Efficient iterative solution of the three-dimensional Helmholtz equation
type: Item
instance of: scholarly article
title: Efficient iterative solution of the three-dimensional Helmholtz equation
zbMATH Open document ID: 0929.65089
author: Howard C. Elman
author: Dianne P. O'Leary
published in: Journal of Computational Physics
publication date: 1999-07-20T00:00:00Z
full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary
review text: The authors examine two types of preconditioners for the discrete indefinite Helmholtz equation with Sommerfeld-like boundary conditions. The first is derived by discretization of a related continuous operator, the second uses the block Toeplitz approximation to the desired problem. The resulting preconditioning matrices allow the use of fast transform methods (e.g. fast Fourier transform) and differ from the discrete Helmholtz operator by an operator of low rank. Some numerical experiments presented in the paper demonstrate the efficiency of the method when combined with Krylov subspace iteration. The authors show that the performance of restared GMRES with the proposed preconditioners is relatevely insensitive to the discretization mesh size and the wave number, and the algorithms are highly parallelizable. The presented technique is potentially applicable to inhomogeneous media, exterior domain problems and non-Cartesian grids.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
zbMATH DE Number: 1290137
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: Sommerfeld-like boundary conditions
zbMATH Keywords: preconditioners
zbMATH Keywords: Krylov subspace iterations
zbMATH Keywords: parallel computation
zbMATH Keywords: numerical experiments
describes a project that uses: LAPACK
describes a project that uses: MPI
MaRDI profile type: Publication
OpenAlex ID: W2147235190
cites work: Q4003886
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DOI: 10.1006/JCPH.1998.5939
description: scientific article; zbMATH DE number 1290137