Year: 2015
Numerical Mathematics: Theory, Methods and Applications, Vol. 8 (2015), Iss. 1 : pp. 136–148
Abstract
A shifted Laplacian operator is obtained from the Helmholtz operator by adding a complex damping. It serves as a basic tool in the most successful multigrid approach for solving highly indefinite Helmholtz equations — a Shifted Laplacian preconditioner for Krylov-type methods. Such preconditioning significantly accelerates Krylov iterations, much more so than the multigrid based on original Helmholtz equations. In this paper, we compare approximation and relaxation properties of the Helmholtz operator with and without the complex shift, and, based on our observations, propose a new hybrid approach that combines the two. Our analytical conclusions are supported by two-dimensional numerical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2015.w03si
Numerical Mathematics: Theory, Methods and Applications, Vol. 8 (2015), Iss. 1 : pp. 136–148
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13