Efficient Algebraic Two-Level Schwarz Preconditioner for Sparse Matrices
Hussam Al Daas, Pierre Jolivet, Tyrone Rees · SIAM Journal on Scientific Computing · 2023
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 results for Hermitian positive definite diagonally dominant matrices. Numerical experiments and comparison 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.