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Heinlein, A. (author), Perego, Mauro (author), Rajamanickam, Sivasankaran (author)Numerical simulations of Greenland and Antarctic ice sheets involve the solution of largescale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of...journal article 2022
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Heinlein, A. (author), Rheinbach, Oliver (author), Röver, Friederike (author)The parallel performance of the threelevel fast and robust overlapping Schwarz (FROSch) preconditioners is investigated for linear elasticity. The FROSch framework is part of the Trilinos software library and contains a parallel implementation of different preconditioners with energy minimizing coarse spaces of generalized DryjaSmithWidlund...journal article 2022
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Liu, Runfei (author)Phase Retrieval Problem is very common and has a lot of applications in fields such as microscope, astronomy, crystallography, optical imaging etc.. In this problem, PSF and the pupil function are given, and the goal is to reconstruct the phase of the object. For camera which has 8 bits color depth, the maximum number of colors that can be...master thesis 2021
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Pouw, Dennis (author)In order to decrease the time that the viscousflow solver PARNASSOS needs to simulate shipgenerated waves, direct solvers are introduced in order to make the iterative solver used in PARNASSOS converge fastermaster thesis 2021
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Qiu, Yue (author), van Gijzen, M.B. (author), van Wingerden, J.W. (author), Verhaegen, M.H.G. (author), Vuik, Cornelis (author)In this article, we study preconditioning techniques for the control of the Navier–Stokes equation, where the control only acts on a few parts of the domain. Optimization, discretization, and linearization of the control problem results in a generalized linear saddlepoint system. The Schur complement for the generalized saddlepoint system...journal article 2021
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He, Xin (author), Vuik, Cornelis (author)This paper introduces three new Schur complement approximations for the augmented Lagrangian preconditioner. The incompressible NavierStokes equations discretized by a stabilized finite element method are utilized to evaluate these new approximations of the Schur complement. A wide range of numerical experiments in the laminar context...journal article 2020
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Buwalda, Floris (author)In the past 15 years the field of general purpose computing on graphics processing units, or GPUs, has become well developed and the practice is becoming more mainstream. Computational demands of simulation software are continuously increasing. As such for many applications traditionally computed on the central processing unit the question...master thesis 2020
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Horníková, Hana (author), Vuik, Cornelis (author), Egermaier, Jiří (author)We deal with numerical solution of the incompressible Navier–Stokes equations discretized using the isogeometric analysis (IgA) approach. Similarly to finite elements, the discretization leads to sparse nonsymmetric saddlepoint linear systems. The IgA discretization basis has several specific properties different from standard FEM basis,...journal article 2020
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Baumann, M.M. (author), van Gijzen, M.B. (author)We consider wave propagation problems that are modeled in the frequencydomain, and that need to be solved simultaneously for multiple frequencies within a fixed range. For this, a single shiftandinvert preconditioner at a socalled seed frequency is applied. The choice of the seed is crucial for the performance of preconditioned multi...journal article 2019
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Qiu, Y. (author), van Gijzen, M.B. (author), van Wingerden, J.W. (author), Verhaegen, M.H.G. (author), Vuik, Cornelis (author)This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations in computational fluid dynamics problems. This preconditioning technique exploits the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a datasparse way to...journal article 2018
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He, X. (author), Vuik, Cornelis (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 NavierStokes 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 shiftandinvert 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 largescale 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 finitedimensional 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 lowrank offdiagonal structure, which allows the matrixmatrix 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 indomain control of the NavierStokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal indomain control problem results in a generalized linear saddlepoint 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 largescale 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 finitedimensional 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 indomain control of the NavierStokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal indomain control problem results in a generalized linear saddlepoint 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 PDEconstrained optimization problems. The underlying problems yield a linear saddlepoint 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 saddlepoint...report 2014