Parallel Preconditioners for Plane Wave Helmholtz and Maxwell Systems with Large Wave Numbers

Parallel Preconditioners for Plane Wave Helmholtz and Maxwell Systems with Large Wave Numbers

Year:    2016

International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 5 : pp. 802–819

Abstract

A kind of non-overlapping domain decomposition preconditioner was proposed to solve the systems generated by the plane wave least-squares (PWLS) method for discretization of Helmholtz equation and Maxwell equations respectively in [13] and [14]. In this paper we introduce overlapping variants of this kind of preconditioner and give some comparison among these domain decomposition preconditioners. The main goal of this paper is to implement in parallel these domain decomposition preconditioners for the system with large wave numbers. The numerical results indicate that the preconditioners are highly scalable and are effective for solving Helmholtz equation and Maxwell's equations with large wave numbers.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2016-IJNAM-466

International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 5 : pp. 802–819

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Helmholtz equations Maxwell's equations large wave number variational formulation plane-wave basis preconditioner iteration counts.