Year: 2013
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 6 : pp. 791–808
Abstract
An interesting discretization method for Helmholtz equations was introduced in B. Després [1]. This method is based on the ultra weak variational formulation (UWVF) and the wave shape functions, which are exact solutions of the governing Helmholtz equation. In this paper we are concerned with fast solver for the system generated by the method in [1]. We propose a new preconditioner for such system, which can be viewed as a combination between a coarse solver and the block diagonal preconditioner introduced in [13]. In our numerical experiments, this preconditioner is applied to solve both two-dimensional and three-dimensional Helmholtz equations, and the numerical results illustrate that the new preconditioner is much more efficient than the original block diagonal preconditioner.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.12-m12142
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 6 : pp. 791–808
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Helmholtz equation ultra weak variational formulation wave shape functions preconditioner iteration counts.
Author Details
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