A Weighted Variational Formulation Based on Plane Wave Basis for Discretization of Helmholtz Equations
Year: 2014
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 3 : pp. 587–607
Abstract
In this paper we are concerned with numerical methods for solving Helmholtz equations. We propose a new variant of the Variational Theory of Complex Rays (VTCR) method introduced in [15, 16]. The approximate solution generated by the new variant has higher accuracy than that generated by the original VTCR method. Moreover, the accuracy of the resulting approximate solution can be further increased by adding two suitable positive relaxation parameters into the new variational formula. Besides, a simple domain decomposition preconditioner is introduced for the system generated by the proposed variational formula. Numerical results confirm the efficiency of the new method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2014-IJNAM-543
International Journal of Numerical Analysis and Modeling, Vol. 11 (2014), Iss. 3 : pp. 587–607
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Helmholtz equations wave basis functions variational formulation error estimate preconditioner iteration counts.