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A Solver for Helmholtz System Generated by the Discretization of Wave Shape Functions

Published online by Cambridge University Press:  03 June 2015

Long Yuan  and
Qiya Hu
Long Yuan*
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Qiya Hu*
Affiliation:
LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
*
Email: yuanlong@lsec.cc.ac.cn
Corresponding author. Email: hqy@lsec.cc.ac.cn
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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.

Keywords

65F0865N55Helmholtz equationultra weak variational formulationwave shape functionspreconditioneriteration counts
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 6 , December 2013 , pp. 791 - 808
Copyright
Copyright © Global-Science Press 2013

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