Algebraic multilevel preconditioner for the Helmholtz equation in heterogeneous media
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
ID 138391
Author(s) Bollhoefer, Matthias; Grote, Marcus J.; Schenk, Olaf
Author(s) at UniBasel Grote, Marcus J.
Schenk, Olaf
Year 2009
Year: comment 2009
Title Algebraic multilevel preconditioner for the Helmholtz equation in heterogeneous media
Journal SIAM journal on scientific computing
Volume 31
Number 5
Pages / Article-Number 3781-3805
Keywords Helmholtz equation, inhomogeneous media, symmetric indefinite matrix, algebraic multilevel preconditioning, graph-pivoting, inverse-based pivoting
Abstract An algebraic multilevel (ML) preconditioner is presented for the Helmholtz equation in heterogeneous media. It is based on a multilevel incomplete LDL(T) factorization and preserves the inherent (complex) symmetry of the Helmholtz equation. The ML preconditioner incorporates two key components for efficiency and numerical stability: symmetric maximum weight matchings and an inverse-based pivoting strategy. The former increases the block-diagonal dominance of the system, whereas the latter controls parallel to L(-1)parallel to for numerical stability. When applied recursively, their combined effect yields an algebraic coarsening strategy, similar to algebraic multigrid methods, even for highly indefinite matrices. The ML preconditioner is combined with a Krylov subspace method and applied as a "black-box" solver to a series of challenging two-and three-dimensional test problems, mainly from geophysical seismic imaging. The numerical results demonstrate the robustness and efficiency of the ML preconditioner, even at higher frequency regimes.
Publisher SIAM
ISSN/ISBN 1064-8275
Full Text on edoc No
Digital Object Identifier DOI 10.1137/080725702
ISI-Number WOS:000271747300024
Document type (ISI) Article

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