An operator splitting preconditioner for matrices arising from a wavelet boundary element method for the Helmholtz equation

Hawkins, S.C., Chen, K. and Harris, P.J. (2005) An operator splitting preconditioner for matrices arising from a wavelet boundary element method for the Helmholtz equation International Journal of Wavelets, Multiresolution and Information Processing (ijwmip), 3 (4). pp. 601-620. ISSN 0219-6913

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Official URL: http://dx.doi.org/10.1142/S0219691305001044

Abstract

An operator splitting type preconditioner is presented for fast solution of linear systems obtained by Galerkin discretization of the Burton and Miller formulation for the Helmholtz equation. Our approach differs from usual boundary element treatments of the three-dimensional scattering problem because we use a basis of biorthogonal wavelets. Such wavelets result in a sparse linear system and that facilitates preconditioning and makes matrix vector products cheap to form. In this Part I of our work, we implement a biorthogonal wavelet transform on a closed surface in three dimensions. Numerical results demonstrate the gains in efficiency that are already achievable with this convenient but non-optimal implementation.

Item Type:Journal article
Uncontrolled Keywords:Preconditioning, boundary element
Subjects:G000 Computing and Mathematical Sciences > G100 Mathematics
G000 Computing and Mathematical Sciences > G400 Computing
DOI (a stable link to the resource):10.1142/S0219691305001044
Faculties:Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Computational Mathematics
ID Code:3153
Deposited By:Helen Webb
Deposited On:14 Nov 2007
Last Modified:03 May 2012 12:26

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