Searched for: subject:"preconditioners"
(1 - 20 of 44)

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He, X. (author), Vuik, C. (author), Klaij, Christiaan M. (author)
The augmented Lagrangian (AL) preconditioner and its variant have been successfully applied to solve saddle point systems arising from the incompressible Navier-Stokes equations discretized by the finite element method. Attractive features are the purely algebraic construction and robustness with respect to the Reynolds number and mesh renement....
journal article 2018
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Baumann, M.M. (author), van Gijzen, M.B. (author)
In this paper we present a comparison study for three different iterative Krylov methods that we have recently developed for the simultaneous numerical solution of wave propagation problems at multiple frequencies. The three approaches have in common that they require the application of a single shift-and-invert preconditioner at a suitable seed...
conference paper 2017
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Astudillo Rengifo, R.A. (author), van Gijzen, M.B. (author)
This paper discusses the solution of large-scale linear matrix equations using the Induced Dimension reduction method (IDR(s)). IDR(s) was originally presented to solve system of linear equations, and is based on the IDR(s) theorem. We generalize the IDR(s) theorem to solve linear problems in any finite-dimensional space. This generalization...
journal article 2016
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Qiu, Y. (author), van Gijzen, M.B. (author), van Wingerden, J.W. (author), Verhaegen, M. (author), Vuik, C. (author)
Multilevel sequentially semiseparable (MSSS) matrices form a class of structured matrices that have low-rank off-diagonal structure, which allows the matrix-matrix operations to be performed in linear computational complexity. MSSS preconditioners are computed by replacing the Schur complements in the block LU factorization of the global linear...
report 2015
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Qiu, Y. (author), Van Gijzen, M.B. (author), Van Wingerden, J.W. (author), Verhaegen, M.H.G. (author), Vuik, C. (author)
In this manuscript, we study preconditioning techniques for optimal in-domain control of the Navier-Stokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal in-domain control problem results in a generalized linear saddle-point system. The Schur complement for the generalized saddle...
report 2015
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Astudillo, R. (author), Van Gijzen, M.B. (author)
This paper discusses the solution of large-scale linear matrix equations using the Induced Dimension reduction method (IDR(s)). IDR(s) was originally presented to solve system of linear equations, and is based on the IDR(s) theorem. We generalize the IDR(s) theorem to solve linear problems in any finite-dimensional space. This generalization...
report 2015
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Qiu, Y. (author), Van Gijzen, M.B. (author), Van Wingerden, J.W. (author), Verhaegen, M. (author), Vuik, C. (author)
In this manuscript, we study preconditioning techniques for optimal in-domain control of the Navier-Stokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal in-domain control problem results in a generalized linear saddle-point system. The Schur complement for the generalized saddle...
report 2015
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Knibbe, H.P. (author)
The oil and gas industry makes use of computational intensive algorithms to provide an image of the subsurface. The image is obtained by sending wave energy into the subsurface and recording the signal required for a seismic wave to reflect back to the surface from the Earth interfaces that may have different physical properties. A seismic wave...
doctoral thesis 2015
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Zhao, J. (author), Vollebregt, E.A.H. (author), Oosterlee, C.W. (author)
This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from a 3D frictional contact problem. It incorporates an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar coordinate system, and use azimuth angles as...
report 2014
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Qiu, Y. (author), Van Gijzen, M.B. (author), Van Wingerden, J.W. (author), Verhaegen, M. (author), Vuik, C. (author)
In this paper, we consider preconditioning for PDE-constrained optimization problems. The underlying problems yield a linear saddle-point system. We study a class of preconditioners based on multilevel sequentially semiseparable (MSSS) matrix computations. The novel global preconditioner is to make use of the global structure of the saddle-point...
report 2014
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Qiu, Y. (author), Van Gijzen, M.B. (author), Van Wingerden, J. (author), Verhaegen, M. (author), Vuik, C. (author)
This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations (PDEs) in computational fluid dynamics (CFD), which exploit the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a data-sparse way to approximate the LU...
report 2013
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He, X. (author), Vuik, C. (author)
In this report we explore the performance of the SIMPLER , augmented Lagrangian, ’grad-div’ preconditioners and their variants for the two-by-two block systems arising in the incompressible Navier-Stokes equations. The lid-driven cavity and flow over a finite flat plate are chosen as the benchmark problems. For each problem Reynolds number...
report 2013
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Qiu, Y. (author), Van Gijzen, M.B. (author), Van Winderden, J.W. (author), Verhaegen, M.H.G. (author)
This paper presents a class of preconditioners for sparse systems arising from discretized partial differential equations (PDEs). In this class of preconditioners, we exploit the multilevel sequentially semiseparable (MSSS) structure of the system matrix. The off-diagonal blocks of MSSS matrices are of low-rank, which enables fast computations...
conference paper 2013
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Echeverria Serur, C. (author)
This thesis approaches the solution of the linearized finite element discretization of the Navier-Stokes operator matrix via the use of Krylov subspace methods preconditioned by SIMPLE-type pre conditioners aided by deflation. It includes an explanation of the theoretical setting of the problem as well as a collection of numerical experiments...
master thesis 2013
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He, X. (author), Neytcheva, M. (author), Vuik, C. (author)
This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the finite element method and...
report 2013
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Jönsthövel, T.B. (author), Van Gijzen, M.B. (author), Vuik, C. (author), Scarpas, A. (author)
Large discontinuities in material properties, such as those encountered in composite materials, lead to ill-conditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the preconditioned conjugate gradient method. This paper...
journal article 2013
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Diao, H. (author)
This thesis attempts to explain the convergence behaviour of solving Helmholtz problem by investigating its spectral properties. Fourier analysis is employ to solve the eigenvalues of the matrices that are involved in the iterative methods. The numerical experiment is conducted to verify the conclusions by Fourier analysis and also to reveal...
master thesis 2012
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Van Zwieten, J.S.B. (author)
master thesis 2012
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Jönsthövel, T.B. (author), Van Gijzen, M.B. (author), MacLachlan, S. (author), Vuik, C. (author), Scarpas, A. (author)
Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms....
journal article 2012
document
Van de Sande, G.E.M. (author)
master thesis 2012
Searched for: subject:"preconditioners"
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