the sensor transfer function, expected linearization accuracy and microcontroller capacity. Copyright © 2010 ISA. Published by Elsevier Ltd. All rights reserved.

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

International Nuclear Information System (INIS)

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

2012-01-01

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

Nonlinear dynamical system approaches towards neural prosthesis

International Nuclear Information System (INIS)

Torikai, Hiroyuki; Hashimoto, Sho

2011-01-01

An asynchronous discrete-state spiking neurons is a wired system of shift registers that can mimic nonlinear dynamics of an ODE-based neuron model. The control parameter of the neuron is the wiring pattern among the registers and thus they are suitable for on-chip learning. In this paper an asynchronous discrete-state spiking neuron is introduced and its typical nonlinear phenomena are demonstrated. Also, a learning algorithm for a set of neurons is presented and it is demonstrated that the algorithm enables the set of neurons to reconstruct nonlinear dynamics of another set of neurons with unknown parameter values. The learning function is validated by FPGA experiments.

Experimental verification of transient nonlinear acoustical holography.

Science.gov (United States)

Jing, Yun; Cannata, Jonathan; Wang, Tianren

2013-05-01

This paper presents an experimental study on nonlinear transient acoustical holography. The validity and effectiveness of a recently proposed nonlinear transient acoustical holography algorithm is evaluated in the presence of noise. The acoustic field measured on a post-focal plane of a high-intensity focused transducer is backward projected to reconstruct the pressure distributions on the focal and a pre-focal plane, which are shown to be in good agreement with the measurement. In contrast, the conventional linear holography produces erroneous results in this case where the nonlinearity involved is strong. Forward acoustic field projection was also carried out to further verify the algorithm.

Parallel processors and nonlinear structural dynamics algorithms and software

Science.gov (United States)

Belytschko, Ted

1989-01-01

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

Fast multigrid-based computation of the induced electric field for transcranial magnetic stimulation

Science.gov (United States)

Laakso, Ilkka; Hirata, Akimasa

2012-12-01

In transcranial magnetic stimulation (TMS), the distribution of the induced electric field, and the affected brain areas, depends on the position of the stimulation coil and the individual geometry of the head and brain. The distribution of the induced electric field in realistic anatomies can be modelled using computational methods. However, existing computational methods for accurately determining the induced electric field in realistic anatomical models have suffered from long computation times, typically in the range of tens of minutes or longer. This paper presents a matrix-free implementation of the finite-element method with a geometric multigrid method that can potentially reduce the computation time to several seconds or less even when using an ordinary computer. The performance of the method is studied by computing the induced electric field in two anatomically realistic models. An idealized two-loop coil is used as the stimulating coil. Multiple computational grid resolutions ranging from 2 to 0.25 mm are used. The results show that, for macroscopic modelling of the electric field in an anatomically realistic model, computational grid resolutions of 1 mm or 2 mm appear to provide good numerical accuracy compared to higher resolutions. The multigrid iteration typically converges in less than ten iterations independent of the grid resolution. Even without parallelization, each iteration takes about 1.0 s or 0.1 s for the 1 and 2 mm resolutions, respectively. This suggests that calculating the electric field with sufficient accuracy in real time is feasible.

Nonlinear filtering for LIDAR signal processing

Directory of Open Access Journals (Sweden)

D. G. Lainiotis

1996-01-01

Full Text Available LIDAR (Laser Integrated Radar is an engineering problem of great practical importance in environmental monitoring sciences. Signal processing for LIDAR applications involves highly nonlinear models and consequently nonlinear filtering. Optimal nonlinear filters, however, are practically unrealizable. In this paper, the Lainiotis's multi-model partitioning methodology and the related approximate but effective nonlinear filtering algorithms are reviewed and applied to LIDAR signal processing. Extensive simulation and performance evaluation of the multi-model partitioning approach and its application to LIDAR signal processing shows that the nonlinear partitioning methods are very effective and significantly superior to the nonlinear extended Kalman filter (EKF, which has been the standard nonlinear filter in past engineering applications.

Convergence criteria for systems of nonlinear elliptic partial differential equations

International Nuclear Information System (INIS)

Sharma, R.K.

1986-01-01

This thesis deals with convergence criteria for a special system of nonlinear elliptic partial differential equations. A fixed-point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. Conditions are established that help foresee the convergence of the algorithm. Under reasonable hypotheses it is proved that the algorithm converges for such nonlinear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis

Spurious Solutions Of Nonlinear Differential Equations

Science.gov (United States)

Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

1992-01-01

Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.

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

Science.gov (United States)

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

2018-01-01

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

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

KAUST Repository

Bonito, Andrea; Pasciak, Joseph E.

2012-01-01

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

Nonlinear observer based fault detection and isolation for a momentum wheel

DEFF Research Database (Denmark)

Jensen, Hans-Christian Becker; Wisniewski, Rafal

2001-01-01

This article realizes nonlinear Fault Detection and Isolation for a momentum wheel. The Fault Detection and Isolation is based on a Failure Mode and Effect Analysis, which states which faults might occur and can be detected. The algorithms presented in this paper are based on a geometric approach...... toachieve nonlinear Fault Detection and Isolation. The proposed algorithms are tested in a simulation study and the pros and cons of the algorithm are discussed....

Genetic Algorithms for a Parameter Estimation of a Fermentation Process Model: A Comparison

Directory of Open Access Journals (Sweden)

Olympia Roeva

2005-12-01

Full Text Available In this paper the problem of a parameter estimation using genetic algorithms is examined. A case study considering the estimation of 6 parameters of a nonlinear dynamic model of E. coli fermentation is presented as a test problem. The parameter estimation problem is stated as a nonlinear programming problem subject to nonlinear differential-algebraic constraints. This problem is known to be frequently ill-conditioned and multimodal. Thus, traditional (gradient-based local optimization methods fail to arrive satisfied solutions. To overcome their limitations, the use of different genetic algorithms as stochastic global optimization methods is explored. These algorithms are proved to be very suitable for the optimization of highly non-linear problems with many variables. Genetic algorithms can guarantee global optimality and robustness. These facts make them advantageous in use for parameter identification of fermentation models. A comparison between simple, modified and multi-population genetic algorithms is presented. The best result is obtained using the modified genetic algorithm. The considered algorithms converged very closely to the cost value but the modified algorithm is in times faster than other two.

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

Directory of Open Access Journals (Sweden)

Guang Xu

2017-12-01

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

Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography.

Science.gov (United States)

Yang, Qiang; Vogel, Curtis R; Ellerbroek, Brent L

2006-07-20

By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty.

LOO: a low-order nonlinear transport scheme for acceleration of method of characteristics

International Nuclear Information System (INIS)

Li, Lulu; Smith, Kord; Forget, Benoit; Ferrer, Rodolfo

2015-01-01

This paper presents a new physics-based multi-grid nonlinear acceleration method: the low-order operator method, or LOO. LOO uses a coarse space-angle multi-group method of characteristics (MOC) neutron transport calculation to accelerate the fine space-angle MOC calculation. LOO is designed to capture more angular effects than diffusion-based acceleration methods through a transport-based low-order solver. LOO differs from existing transport-based acceleration schemes in that it emphasizes simplified coarse space-angle characteristics and preserves physics in quadrant phase-space. The details of the method, including the restriction step, the low-order iterative solver and the prolongation step are discussed in this work. LOO shows comparable convergence behavior to coarse mesh finite difference on several two-dimensional benchmark problems while not requiring any under-relaxation, making it a robust acceleration scheme. (author)

Recent Advances in Explicit Multiparametric Nonlinear Model Predictive Control

KAUST Repository

Domínguez, Luis F.

2011-01-19

In this paper we present recent advances in multiparametric nonlinear programming (mp-NLP) algorithms for explicit nonlinear model predictive control (mp-NMPC). Three mp-NLP algorithms for NMPC are discussed, based on which novel mp-NMPC controllers are derived. The performance of the explicit controllers are then tested and compared in a simulation example involving the operation of a continuous stirred-tank reactor (CSTR). © 2010 American Chemical Society.

A fast method to emulate an iterative POCS image reconstruction algorithm.

Science.gov (United States)

Zeng, Gengsheng L

2017-10-01

Iterative image reconstruction algorithms are commonly used to optimize an objective function, especially when the objective function is nonquadratic. Generally speaking, the iterative algorithms are computationally inefficient. This paper presents a fast algorithm that has one backprojection and no forward projection. This paper derives a new method to solve an optimization problem. The nonquadratic constraint, for example, an edge-preserving denoising constraint is implemented as a nonlinear filter. The algorithm is derived based on the POCS (projections onto projections onto convex sets) approach. A windowed FBP (filtered backprojection) algorithm enforces the data fidelity. An iterative procedure, divided into segments, enforces edge-enhancement denoising. Each segment performs nonlinear filtering. The derived iterative algorithm is computationally efficient. It contains only one backprojection and no forward projection. Low-dose CT data are used for algorithm feasibility studies. The nonlinearity is implemented as an edge-enhancing noise-smoothing filter. The patient studies results demonstrate its effectiveness in processing low-dose x ray CT data. This fast algorithm can be used to replace many iterative algorithms. © 2017 American Association of Physicists in Medicine.

Nonlinear Time Series Prediction Using Chaotic Neural Networks

Science.gov (United States)

Li, Ke-Ping; Chen, Tian-Lun

2001-06-01

A nonlinear feedback term is introduced into the evaluation equation of weights of the backpropagation algorithm for neural network, the network becomes a chaotic one. For the purpose of that we can investigate how the different feedback terms affect the process of learning and forecasting, we use the model to forecast the nonlinear time series which is produced by Makey-Glass equation. By selecting the suitable feedback term, the system can escape from the local minima and converge to the global minimum or its approximate solutions, and the forecasting results are better than those of backpropagation algorithm. The project supported by National Basic Research Project "Nonlinear Science" and National Natural Science Foundation of China under Grant No. 60074020

Partially linearized algorithms in gyrokinetic particle simulation

Energy Technology Data Exchange (ETDEWEB)

Dimits, A.M.; Lee, W.W.

1990-10-01

In this paper, particle simulation algorithms with time-varying weights for the gyrokinetic Vlasov-Poisson system have been developed. The primary purpose is to use them for the removal of the selected nonlinearities in the simulation of gradient-driven microturbulence so that the relative importance of the various nonlinear effects can be assessed. It is hoped that the use of these procedures will result in a better understanding of the transport mechanisms and scaling in tokamaks. Another application of these algorithms is for the improvement of the numerical properties of the simulation plasma. For instance, implementations of such algorithms (1) enable us to suppress the intrinsic numerical noise in the simulation, and (2) also make it possible to regulate the weights of the fast-moving particles and, in turn, to eliminate the associated high frequency oscillations. Examples of their application to drift-type instabilities in slab geometry are given. We note that the work reported here represents the first successful use of the weighted algorithms in particle codes for the nonlinear simulation of plasmas.

Partially linearized algorithms in gyrokinetic particle simulation

International Nuclear Information System (INIS)

Dimits, A.M.; Lee, W.W.

1990-10-01

In this paper, particle simulation algorithms with time-varying weights for the gyrokinetic Vlasov-Poisson system have been developed. The primary purpose is to use them for the removal of the selected nonlinearities in the simulation of gradient-driven microturbulence so that the relative importance of the various nonlinear effects can be assessed. It is hoped that the use of these procedures will result in a better understanding of the transport mechanisms and scaling in tokamaks. Another application of these algorithms is for the improvement of the numerical properties of the simulation plasma. For instance, implementations of such algorithms (1) enable us to suppress the intrinsic numerical noise in the simulation, and (2) also make it possible to regulate the weights of the fast-moving particles and, in turn, to eliminate the associated high frequency oscillations. Examples of their application to drift-type instabilities in slab geometry are given. We note that the work reported here represents the first successful use of the weighted algorithms in particle codes for the nonlinear simulation of plasmas

Implementation of the Vanka-type multigrid solver for the finite element approximation of the Navier-Stokes equations on GPU

Czech Academy of Sciences Publication Activity Database

Bauer, Petr; Klement, V.; Oberhuber, T.; Žabka, V.

2016-01-01

Roč. 200, March (2016), s. 50-56 ISSN 0010-4655 R&D Projects: GA ČR GB14-36566G Institutional support: RVO:61388998 Keywords : Navier–Stokes equations * mixed finite elements * multigrid * Vanka-type smoothers * Gauss–Seidel * red–black coloring * parallelization * GPU Subject RIV: BK - Fluid Dynamics Impact factor: 3.936, year: 2016

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....

Ripple distribution for nonlinear fiber-optic channels.

Science.gov (United States)

Sorokina, Mariia; Sygletos, Stylianos; Turitsyn, Sergei

2017-02-06

We demonstrate data rates above the threshold imposed by nonlinearity on conventional optical signals by applying novel probability distribution, which we call ripple distribution, adapted to the properties of the fiber channel. Our results offer a new direction for signal coding, modulation and practical nonlinear distortions compensation algorithms.

Indirect learning control for nonlinear dynamical systems

Science.gov (United States)

Ryu, Yeong Soon; Longman, Richard W.

1993-01-01

In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.

Large-scale sequential quadratic programming algorithms

Energy Technology Data Exchange (ETDEWEB)

Eldersveld, S.K.

1992-09-01

The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.

Comparative efficiencies of three parallel algorithms for nonlinear ...

Indian Academy of Sciences (India)

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

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

Continuous nonlinear optimization for engineering applications in GAMS technology

CERN Document Server

Andrei, Neculai

2017-01-01

This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical opti...

Measurement and fitting techniques for the assessment of material nonlinearity using nonlinear Rayleigh waves

Energy Technology Data Exchange (ETDEWEB)

Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)

2015-03-31

This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.

The (G/G)-expansion method for a discrete nonlinear Schrödinger ...

Indian Academy of Sciences (India)

With the aid of symbolic computation, we choose a discrete nonlinear Schrödinger equation to illustrate the validity and advantages of the improved algorithm. As a result ... It is shown that the improved algorithm is effective and can be used for many other nonlinear differential-difference equations in mathematical physics.

Nonlinear Impairment Compensation Using Expectation Maximization for PDM 16-QAM Systems

DEFF Research Database (Denmark)

Zibar, Darko; Winther, Ole; Franceschi, Niccolo

2012-01-01

We show experimentally that by using non-linear signal processing based algorithm, expectation maximization, nonlinear system tolerance can be increased by 2 dB. Expectation maximization is also effective in combating I/Q modulator nonlinearities and laser linewidth....

Estimation of dynamic reactivity using an H∞ optimal filter with a nonlinear term

International Nuclear Information System (INIS)

Suzuki, Katsuo; Watanabe, Koiti

1996-01-01

A method of nonlinear filtering is applied to the problem of estimating the dynamic reactivity of a nonlinear reactor system. The nonlinear filtering algorithm developed is a simple modification of a linear H ∞ optimal filter with a nonlinear feedback loop added. The linear filter is designed on the basis of a linearized dynamical system model that consists of linearized point reactor kinetic equations and a reactivity state equation driven by a fictitious signal. The latter is artificially introduced to deal with the reactivity as a state variable. The results of the computer simulation show that the nonlinear filtering algorithm can be applied to estimate the dynamic reactivity of the nonlinear reactor system, even under relatively large reactivity disturbances

The second order extended Kalman filter and Markov nonlinear filter for data processing in interferometric systems

International Nuclear Information System (INIS)

Ermolaev, P; Volynsky, M

2014-01-01

Recurrent stochastic data processing algorithms using representation of interferometric signal as output of a dynamic system, which state is described by vector of parameters, in some cases are more effective, compared with conventional algorithms. Interferometric signals depend on phase nonlinearly. Consequently it is expedient to apply algorithms of nonlinear stochastic filtering, such as Kalman type filters. An application of the second order extended Kalman filter and Markov nonlinear filter that allows to minimize estimation error is described. Experimental results of signals processing are illustrated. Comparison of the algorithms is presented and discussed.

Limits to Nonlinear Inversion

DEFF Research Database (Denmark)

Mosegaard, Klaus

2012-01-01

For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...... pure meta-heuristics. We study problem-adapted inversion algorithms that exploit the knowledge of the smoothness of the misfit function of the problem. Optimal sampling strategies exist for such problems, but many of these problems remain hard. © 2012 Springer-Verlag....

Iterative solution of a nonlinear system arising in phase change problems

International Nuclear Information System (INIS)

Williams, M.A.

1987-01-01

We consider several iterative methods for solving the nonlinear system arising from an enthalpy formulation of a phase change problem. We present the formulation of the problem. Implicit discretization of the governing equations results in a mildly nonlinear system at each time step. We discuss solving this system using Jacobi, Gauss-Seidel, and SOR iterations and a new modified preconditioned conjugate gradient (MPCG) algorithm. The new MPCG algorithm and its properties are discussed in detail. Numerical results are presented comparing the performance of the SOR algorithm and the MPCG algorithm with 1-step SSOR preconditioning. The MPCG algorithm exhibits a superlinear rate of convergence. The SOR algorithm exhibits a linear rate of convergence. Thus, the MPCG algorithm requires fewer iterations to converge than the SOR algorithm. However in most cases, the SOR algorithm requires less total computation time than the MPCG algorithm. Hence, the SOR algorithm appears to be more appropriate for the class of problems considered. 27 refs., 11 figs

Retrieval of high-order susceptibilities of nonlinear metamaterials

International Nuclear Information System (INIS)

Wang Zhi-Yu; Qiu Jin-Peng; Chen Hua; Mo Jiong-Jiong; Yu Fa-Xin

2017-01-01

Active metamaterials embedded with nonlinear elements are able to exhibit strong nonlinearity in microwave regime. However, existing S -parameter based parameter retrieval approaches developed for linear metamaterials do not apply in nonlinear cases. In this paper, a retrieval algorithm of high-order susceptibilities for nonlinear metamaterials is derived. Experimental demonstration shows that, by measuring the power level of each harmonic while sweeping the incident power, high-order susceptibilities of a thin-layer nonlinear metamaterial can be effectively retrieved. The proposedapproach can be widely used in the research of active metamaterials. (paper)

NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES

Directory of Open Access Journals (Sweden)

SILVA R. G.

1999-01-01

Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.

Physics constrained nonlinear regression models for time series

International Nuclear Information System (INIS)

Majda, Andrew J; Harlim, John

2013-01-01

A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data. (paper)

Nonlinear dynamics aspects of particle accelerators

International Nuclear Information System (INIS)

Jowett, J.M.; Turner, S.; Month, M.

1986-01-01

These proceedings contain the lectures presented at the named winter school. They deal with the application of dynamical systems to accelerator theory. Especially considered are the statistical description of charged-beam plasmas, integrable and nonintegrable Hamiltonian systems, single particle dynamics and nonlinear resonances in circular accelerators, nonlinear dynamics aspects of modern storage rings, nonlinear beam-beam resonances, synchro-betatron resonances, observations of the beam-beam interactions, the dynamics of the beam-beam interactions, beam-beam simulations, the perturbation method in nonlinear dynamics, theories of statistical equilibrium in electron-positron storage rings, nonlinear dissipative phenomena in electron storage rings, the dynamical aperture, the transition to chaos for area-preserving maps, special processors for particle tracking, algorithms for tracking of charged particles in circular accelerators, the breakdown of stability, and a personal perspective of nonlinear dynamics. (HSI)

Nonlinear adaptive optimization of biomass productivity in continuous bioreactors

Energy Technology Data Exchange (ETDEWEB)

Sauvaire, P; Mellichamp, D A; Agrawal, P [California Univ., Santa Barbara, CA (United States). Dept. of Chemical and Nuclear Engineering

1991-11-01

A novel on-line adaptive optimization algorithm is developed and applied to continuous biological reactors. The algorithm makes use of a simple nonlinear estimation model that relates either the cell-mass productivity or the cell-mass concentration to the dilution rate. On-line estimation is used to recursively identify the parameters in the nonlinear process model and to periodically calculate and steer the bioreactor to the dilution rate that yields optimum cell-mass productivity. Thus, the algorithm does not require an accurate process model, locates the optimum dilution rate online, and maintains the bioreactors at this optimum condition at all times. The features of the proposed new algorithm are compared with those of other adaptive optimization techniques presented in the literature. A detailed simulation study using three different microbial system models was conducted to illustrate the performance of the optimization algorithms. (orig.).

Novel procedure for characterizing nonlinear systems with memory: 2017 update

Science.gov (United States)

Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.

2017-05-01

The present article discusses novel improvements in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra or 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] . The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order and alleviate the Curse of Dimensionality (COD) in order to realize practical nonlinear solutions of scientific and engineering interest.

Feedforward Nonlinear Control Using Neural Gas Network

Directory of Open Access Journals (Sweden)

Iván Machón-González

2017-01-01

Full Text Available Nonlinear systems control is a main issue in control theory. Many developed applications suffer from a mathematical foundation not as general as the theory of linear systems. This paper proposes a control strategy of nonlinear systems with unknown dynamics by means of a set of local linear models obtained by a supervised neural gas network. The proposed approach takes advantage of the neural gas feature by which the algorithm yields a very robust clustering procedure. The direct model of the plant constitutes a piece-wise linear approximation of the nonlinear system and each neuron represents a local linear model for which a linear controller is designed. The neural gas model works as an observer and a controller at the same time. A state feedback control is implemented by estimation of the state variables based on the local transfer function that was provided by the local linear model. The gradient vectors obtained by the supervised neural gas algorithm provide a robust procedure for feedforward nonlinear control, that is, supposing the inexistence of disturbances.

Epsilon topological accelerating algorithms for difference method for initial-value problems

International Nuclear Information System (INIS)

Hristea, V.; Posirca, M.

1992-01-01

Linear and nonlinear parabolic equations can be solved by discretization methods which lead to linear and nonlinear algebraic systems. The iterative methods (e.g. Gauss - Seidel) show a very slow convergence and instability in the case of nonlinear equations. This paper proposes an ε topological algorithm for accelerating slow iterative methods used in the thermohydraulic code COBRA and the dynamic code ADEP. The results show an executing time approximately ten times lower than original algorithms. (Author)

Algorithmic Verification of Linearizability for Ordinary Differential Equations

KAUST Repository

Lyakhov, Dmitry A.

2017-07-19

For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a linear one by a point transformation of the dependent and independent variables. The first algorithm is based on a construction of the Lie point symmetry algebra and on the computation of its derived algebra. The second algorithm exploits the differential Thomas decomposition and allows not only to test the linearizability, but also to generate a system of nonlinear partial differential equations that determines the point transformation and the coefficients of the linearized equation. The implementation of both algorithms is discussed and their application is illustrated using several examples.

On the complexity of computing two nonlinearity measures

DEFF Research Database (Denmark)

Find, Magnus Gausdal

2014-01-01

We study the computational complexity of two Boolean nonlinearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time 2O(n) given the truth table of length 2n, in fact under the same ...

Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations

CERN Document Server

Aliyu, MDS

2011-01-01

A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter

KERNEL MAD ALGORITHM FOR RELATIVE RADIOMETRIC NORMALIZATION

Directory of Open Access Journals (Sweden)

Y. Bai

2016-06-01

Full Text Available The multivariate alteration detection (MAD algorithm is commonly used in relative radiometric normalization. This algorithm is based on linear canonical correlation analysis (CCA which can analyze only linear relationships among bands. Therefore, we first introduce a new version of MAD in this study based on the established method known as kernel canonical correlation analysis (KCCA. The proposed method effectively extracts the non-linear and complex relationships among variables. We then conduct relative radiometric normalization experiments on both the linear CCA and KCCA version of the MAD algorithm with the use of Landsat-8 data of Beijing, China, and Gaofen-1(GF-1 data derived from South China. Finally, we analyze the difference between the two methods. Results show that the KCCA-based MAD can be satisfactorily applied to relative radiometric normalization, this algorithm can well describe the nonlinear relationship between multi-temporal images. This work is the first attempt to apply a KCCA-based MAD algorithm to relative radiometric normalization.

Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter.

Science.gov (United States)

Song, Xuegang; Zhang, Yuexin; Liang, Dakai

2017-10-10

This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF) was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter

Directory of Open Access Journals (Sweden)

Xuegang Song

2017-10-01

Full Text Available This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

Nonlinear Dot Plots.

Science.gov (United States)

Rodrigues, Nils; Weiskopf, Daniel

2018-01-01

Conventional dot plots use a constant dot size and are typically applied to show the frequency distribution of small data sets. Unfortunately, they are not designed for a high dynamic range of frequencies. We address this problem by introducing nonlinear dot plots. Adopting the idea of nonlinear scaling from logarithmic bar charts, our plots allow for dots of varying size so that columns with a large number of samples are reduced in height. For the construction of these diagrams, we introduce an efficient two-way sweep algorithm that leads to a dense and symmetrical layout. We compensate aliasing artifacts at high dot densities by a specifically designed low-pass filtering method. Examples of nonlinear dot plots are compared to conventional dot plots as well as linear and logarithmic histograms. Finally, we include feedback from an expert review.

Weighted Optimization-Based Distributed Kalman Filter for Nonlinear Target Tracking in Collaborative Sensor Networks.

Science.gov (United States)

Chen, Jie; Li, Jiahong; Yang, Shuanghua; Deng, Fang

2017-11-01

The identification of the nonlinearity and coupling is crucial in nonlinear target tracking problem in collaborative sensor networks. According to the adaptive Kalman filtering (KF) method, the nonlinearity and coupling can be regarded as the model noise covariance, and estimated by minimizing the innovation or residual errors of the states. However, the method requires large time window of data to achieve reliable covariance measurement, making it impractical for nonlinear systems which are rapidly changing. To deal with the problem, a weighted optimization-based distributed KF algorithm (WODKF) is proposed in this paper. The algorithm enlarges the data size of each sensor by the received measurements and state estimates from its connected sensors instead of the time window. A new cost function is set as the weighted sum of the bias and oscillation of the state to estimate the "best" estimate of the model noise covariance. The bias and oscillation of the state of each sensor are estimated by polynomial fitting a time window of state estimates and measurements of the sensor and its neighbors weighted by the measurement noise covariance. The best estimate of the model noise covariance is computed by minimizing the weighted cost function using the exhaustive method. The sensor selection method is in addition to the algorithm to decrease the computation load of the filter and increase the scalability of the sensor network. The existence, suboptimality and stability analysis of the algorithm are given. The local probability data association method is used in the proposed algorithm for the multitarget tracking case. The algorithm is demonstrated in simulations on tracking examples for a random signal, one nonlinear target, and four nonlinear targets. Results show the feasibility and superiority of WODKF against other filtering algorithms for a large class of systems.

Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2015-01-01

A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.

Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding

KAUST Repository

Desmal, Abdulla

2015-04-13

A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.

Nonlinear system identification NARMAX methods in the time, frequency, and spatio-temporal domains

CERN Document Server

Billings, Stephen A

2013-01-01

Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) modelThe orthogonal least squares algorithm that allows models to be built term by

Global Optimization of Nonlinear Blend-Scheduling Problems

Directory of Open Access Journals (Sweden)

Pedro A. Castillo Castillo

2017-04-01

Full Text Available The scheduling of gasoline-blending operations is an important problem in the oil refining industry. This problem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but also non-convex nonlinear behavior, due to the blending of various materials with different quality properties. In this work, a global optimization algorithm is proposed to solve a previously published continuous-time mixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimization, the distribution problem, and several important operational features and constraints. The algorithm employs piecewise McCormick relaxation (PMCR and normalized multiparametric disaggregation technique (NMDT to compute estimates of the global optimum. These techniques partition the domain of one of the variables in a bilinear term and generate convex relaxations for each partition. By increasing the number of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates of the global solution. The algorithm is compared to two commercial global solvers and two heuristic methods by solving four examples from the literature. Results show that the proposed global optimization algorithm performs on par with commercial solvers but is not as fast as heuristic approaches.

Nonlinear dynamics aspects of particle accelerators. Proceedings

Energy Technology Data Exchange (ETDEWEB)

Jowett, J M; Turner, S; Month, M

1986-01-01

These proceedings contain the lectures presented at the named winter school. They deal with the application of dynamical systems to accelerator theory. Especially considered are the statistical description of charged-beam plasmas, integrable and nonintegrable Hamiltonian systems, single particle dynamics and nonlinear resonances in circular accelerators, nonlinear dynamics aspects of modern storage rings, nonlinear beam-beam resonances, synchro-betatron resonances, observations of the beam-beam interactions, the dynamics of the beam-beam interactions, beam-beam simulations, the perturbation method in nonlinear dynamics, theories of statistical equilibrium in electron-positron storage rings, nonlinear dissipative phenomena in electron storage rings, the dynamical aperture, the transition to chaos for area-preserving maps, special processors for particle tracking, algorithms for tracking of charged particles in circular accelerators, the breakdown of stability, and a personal perspective of nonlinear dynamics. (HSI).

Final report for “Extreme-scale Algorithms and Solver Resilience”

Energy Technology Data Exchange (ETDEWEB)

Gropp, William Douglas [Univ. of Illinois, Urbana-Champaign, IL (United States)

2017-06-30

This is a joint project with principal investigators at Oak Ridge National Laboratory, Sandia National Laboratories, the University of California at Berkeley, and the University of Tennessee. Our part of the project involves developing performance models for highly scalable algorithms and the development of latency tolerant iterative methods. During this project, we extended our performance models for the Multigrid method for solving large systems of linear equations and conducted experiments with highly scalable variants of conjugate gradient methods that avoid blocking synchronization. In addition, we worked with the other members of the project on alternative techniques for resilience and reproducibility. We also presented an alternative approach for reproducible dot-products in parallel computations that performs almost as well as the conventional approach by separating the order of computation from the details of the decomposition of vectors across the processes.

Nonlinear Principal Component Analysis Using Strong Tracking Filter

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

The paper analyzes the problem of blind source separation (BSS) based on the nonlinear principal component analysis (NPCA) criterion. An adaptive strong tracking filter (STF) based algorithm was developed, which is immune to system model mismatches. Simulations demonstrate that the algorithm converges quickly and has satisfactory steady-state accuracy. The Kalman filtering algorithm and the recursive leastsquares type algorithm are shown to be special cases of the STF algorithm. Since the forgetting factor is adaptively updated by adjustment of the Kalman gain, the STF scheme provides more powerful tracking capability than the Kalman filtering algorithm and recursive least-squares algorithm.

Non-Uniformity Correction Using Nonlinear Characteristic Performance Curves for Calibration

Science.gov (United States)

Lovejoy, McKenna Roberts

Infrared imaging is an expansive field with many applications. Advances in infrared technology have lead to a greater demand from both commercial and military sectors. However, a known problem with infrared imaging is its non-uniformity. This non-uniformity stems from the fact that each pixel in an infrared focal plane array has its own photoresponse. Many factors such as exposure time, temperature, and amplifier choice affect how the pixels respond to incoming illumination and thus impact image uniformity. To improve performance non-uniformity correction (NUC) techniques are applied. Standard calibration based techniques commonly use a linear model to approximate the nonlinear response. This often leaves unacceptable levels of residual non-uniformity. Calibration techniques often have to be repeated during use to continually correct the image. In this dissertation alternates to linear NUC algorithms are investigated. The goal of this dissertation is to determine and compare nonlinear non-uniformity correction algorithms. Ideally the results will provide better NUC performance resulting in less residual non-uniformity as well as reduce the need for recalibration. This dissertation will consider new approaches to nonlinear NUC such as higher order polynomials and exponentials. More specifically, a new gain equalization algorithm has been developed. The various nonlinear non-uniformity correction algorithms will be compared with common linear non-uniformity correction algorithms. Performance will be compared based on RMS errors, residual non-uniformity, and the impact quantization has on correction. Performance will be improved by identifying and replacing bad pixels prior to correction. Two bad pixel identification and replacement techniques will be investigated and compared. Performance will be presented in the form of simulation results as well as before and after images taken with short wave infrared cameras. The initial results show, using a third order

Numerical Methods for Forward and Inverse Problems in Discontinuous Media

Energy Technology Data Exchange (ETDEWEB)

Chartier, Timothy P.

2011-03-08

The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise to medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.

Use of a multigrid technique to study effects of limited sampling of heterogeneity on transport prediction

International Nuclear Information System (INIS)

Cole, C.R.; Foote, H.P.

1987-02-01

Reliable ground water transport prediction requires accurate spatial and temporal characterization of a hydrogeologic system. However, cost constraints and the desire to maintain site integrity by minimizing drilling can restrict the amount of spatial sampling that can be obtained to resolve the flow parameter variability associated with heterogeneities. This study quantifies the errors in subsurface transport predictions resulting from incomplete characterization of hydraulic conductivity heterogeneity. A multigrid technique was used to simulate two-dimensional flow velocity fields with high resolution. To obtain these velocity fields, the finite difference code MGRID, which implements a multigrid solution technique, was applied to compute stream functions on a 256-by-256 grid for a variety of hypothetical systems having detailed distributions of hydraulic conductivity. Spatial variability in hydraulic conductivity distributions was characterized by the components in the spectrum of spatial frequencies. A low-pass spatial filtering technique was applied to the base case hydraulic conductivity distribution to produce a data set with lower spatial frequency content. Arrival time curves were then calculated for filtered hydraulic conductivity distribution and compared to base case results to judge the relative importance of the higher spatial frequency components. Results indicate a progression from multimode to single-mode arrival time curves as the number and extent of distinct flow pathways are reduced by low-pass filtering. This relationship between transport predictions and spatial frequencies was used to judge the consequences of sampling the hydraulic conductivity with reduced spatial resolution. 22 refs., 17 figs

Parameter Estimation and Prediction of a Nonlinear Storage Model: an algebraic approach

NARCIS (Netherlands)

Doeswijk, T.G.; Keesman, K.J.

2005-01-01

Generally, parameters that are nonlinear in system models are estimated by nonlinear least-squares optimization algorithms. In this paper, if a nonlinear discrete-time model with a polynomial quotient structure in input, output, and parameters, a method is proposed to re-parameterize the model such

Nonlinear Vibration Signal Tracking of Large Offshore Bridge Stayed Cable Based on Particle Filter

Directory of Open Access Journals (Sweden)

Ye Qingwei

2015-12-01

Full Text Available The stayed cables are key stress components of large offshore bridge. The fault detection of stayed cable is very important for safe of large offshore bridge. A particle filter model and algorithm of nonlinear vibration signal are used in this paper. Firstly, the particle filter model of stayed cable of large offshore bridge is created. Nonlinear dynamic model of the stayed-cable and beam coupling system is dispersed in temporal dimension by using the finite difference method. The discrete nonlinear vibration equations of any cable element are worked out. Secondly, a state equation of particle filter is fitted by least square algorithm from the discrete nonlinear vibration equations. So the particle filter algorithm can use the accurate state equations. Finally, the particle filter algorithm is used to filter the vibration signal of bridge stayed cable. According to the particle filter, the de-noised vibration signal can be tracked and be predicted for a short time accurately. Many experiments are done at some actual bridges. The simulation experiments and the actual experiments on the bridge stayed cables are all indicating that the particle filter algorithm in this paper has good performance and works stably.

TAO-robust backpropagation learning algorithm.

Science.gov (United States)

Pernía-Espinoza, Alpha V; Ordieres-Meré, Joaquín B; Martínez-de-Pisón, Francisco J; González-Marcos, Ana

2005-03-01

In several fields, as industrial modelling, multilayer feedforward neural networks are often used as universal function approximations. These supervised neural networks are commonly trained by a traditional backpropagation learning format, which minimises the mean squared error (mse) of the training data. However, in the presence of corrupted data (outliers) this training scheme may produce wrong models. We combine the benefits of the non-linear regression model tau-estimates [introduced by Tabatabai, M. A. Argyros, I. K. Robust Estimation and testing for general nonlinear regression models. Applied Mathematics and Computation. 58 (1993) 85-101] with the backpropagation algorithm to produce the TAO-robust learning algorithm, in order to deal with the problems of modelling with outliers. The cost function of this approach has a bounded influence function given by the weighted average of two psi functions, one corresponding to a very robust estimate and the other to a highly efficient estimate. The advantages of the proposed algorithm are studied with an example.

Recent advances in multiparametric nonlinear programming

KAUST Repository

Domí nguez, Luis F.; Narciso, Diogo A.; Pistikopoulos, Efstratios N.

2010-01-01

In this paper, we present recent developments in multiparametric nonlinear programming. For the case of convex problems, we highlight key issues regarding the full characterization of the parametric solution space and we discuss, through an illustrative example problem, four alternative state-of-the-art multiparametric nonlinear programming algorithms. We also identify a number of main challenges for the non-convex case and highlight future research directions. © 2009 Elsevier Ltd. All rights reserved.

Recent advances in multiparametric nonlinear programming

KAUST Repository

Domínguez, Luis F.

2010-05-01

In this paper, we present recent developments in multiparametric nonlinear programming. For the case of convex problems, we highlight key issues regarding the full characterization of the parametric solution space and we discuss, through an illustrative example problem, four alternative state-of-the-art multiparametric nonlinear programming algorithms. We also identify a number of main challenges for the non-convex case and highlight future research directions. © 2009 Elsevier Ltd. All rights reserved.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

Science.gov (United States)

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

Nonlinear dynamics of structures

CERN Document Server

Oller, Sergio

2014-01-01

This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics.   This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects.   Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution  are studied, and the theoretical concepts and its programming algorithms are presented.  

Introduction to nonlinear finite element analysis

CERN Document Server

Kim, Nam-Ho

2015-01-01

This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: ·         Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems ·         Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory ·    ...

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

Energy Technology Data Exchange (ETDEWEB)

Sandhu, Rimple [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Poirel, Dominique [Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario (Canada); Pettit, Chris [Department of Aerospace Engineering, United States Naval Academy, Annapolis, MD (United States); Khalil, Mohammad [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada)

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.

Multi-frequency Defect Selective Imaging via Nonlinear Ultrasound

Science.gov (United States)

Solodov, Igor; Busse, Gerd

The concept of defect-selective ultrasonic nonlinear imaging is based on visualization of strongly nonlinear inclusions in the form of localized cracked defects. For intense excitation, the ultrasonic response of defects is affected by mechanical constraint between their fragments that makes their vibrations extremely nonlinear. The cracked flaws, therefore, efficiently generate multiple new frequencies, which can be used as a nonlinear "tag" to detect and image them. In this paper, the methodologies of nonlinear scanning laser vibrometry (NSLV) and nonlinear air-coupled emission (NACE) are applied for nonlinear imaging of various defects in hi-tech and constructional materials. A broad database obtained demonstrates evident advantages of the nonlinear approach over its linear counterpart. The higher-order nonlinear frequencies provide increase in signal-to-noise ratio and enhance the contrast of imaging. Unlike conventional ultrasonic instruments, the nonlinear approach yields abundant multi-frequency information on defect location. The application of image recognition and processing algorithms is described and shown to improve reliability and quality of ultrasonic imaging.

Nonlinear Control of Hydraulic Manipulator for Decommissioning Nuclear Reactor

Energy Technology Data Exchange (ETDEWEB)

Kim, Myoung-Ho; Lee, Sung-Uk; Kim, Chang-Hoi; Choi, Byung-Seon; Moon, Jei-Kwon [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2016-10-15

Robot technique is need to decommission nuclear reactor because of high radiation environment. Especially, Manipulator systems are useful for dismantling complex structure in a nuclear facility. In addition, Hydraulic system is applied to handle heavy duty object. Since hydraulic system can demonstrate high power. The manipulator with hydraulic power is already developed. To solve this problem, various nonlinear control method includes acceleration control. But, it is difficult because acceleration value is highly noisy. In this paper, the nonlinear control algorithm without acceleration control is studied. To verify, the hydraulic manipulator model had been developed. Furthermore, the numerical simulation is carried out. The nonlinear control without acceleration parameter method is developed for hydraulic manipulator. To verify control algorithm, the manipulator is modeled by MBD and the hydraulic servo system is also derived. In addition, the numerical simulation is also carried out. Especially, PID gain is determined though TDC algorithm. In the result of numerical simulation, tracking performance is good without acceleration control. Thus, the PID though TDC with SMC is good for hydraulic manipulator control.

Nonlinear Control of Hydraulic Manipulator for Decommissioning Nuclear Reactor

International Nuclear Information System (INIS)

Kim, Myoung-Ho; Lee, Sung-Uk; Kim, Chang-Hoi; Choi, Byung-Seon; Moon, Jei-Kwon

2016-01-01

Robot technique is need to decommission nuclear reactor because of high radiation environment. Especially, Manipulator systems are useful for dismantling complex structure in a nuclear facility. In addition, Hydraulic system is applied to handle heavy duty object. Since hydraulic system can demonstrate high power. The manipulator with hydraulic power is already developed. To solve this problem, various nonlinear control method includes acceleration control. But, it is difficult because acceleration value is highly noisy. In this paper, the nonlinear control algorithm without acceleration control is studied. To verify, the hydraulic manipulator model had been developed. Furthermore, the numerical simulation is carried out. The nonlinear control without acceleration parameter method is developed for hydraulic manipulator. To verify control algorithm, the manipulator is modeled by MBD and the hydraulic servo system is also derived. In addition, the numerical simulation is also carried out. Especially, PID gain is determined though TDC algorithm. In the result of numerical simulation, tracking performance is good without acceleration control. Thus, the PID though TDC with SMC is good for hydraulic manipulator control

Global Format for Conservative Time Integration in Nonlinear Dynamics

DEFF Research Database (Denmark)

Krenk, Steen

2014-01-01

The widely used classic collocation-based time integration procedures like Newmark, Generalized-alpha etc. generally work well within a framework of linear problems, but typically may encounter problems, when used in connection with essentially nonlinear structures. These problems are overcome....... In the present paper a conservative time integration algorithm is developed in a format using only the internal forces and the associated tangent stiffness at the specific time integration points. Thus, the procedure is computationally very similar to a collocation method, consisting of a series of nonlinear...... equivalent static load steps, easily implemented in existing computer codes. The paper considers two aspects: representation of nonlinear internal forces in a form that implies energy conservation, and the option of an algorithmic damping with the purpose of extracting energy from undesirable high...

3D inversion based on multi-grid approach of magnetotelluric data from Northern Scandinavia

Science.gov (United States)

Cherevatova, M.; Smirnov, M.; Korja, T. J.; Egbert, G. D.

2012-12-01

In this work we investigate the geoelectrical structure of the cratonic margin of Fennoscandian Shield by means of magnetotelluric (MT) measurements carried out in Northern Norway and Sweden during summer 2011-2012. The project Magnetotellurics in the Scandes (MaSca) focuses on the investigation of the crust, upper mantle and lithospheric structure in a transition zone from a stable Precambrian cratonic interior to a passive continental margin beneath the Caledonian Orogen and the Scandes Mountains in western Fennoscandia. Recent MT profiles in the central and southern Scandes indicated a large contrast in resistivity between Caledonides and Precambrian basement. The alum shales as a highly conductive layers between the resistive Precambrian basement and the overlying Caledonian nappes are revealed from this profiles. Additional measurements in the Northern Scandes were required. All together data from 60 synchronous long period (LMT) and about 200 broad band (BMT) sites were acquired. The array stretches from Lofoten and Bodo (Norway) in the west to Kiruna and Skeleftea (Sweden) in the east covering an area of 500x500 square kilometers. LMT sites were occupied for about two months, while most of the BMT sites were measured during one day. We have used new multi-grid approach for 3D electromagnetic (EM) inversion and modelling. Our approach is based on the OcTree discretization where the spatial domain is represented by rectangular cells, each of which might be subdivided (recursively) into eight sub-cells. In this simplified implementation the grid is refined only in the horizontal direction, uniformly in each vertical layer. Using multi-grid we manage to have a high grid resolution near the surface (for instance, to tackle with galvanic distortions) and lower resolution at greater depth as the EM fields decay in the Earth according to the diffusion equation. We also have a benefit in computational costs as number of unknowns decrease. The multi-grid forward

A hybrid Jaya algorithm for reliability-redundancy allocation problems

Science.gov (United States)

Ghavidel, Sahand; Azizivahed, Ali; Li, Li

2018-04-01

This article proposes an efficient improved hybrid Jaya algorithm based on time-varying acceleration coefficients (TVACs) and the learning phase introduced in teaching-learning-based optimization (TLBO), named the LJaya-TVAC algorithm, for solving various types of nonlinear mixed-integer reliability-redundancy allocation problems (RRAPs) and standard real-parameter test functions. RRAPs include series, series-parallel, complex (bridge) and overspeed protection systems. The search power of the proposed LJaya-TVAC algorithm for finding the optimal solutions is first tested on the standard real-parameter unimodal and multi-modal functions with dimensions of 30-100, and then tested on various types of nonlinear mixed-integer RRAPs. The results are compared with the original Jaya algorithm and the best results reported in the recent literature. The optimal results obtained with the proposed LJaya-TVAC algorithm provide evidence for its better and acceptable optimization performance compared to the original Jaya algorithm and other reported optimal results.

Hash function based on piecewise nonlinear chaotic map

International Nuclear Information System (INIS)

Akhavan, A.; Samsudin, A.; Akhshani, A.

2009-01-01

Chaos-based cryptography appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an algorithm for one-way hash function construction based on piecewise nonlinear chaotic map with a variant probability parameter is proposed. Also the proposed algorithm is an attempt to present a new chaotic hash function based on multithreaded programming. In this chaotic scheme, the message is connected to the chaotic map using probability parameter and other parameters of chaotic map such as control parameter and initial condition, so that the generated hash value is highly sensitive to the message. Simulation results indicate that the proposed algorithm presented several interesting features, such as high flexibility, good statistical properties, high key sensitivity and message sensitivity. These properties make the scheme a suitable choice for practical applications.

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

Science.gov (United States)

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

2016-01-15

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

Mathematics and computational methods development in U.S. department of energy-sponsored research (nuclear energy research initiative and nuclear engineering education research). 5. Analysis of Angular V-Cycle Multigrid Formulation for Three-Dimensional Discrete Ordinates Shielding Problems

International Nuclear Information System (INIS)

Kucukboyaci, Vefa; Haghighat, Alireza

2001-01-01

We have developed new angular multigrid formulations, including the Simplified Angular Multigrid (SAM), Nested Iteration (NI), and V-Cycle schemes, that are compatible with the parallel environment and the adaptive differencing strategy of the PENTRAN three-dimensional parallel S N code. Using the Fourier analysis method for an infinite, homogenous medium, we have investigated the effectiveness of the V-Cycle scheme for different problem parameters including scattering ratio, spatial differencing weights, quadrature order, and mesh size. We have further investigated the effectiveness of the new schemes for practical shielding applications such as the Kobayashi benchmark problem and the boiling water reactor core shroud problem. In this paper, we summarize the angular V-Cycle scheme implemented in the PENTRAN code, the Fourier Analysis of the V-Cycle scheme, and results of convergence analysis of the V-Cycle scheme using different problem parameters. The theoretical analysis reveals that the V-Cycle scheme is effective for a large range of scattering ratios and is insensitive to mesh size. Besides the theoretical analysis, we have applied the new angular multigrid schemes to shielding problems. In comparison to the standard PCR formulation, combinations of the new angular multigrid schemes and PCR (e.g., SAM+V-Cycle+PCR) have proved to be very effective for scattering ratios in a range of 0.6 to 0.9. (authors)

A predictor-corrector algorithm to estimate the fractional flow in oil-water models

International Nuclear Information System (INIS)

Savioli, Gabriela B; Berdaguer, Elena M Fernandez

2008-01-01

We introduce a predictor-corrector algorithm to estimate parameters in a nonlinear hyperbolic problem. It can be used to estimate the oil-fractional flow function from the Buckley-Leverett equation. The forward model is non-linear: the sought- for parameter is a function of the solution of the equation. Traditionally, the estimation of functions requires the selection of a fitting parametric model. The algorithm that we develop does not require a predetermined parameter model. Therefore, the estimation problem is carried out over a set of parameters which are functions. The algorithm is based on the linearization of the parameter-to-output mapping. This technique is new in the field of nonlinear estimation. It has the advantage of laying aside parametric models. The algorithm is iterative and is of predictor-corrector type. We present theoretical results on the inverse problem. We use synthetic data to test the new algorithm.

Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems

National Research Council Canada - National Science Library

Abramson, Mark A; Audet, Charles; Dennis, Jr, J. E

2004-01-01

.... This class combines and extends the Audet-Dennis Generalized Pattern Search (GPS) algorithms for bound constrained mixed variable optimization, and their GPS-filter algorithms for general nonlinear constraints...

The Volterra's integral equation theory for accelerator single-freedom nonlinear components

International Nuclear Information System (INIS)

Wang Sheng; Xie Xi

1996-01-01

The Volterra's integral equation equivalent to the dynamic equation of accelerator single-freedom nonlinear components is given, starting from which the transport operator of accelerator single-freedom nonlinear components and its inverse transport operator are obtained. Therefore, another algorithm for the expert system of the beam transport operator of accelerator single-freedom nonlinear components is developed

Mixed error compensation in a heterodyne interferometer using the iterated dual-EKF algorithm

International Nuclear Information System (INIS)

Lee, Woo Ram; Kim, Chang Rai; You, Kwan Ho

2010-01-01

The heterodyne laser interferometer has been widely used in the field of precise measurements. The limited measurement accuracy of a heterodyne laser interferometer arises from the periodic nonlinearity caused by non-ideal laser sources and imperfect optical components. In this paper, the iterated dual-EKF algorithm is used to compensate for the error caused by nonlinearity and external noise. With the iterated dual-EKF algorithm, the weight filter estimates the parameter uncertainties in the state equation caused by nonlinearity errors and has a high convergence rate of weight values due to the iteration process. To verify the performance of the proposed compensation algorithm, we present experimental results obtained by using the iterated dual-EKF algorithm and compare them with the results obtained by using a capacitance displacement sensor.

Mixed error compensation in a heterodyne interferometer using the iterated dual-EKF algorithm

Energy Technology Data Exchange (ETDEWEB)

Lee, Woo Ram; Kim, Chang Rai; You, Kwan Ho [Sungkyunkwan University, Suwon (Korea, Republic of)

2010-10-15

The heterodyne laser interferometer has been widely used in the field of precise measurements. The limited measurement accuracy of a heterodyne laser interferometer arises from the periodic nonlinearity caused by non-ideal laser sources and imperfect optical components. In this paper, the iterated dual-EKF algorithm is used to compensate for the error caused by nonlinearity and external noise. With the iterated dual-EKF algorithm, the weight filter estimates the parameter uncertainties in the state equation caused by nonlinearity errors and has a high convergence rate of weight values due to the iteration process. To verify the performance of the proposed compensation algorithm, we present experimental results obtained by using the iterated dual-EKF algorithm and compare them with the results obtained by using a capacitance displacement sensor.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

Directory of Open Access Journals (Sweden)

Gonglin Yuan

Full Text Available Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1 βk ≥ 0 2 the search direction has the trust region property without the use of any line search method 3 the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

Recursive prediction error methods for online estimation in nonlinear state-space models

Directory of Open Access Journals (Sweden)

Dag Ljungquist

1994-04-01

Full Text Available Several recursive algorithms for online, combined state and parameter estimation in nonlinear state-space models are discussed in this paper. Well-known algorithms such as the extended Kalman filter and alternative formulations of the recursive prediction error method are included, as well as a new method based on a line-search strategy. A comparison of the algorithms illustrates that they are very similar although the differences can be important for the online tracking capabilities and robustness. Simulation experiments on a simple nonlinear process show that the performance under certain conditions can be improved by including a line-search strategy.

A Formally Verified Conflict Detection Algorithm for Polynomial Trajectories

Science.gov (United States)

Narkawicz, Anthony; Munoz, Cesar

2015-01-01

In air traffic management, conflict detection algorithms are used to determine whether or not aircraft are predicted to lose horizontal and vertical separation minima within a time interval assuming a trajectory model. In the case of linear trajectories, conflict detection algorithms have been proposed that are both sound, i.e., they detect all conflicts, and complete, i.e., they do not present false alarms. In general, for arbitrary nonlinear trajectory models, it is possible to define detection algorithms that are either sound or complete, but not both. This paper considers the case of nonlinear aircraft trajectory models based on polynomial functions. In particular, it proposes a conflict detection algorithm that precisely determines whether, given a lookahead time, two aircraft flying polynomial trajectories are in conflict. That is, it has been formally verified that, assuming that the aircraft trajectories are modeled as polynomial functions, the proposed algorithm is both sound and complete.

Compact and accurate linear and nonlinear autoregressive moving average model parameter estimation using laguerre functions

DEFF Research Database (Denmark)

Chon, K H; Cohen, R J; Holstein-Rathlou, N H

1997-01-01

A linear and nonlinear autoregressive moving average (ARMA) identification algorithm is developed for modeling time series data. The algorithm uses Laguerre expansion of kernals (LEK) to estimate Volterra-Wiener kernals. However, instead of estimating linear and nonlinear system dynamics via moving...... average models, as is the case for the Volterra-Wiener analysis, we propose an ARMA model-based approach. The proposed algorithm is essentially the same as LEK, but this algorithm is extended to include past values of the output as well. Thus, all of the advantages associated with using the Laguerre...

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

International Nuclear Information System (INIS)

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

2013-01-01

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

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

DEFF Research Database (Denmark)

Boiroux, Dimitri; Hagdrup, Morten; Mahmoudi, Zeinab

2016-01-01

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

Inferring nonlinear gene regulatory networks from gene expression data based on distance correlation.

Directory of Open Access Journals (Sweden)

Xiaobo Guo

Full Text Available Nonlinear dependence is general in regulation mechanism of gene regulatory networks (GRNs. It is vital to properly measure or test nonlinear dependence from real data for reconstructing GRNs and understanding the complex regulatory mechanisms within the cellular system. A recently developed measurement called the distance correlation (DC has been shown powerful and computationally effective in nonlinear dependence for many situations. In this work, we incorporate the DC into inferring GRNs from the gene expression data without any underling distribution assumptions. We propose three DC-based GRNs inference algorithms: CLR-DC, MRNET-DC and REL-DC, and then compare them with the mutual information (MI-based algorithms by analyzing two simulated data: benchmark GRNs from the DREAM challenge and GRNs generated by SynTReN network generator, and an experimentally determined SOS DNA repair network in Escherichia coli. According to both the receiver operator characteristic (ROC curve and the precision-recall (PR curve, our proposed algorithms significantly outperform the MI-based algorithms in GRNs inference.

Nonlinear Algorithms for Channel Equalization and Map Symbol Detection.

Science.gov (United States)

Giridhar, K.

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

Controller Design of Complex System Based on Nonlinear Strength

Directory of Open Access Journals (Sweden)

Rongjun Mu

2015-01-01

Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schroedinger Equation

International Nuclear Information System (INIS)

Yang Qin; Dai Chaoqing; Zhang Jiefang

2005-01-01

Some new exact travelling wave and period solutions of discrete nonlinear Schroedinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.

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

Directory of Open Access Journals (Sweden)

Ming Dong

2010-01-01

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

FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE) NONLINEAR CALCULATIONS OF PLATES AND SHELLS

OpenAIRE

Bazhenov V.A.; Sacharov A.S.; Guliar A. I.; Pyskunov S.O.; Maksymiuk Y.V.

2014-01-01

Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

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

Directory of Open Access Journals (Sweden)

Chouaib Labiod

2017-01-01

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

Numerical study of propagation properties of surface plasmon polaritons in nonlinear media

KAUST Repository

Sagor, Rakibul Hasan; Ghulam Saber, Md.; Alsunaidi, Mohammad

2016-01-01

We present a time-domain algorithm for simulating nonlinear propagation of surface plasmon polaritons (SPPs) in chalcogenide glass. Due to the high non-linearity property and strong dispersion and confinement chalcogenide glasses are widely known

Optimization of Straight Cylindrical Turning Using Artificial Bee Colony (ABC) Algorithm

Science.gov (United States)

Prasanth, Rajanampalli Seshasai Srinivasa; Hans Raj, Kandikonda

2017-04-01

Artificial bee colony (ABC) algorithm, that mimics the intelligent foraging behavior of honey bees, is increasingly gaining acceptance in the field of process optimization, as it is capable of handling nonlinearity, complexity and uncertainty. Straight cylindrical turning is a complex and nonlinear machining process which involves the selection of appropriate cutting parameters that affect the quality of the workpiece. This paper presents the estimation of optimal cutting parameters of the straight cylindrical turning process using the ABC algorithm. The ABC algorithm is first tested on four benchmark problems of numerical optimization and its performance is compared with genetic algorithm (GA) and ant colony optimization (ACO) algorithm. Results indicate that, the rate of convergence of ABC algorithm is better than GA and ACO. Then, the ABC algorithm is used to predict optimal cutting parameters such as cutting speed, feed rate, depth of cut and tool nose radius to achieve good surface finish. Results indicate that, the ABC algorithm estimated a comparable surface finish when compared with real coded genetic algorithm and differential evolution algorithm.

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

Science.gov (United States)

El-Qulity, Said Ali; Mohamed, Ali Wagdy

2016-01-01

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

Conference on High Performance Software for Nonlinear Optimization

CERN Document Server

Murli, Almerico; Pardalos, Panos; Toraldo, Gerardo

1998-01-01

This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSN097) which was held in Ischia, Italy, in June 1997. The rapid progress of computer technologies, including new parallel architec­ tures, has stimulated a large amount of research devoted to building software environments and defining algorithms able to fully exploit this new computa­ tional power. In some sense, numerical analysis has to conform itself to the new tools. The impact of parallel computing in nonlinear optimization, which had a slow start at the beginning, seems now to increase at a fast rate, and it is reasonable to expect an even greater acceleration in the future. As with the first HPSNO conference, the goal of the HPSN097 conference was to supply a broad overview of the more recent developments and trends in nonlinear optimization, emphasizing the algorithmic and high performance software aspects. Bringing together new computational methodologies with theoretical...

A different approach to estimate nonlinear regression model using numerical methods

Science.gov (United States)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

On some Aitken-like acceleration of the Schwarz method

Science.gov (United States)

Garbey, M.; Tromeur-Dervout, D.

2002-12-01

In this paper we present a family of domain decomposition based on Aitken-like acceleration of the Schwarz method seen as an iterative procedure with a linear rate of convergence. We first present the so-called Aitken-Schwarz procedure for linear differential operators. The solver can be a direct solver when applied to the Helmholtz problem with five-point finite difference scheme on regular grids. We then introduce the Steffensen-Schwarz variant which is an iterative domain decomposition solver that can be applied to linear and nonlinear problems. We show that these solvers have reasonable numerical efficiency compared to classical fast solvers for the Poisson problem or multigrids for more general linear and nonlinear elliptic problems. However, the salient feature of our method is that our algorithm has high tolerance to slow network in the context of distributed parallel computing and is attractive, generally speaking, to use with computer architecture for which performance is limited by the memory bandwidth rather than the flop performance of the CPU. This is nowadays the case for most parallel. computer using the RISC processor architecture. We will illustrate this highly desirable property of our algorithm with large-scale computing experiments.

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.

Chaotic particle swarm optimization algorithm in a support vector regression electric load forecasting model

International Nuclear Information System (INIS)

Hong, W.-C.

2009-01-01

Accurate forecasting of electric load has always been the most important issues in the electricity industry, particularly for developing countries. Due to the various influences, electric load forecasting reveals highly nonlinear characteristics. Recently, support vector regression (SVR), with nonlinear mapping capabilities of forecasting, has been successfully employed to solve nonlinear regression and time series problems. However, it is still lack of systematic approaches to determine appropriate parameter combination for a SVR model. This investigation elucidates the feasibility of applying chaotic particle swarm optimization (CPSO) algorithm to choose the suitable parameter combination for a SVR model. The empirical results reveal that the proposed model outperforms the other two models applying other algorithms, genetic algorithm (GA) and simulated annealing algorithm (SA). Finally, it also provides the theoretical exploration of the electric load forecasting support system (ELFSS)

Sparse Nonlinear Electromagnetic Imaging Accelerated With Projected Steepest Descent Algorithm

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2017-01-01

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

Nonlinear Multiantenna Detection Methods

Directory of Open Access Journals (Sweden)

Chen Sheng

2004-01-01

Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.

A Novel Real-coded Quantum-inspired Genetic Algorithm and Its Application in Data Reconciliation

Directory of Open Access Journals (Sweden)

Gao Lin

2012-06-01

Full Text Available Traditional quantum-inspired genetic algorithm (QGA has drawbacks such as premature convergence, heavy computational cost, complicated coding and decoding process etc. In this paper, a novel real-coded quantum-inspired genetic algorithm is proposed based on interval division thinking. Detailed comparisons with some similar approaches for some standard benchmark functions test validity of the proposed algorithm. Besides, the proposed algorithm is used in two typical nonlinear data reconciliation problems (distilling process and extraction process and simulation results show its efficiency in nonlinear data reconciliation problems.

A chaos wolf optimization algorithm with self-adaptive variable step-size

Science.gov (United States)

Zhu, Yong; Jiang, Wanlu; Kong, Xiangdong; Quan, Lingxiao; Zhang, Yongshun

2017-10-01

To explore the problem of parameter optimization for complex nonlinear function, a chaos wolf optimization algorithm (CWOA) with self-adaptive variable step-size was proposed. The algorithm was based on the swarm intelligence of wolf pack, which fully simulated the predation behavior and prey distribution way of wolves. It possessed three intelligent behaviors such as migration, summons and siege. And the competition rule as "winner-take-all" and the update mechanism as "survival of the fittest" were also the characteristics of the algorithm. Moreover, it combined the strategies of self-adaptive variable step-size search and chaos optimization. The CWOA was utilized in parameter optimization of twelve typical and complex nonlinear functions. And the obtained results were compared with many existing algorithms, including the classical genetic algorithm, the particle swarm optimization algorithm and the leader wolf pack search algorithm. The investigation results indicate that CWOA possess preferable optimization ability. There are advantages in optimization accuracy and convergence rate. Furthermore, it demonstrates high robustness and global searching ability.

Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.

Energy Technology Data Exchange (ETDEWEB)

Preston, Leiph [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-08-01

Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti) by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.

Nonlinear closed-loop control theory

International Nuclear Information System (INIS)

Perez, R.B.; Otaduy, P.J.; Abdalla, M.

1992-01-01

Traditionally, the control of nuclear power plants has been implemented by the use of proportional-integral (PI) control systems. PI controllers are both simple and, within their calibration range, highly reliable. However, PIs provide little performance information that could be used to diagnose out-of-range events or the nature of unanticipated transients that may occur in the plant. To go beyond the PI controller, the new control algorithms must deal with the physical system nonlinearities and with the reality of uncertain dynamics terms in its mathematical model. The tool to develop a new kind of control algorithm is provided by Optimal Control Theory. In this theory, a norm is minimized which incorporates the constraint that the model equations should be satisfied at all times by means of the Lagrange multipliers. Optimal control algorithms consist of two sets of coupled equations: (1) the model equations, integrated forward in time; and (2) the equations for the Lagrange multipliers (adjoints), integrated backwards in time. There are two challenges: dealing with large sets of coupled nonlinear equations and with a two-point boundary value problem that must be solved iteratively. In this paper, the rigorous conversion of the two-point boundary value problem into an initial value problem is presented. In addition, the incorporation into the control algorithm of ''real world'' constraints such as sensors and actuators, dynamic response functions and time lags introduced by the digitalization of analog signals is presented. (Author)

FEATURES APPLICATION CIRCUIT MOMENT FINITE ELEMENT (MSSE NONLINEAR CALCULATIONS OF PLATES AND SHELLS

Directory of Open Access Journals (Sweden)

Bazhenov V.A.

2014-06-01

Full Text Available Based MSSE created shell CE general type, which allows you to analyze the stress-strain state of axisymmetrical shells and plates in problems of physical and geometric nonlinearity. The principal nonlinear elasticity theory, algorithms for solving systems of nonlinear equations for determining the temperature and plastic deformation.

Localization of Non-Linearly Modeled Autonomous Mobile Robots Using Out-of-Sequence Measurements

Directory of Open Access Journals (Sweden)

Jesus M. de la Cruz

2012-02-01

Full Text Available This paper presents a state of the art of the estimation algorithms dealing with Out-of-Sequence (OOS measurements for non-linearly modeled systems. The state of the art includes a critical analysis of the algorithm properties that takes into account the applicability of these techniques to autonomous mobile robot navigation based on the fusion of the measurements provided, delayed and OOS, by multiple sensors. Besides, it shows a representative example of the use of one of the most computationally efficient approaches in the localization module of the control software of a real robot (which has non-linear dynamics, and linear and non-linear sensors and compares its performance against other approaches. The simulated results obtained with the selected OOS algorithm shows the computational requirements that each sensor of the robot imposes to it. The real experiments show how the inclusion of the selected OOS algorithm in the control software lets the robot successfully navigate in spite of receiving many OOS measurements. Finally, the comparison highlights that not only is the selected OOS algorithm among the best performing ones of the comparison, but it also has the lowest computational and memory cost.

Modeling of memristor-based chaotic systems using nonlinear Wiener adaptive filters based on backslash operator

International Nuclear Information System (INIS)

Zhao, Yibo; Jiang, Yi; Feng, Jiuchao; Wu, Lifu

2016-01-01

Highlights: • A novel nonlinear Wiener adaptive filters based on the backslash operator are proposed. • The identification approach to the memristor-based chaotic systems using the proposed adaptive filters. • The weight update algorithm and convergence characteristics for the proposed adaptive filters are derived. - Abstract: Memristor-based chaotic systems have complex dynamical behaviors, which are characterized as nonlinear and hysteresis characteristics. Modeling and identification of their nonlinear model is an important premise for analyzing the dynamical behavior of the memristor-based chaotic systems. This paper presents a novel nonlinear Wiener adaptive filtering identification approach to the memristor-based chaotic systems. The linear part of Wiener model consists of the linear transversal adaptive filters, the nonlinear part consists of nonlinear adaptive filters based on the backslash operator for the hysteresis characteristics of the memristor. The weight update algorithms for the linear and nonlinear adaptive filters are derived. Final computer simulation results show the effectiveness as well as fast convergence characteristics. Comparing with the adaptive nonlinear polynomial filters, the proposed nonlinear adaptive filters have less identification error.

On the efficiency of chaos optimization algorithms for global optimization

International Nuclear Information System (INIS)

Yang Dixiong; Li Gang; Cheng Gengdong

2007-01-01

Chaos optimization algorithms as a novel method of global optimization have attracted much attention, which were all based on Logistic map. However, we have noticed that the probability density function of the chaotic sequences derived from Logistic map is a Chebyshev-type one, which may affect the global searching capacity and computational efficiency of chaos optimization algorithms considerably. Considering the statistical property of the chaotic sequences of Logistic map and Kent map, the improved hybrid chaos-BFGS optimization algorithm and the Kent map based hybrid chaos-BFGS algorithm are proposed. Five typical nonlinear functions with multimodal characteristic are tested to compare the performance of five hybrid optimization algorithms, which are the conventional Logistic map based chaos-BFGS algorithm, improved Logistic map based chaos-BFGS algorithm, Kent map based chaos-BFGS algorithm, Monte Carlo-BFGS algorithm, mesh-BFGS algorithm. The computational performance of the five algorithms is compared, and the numerical results make us question the high efficiency of the chaos optimization algorithms claimed in some references. It is concluded that the efficiency of the hybrid optimization algorithms is influenced by the statistical property of chaotic/stochastic sequences generated from chaotic/stochastic algorithms, and the location of the global optimum of nonlinear functions. In addition, it is inappropriate to advocate the high efficiency of the global optimization algorithms only depending on several numerical examples of low-dimensional functions

Supersonic Turbulent Fuel-Air Mixing and Evaporation

National Research Council Canada - National Science Library

Moukalled, Fadi

2003-01-01

.... The convergence rate will be accelerated using a full non-linear multi-grid method. The discretization will use a second order scheme for diffusion and a pseudo-third order bounded scheme for convection...

Algorithms for Brownian first-passage-time estimation

Science.gov (United States)

Adib, Artur B.

2009-09-01

A class of algorithms in discrete space and continuous time for Brownian first-passage-time estimation is considered. A simple algorithm is derived that yields exact mean first-passage times (MFPTs) for linear potentials in one dimension, regardless of the lattice spacing. When applied to nonlinear potentials and/or higher spatial dimensions, numerical evidence suggests that this algorithm yields MFPT estimates that either outperform or rival Langevin-based (discrete time and continuous space) estimates.

Evaluation of the performance of different firefly algorithms to the ...

African Journals Online (AJOL)

of firefly algorithms are applied to solve the nonlinear ELD problem. ... problem using those recent variants and the classical firefly algorithm for different test cases. Efficiency ...... International Journal of Machine. Learning and Computing, Vol.

Recent development of the Multi-Grid detector for large area neutron scattering instruments

International Nuclear Information System (INIS)

Guerard, Bruno

2015-01-01

Most of the Neutron Scattering facilities are committed in a continuous program of modernization of their instruments, requiring large area and high performance thermal neutron detectors. Beside scintillators detectors, 3 He detectors, like linear PSDs (Position Sensitive Detectors) and MWPCs (Multi-Wires Proportional Chambers), are the most current techniques nowadays. Time Of Flight instruments are using 3 He PSDs mounted side by side to cover tens of m 2 . As a result of the so-called ' 3 He shortage crisis , the volume of 3He which is needed to build one of these instruments is not accessible anymore. The development of alternative techniques requiring no 3He, has been given high priority to secure the future of neutron scattering instrumentation. This is particularly important in the context where the future ESS (European Spallation Source) will start its operation in 2019-2020. Improved scintillators represent one of the alternative techniques. Another one is the Multi-Grid introduced at the ILL in 2009. A Multi-Grid detector is composed of several independent modules of typically 0.8 m x 3 m sensitive area, mounted side by side in air or in a vacuum TOF chamber. One module is composed of segmented boron-lined proportional counters mounted in a gas vessel; the counters, of square section, are assembled with Aluminium grids electrically insulated and stacked together. This design provides two advantages: First, magnetron sputtering techniques can be used to coat B 4 C films on planar substrates, and second, the neutron position along the anode wires can be measured by reading out individually the grid signals with fast shaping amplifiers followed by comparators. Unlike charge division localisation in linear PSDs, the individual readout of the grids allows operating the Multi-Grid at a low amplification gain, hence this detector is tolerant to mechanical defects and its production accessible to laboratories equipped with standard equipment. Prototypes of

Recent development of the Multi-Grid detector for large area neutron scattering instruments

Energy Technology Data Exchange (ETDEWEB)

Guerard, Bruno [ILL-ESS-LiU collaboration, CRISP project, Institut Laue Langevin - ILL, Grenoble (France)

2015-07-01

Most of the Neutron Scattering facilities are committed in a continuous program of modernization of their instruments, requiring large area and high performance thermal neutron detectors. Beside scintillators detectors, {sup 3}He detectors, like linear PSDs (Position Sensitive Detectors) and MWPCs (Multi-Wires Proportional Chambers), are the most current techniques nowadays. Time Of Flight instruments are using {sup 3}He PSDs mounted side by side to cover tens of m{sup 2}. As a result of the so-called '{sup 3}He shortage crisis{sup ,} the volume of 3He which is needed to build one of these instruments is not accessible anymore. The development of alternative techniques requiring no 3He, has been given high priority to secure the future of neutron scattering instrumentation. This is particularly important in the context where the future ESS (European Spallation Source) will start its operation in 2019-2020. Improved scintillators represent one of the alternative techniques. Another one is the Multi-Grid introduced at the ILL in 2009. A Multi-Grid detector is composed of several independent modules of typically 0.8 m x 3 m sensitive area, mounted side by side in air or in a vacuum TOF chamber. One module is composed of segmented boron-lined proportional counters mounted in a gas vessel; the counters, of square section, are assembled with Aluminium grids electrically insulated and stacked together. This design provides two advantages: First, magnetron sputtering techniques can be used to coat B{sub 4}C films on planar substrates, and second, the neutron position along the anode wires can be measured by reading out individually the grid signals with fast shaping amplifiers followed by comparators. Unlike charge division localisation in linear PSDs, the individual readout of the grids allows operating the Multi-Grid at a low amplification gain, hence this detector is tolerant to mechanical defects and its production accessible to laboratories equipped with standard

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

Science.gov (United States)

Lee, C.

2013-12-01

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

Global format for energy-momentum based time integration in nonlinear dynamics

DEFF Research Database (Denmark)

Krenk, Steen

2014-01-01

A global format is developed for momentum and energy consistent time integration of second‐order dynamic systems with general nonlinear stiffness. The algorithm is formulated by integrating the state‐space equations of motion over the time increment. The internal force is first represented...... of mean value products at the element level or explicit use of a geometric stiffness matrix. An optional monotonic algorithmic damping, increasing with response frequency, is developed in terms of a single damping parameter. In the solution procedure, the velocity is eliminated and the nonlinear...

K-means-clustering-based fiber nonlinearity equalization techniques for 64-QAM coherent optical communication system.

Science.gov (United States)

Zhang, Junfeng; Chen, Wei; Gao, Mingyi; Shen, Gangxiang

2017-10-30

In this work, we proposed two k-means-clustering-based algorithms to mitigate the fiber nonlinearity for 64-quadrature amplitude modulation (64-QAM) signal, the training-sequence assisted k-means algorithm and the blind k-means algorithm. We experimentally demonstrated the proposed k-means-clustering-based fiber nonlinearity mitigation techniques in 75-Gb/s 64-QAM coherent optical communication system. The proposed algorithms have reduced clustering complexity and low data redundancy and they are able to quickly find appropriate initial centroids and select correctly the centroids of the clusters to obtain the global optimal solutions for large k value. We measured the bit-error-ratio (BER) performance of 64-QAM signal with different launched powers into the 50-km single mode fiber and the proposed techniques can greatly mitigate the signal impairments caused by the amplified spontaneous emission noise and the fiber Kerr nonlinearity and improve the BER performance.

Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

International Nuclear Information System (INIS)

Liu Chunliang; Xie Xi; Chen Yinbao

1991-01-01

The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

Prototype Implementation of Two Efficient Low-Complexity Digital Predistortion Algorithms

Directory of Open Access Journals (Sweden)

Timo I. Laakso

2008-01-01

Full Text Available Predistortion (PD lineariser for microwave power amplifiers (PAs is an important topic of research. With larger and larger bandwidth as it appears today in modern WiMax standards as well as in multichannel base stations for 3GPP standards, the relatively simple nonlinear effect of a PA becomes a complex memory-including function, severely distorting the output signal. In this contribution, two digital PD algorithms are investigated for the linearisation of microwave PAs in mobile communications. The first one is an efficient and low-complexity algorithm based on a memoryless model, called the simplicial canonical piecewise linear (SCPWL function that describes the static nonlinear characteristic of the PA. The second algorithm is more general, approximating the pre-inverse filter of a nonlinear PA iteratively using a Volterra model. The first simpler algorithm is suitable for compensation of amplitude compression and amplitude-to-phase conversion, for example, in mobile units with relatively small bandwidths. The second algorithm can be used to linearise PAs operating with larger bandwidths, thus exhibiting memory effects, for example, in multichannel base stations. A measurement testbed which includes a transmitter-receiver chain with a microwave PA is built for testing and prototyping of the proposed PD algorithms. In the testing phase, the PD algorithms are implemented using MATLAB (floating-point representation and tested in record-and-playback mode. The iterative PD algorithm is then implemented on a Field Programmable Gate Array (FPGA using fixed-point representation. The FPGA implementation allows the pre-inverse filter to be tested in a real-time mode. Measurement results show excellent linearisation capabilities of both the proposed algorithms in terms of adjacent channel power suppression. It is also shown that the fixed-point FPGA implementation of the iterative algorithm performs as well as the floating-point implementation.

Flutter analysis of an airfoil with multiple nonlinearities and uncertainties

Directory of Open Access Journals (Sweden)

Haitao Liao

2013-09-01

Full Text Available An original method for calculating the limit cycle oscillations of nonlinear aero-elastic system is presented. The problem of determining the maximum vibration amplitude of limit cycle is transformed into a nonlinear optimization problem. The harmonic balance method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated and used to analyse the limit cycle oscillations of an airfoil with multiple nonlinearities and uncertainties. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

SPP propagation in nonlinear glass-metal interface

KAUST Repository

Sagor, Rakibul Hasan; Alsunaidi, Mohammad A.; Ooi, Boon S.

2011-01-01

The non-linear propagation of Surface-Plasmon-Polaritons (SPP) in single interface of metal and chalcogenide glass (ChG) is considered. A time domain simulation algorithm is developed using the Finite Difference Time Domain (FDTD) method

Sparse calibration of subsurface flow models using nonlinear orthogonal matching pursuit and an iterative stochastic ensemble method

KAUST Repository

Elsheikh, Ahmed H.

2013-06-01

We introduce a nonlinear orthogonal matching pursuit (NOMP) for sparse calibration of subsurface flow models. 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 basis function with the residual from a large pool of basis functions. The discovered basis (aka support) is augmented across the nonlinear iterations. Once a set of basis functions are selected, the solution is obtained by applying Tikhonov regularization. The proposed algorithm relies on stochastically approximated gradient using an iterative stochastic ensemble method (ISEM). In the current study, the search space is parameterized using an overcomplete dictionary of basis functions built using the K-SVD algorithm. The proposed algorithm is the first ensemble based algorithm that tackels the sparse nonlinear parameter estimation problem. © 2013 Elsevier Ltd.

Explicit Nonlinear Model Predictive Control Theory and Applications

CERN Document Server

Grancharova, Alexandra

2012-01-01

Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø  Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...

Dynamic training algorithm for dynamic neural networks