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arXiv · 2201.02250

Efficient Algebraic Two-Level Schwarz Preconditioner For Sparse Matrices

Hussam Al Daas·Pierre Jolivet·Tyrone Rees
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Abstract

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 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 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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Hussam Al Daas, Pierre Jolivet, Tyrone Rees. 2022-01-06. Efficient Algebraic Two-Level Schwarz Preconditioner For Sparse Matrices. https://arxiv.org/abs/2201.02250

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