Several Ways to Achieve Robustness When Solving Wave Propagation Problems

Bootland, Niall; Dolean, Victorita; Jolivet, Pierre; Nataf, Frédéric; Operto, S.; Tournier, Pierre-Henri

doi:10.1007/978-3-030-95025-5_2

Domain Decomposition Methods in Science and Engineering XXVI

2022

DOI: 10.1007/978-3-030-95025-5_2

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Several Ways to Achieve Robustness When Solving Wave Propagation Problems

Niall Bootland

Victorita Dolean

Pierre Jolivet

et al.

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“…For example, spectral coarse spaces for least squares problems and symmetric indefinite saddlepoint systems were proposed in [5,39], where coarse spaces are proposed for related Hermitian positive definite matrices. An exciting new development is that a number of multigrid methods and spectral coarse spaces have been suggested for problems with indefinite or non-self-adjoint operators [9,10,11,12,13,14,22,36,37]. These coarse spaces are mainly based on heuristics and show efficiency on several challenging model problems arising from discretized PDEs.…”

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confidence: 99%

Efficient Algebraic Two-Level Schwarz Preconditioner for Sparse Matrices

Daas

Jolivet²,

Rees

2023

SIAM J. Sci. Comput.

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Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for positive definite self-adjoint operators, spectral coarse spaces have been proposed in the past few years for indefinite and non-self-adjoint operators. This paper presents a new spectral coarse space that can be constructed in a fully-algebraic way, unlike most existing spectral coarse spaces. We present a theoretical convergence result for Hermitian positive definite diagonally dominant matrices. Numerical experiments and comparisons against state-of-the-art preconditioners in the multigrid community show that the resulting two-level Schwarz preconditioner is efficient , especially for non-self-adjoint operators. Furthermore, in this case, our proposed preconditioner outperforms state-of-the-art preconditioners.

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confidence: 99%

Efficient Algebraic Two-Level Schwarz Preconditioner for Sparse Matrices

Daas

Jolivet²,

Rees

2023

SIAM J. Sci. Comput.

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Several Ways to Achieve Robustness When Solving Wave Propagation Problems

Cited by 1 publication

References 18 publications

Efficient Algebraic Two-Level Schwarz Preconditioner for Sparse Matrices

Efficient Algebraic Two-Level Schwarz Preconditioner for Sparse Matrices

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