On efficient preconditioners for iterative solution of a Galerkin boundary element equation for the three-dimensional exterior Helmholtz problem

Harris, P.J. and Chen, K. (2003) On efficient preconditioners for iterative solution of a Galerkin boundary element equation for the three-dimensional exterior Helmholtz problem Journal of Computational and Applied Mathematics, 156 (2). pp. 303-318. ISSN 0377-0427

Full text not available from this repository.

Abstract

The paper presents a Galerkin numerical method for solving the hyper-singular boundary integral equations for the exterior Helmholtz problem in three dimensions with a Neumann's boundary condition. Previous work in the topic has often dealt with the collocation method with a piecewise constant approximation because high order collocation and Galerkin methods are not available due to the presence of a hypersingular integral operator. This paper proposes a high order Galerkin method by using singularity subtraction technique to reduce the hyper-singular operator to a weakly singular one. Moreover, we show here how to extend the previous work (J. Appl. Numer. Math. 36 (4) (2001) 475–489) on sparse preconditioners to the Galerkin case leading to fast convergence of two iterative solvers: the conjugate gradient normal method and the generalised minimal residual method. A comparison with the collocation method is also presented for the Helmholtz problem with several wavenumbers.

Item Type:Journal article
Uncontrolled Keywords:Exterior Helmholtz; Boundary integral equation; Burton–Miller; Hyper-singular operators; Galerkin; Preconditioners; CGN; GMRES
Subjects:G000 Computing and Mathematical Sciences > G100 Mathematics
DOI (a stable link to the resource):10.1016/S0377-0427(02)00918-4
Faculties:Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Computational Mathematics
ID Code:1065
Deposited By:editor cmis
Deposited On:21 May 2007
Last Modified:03 May 2012 12:36

Repository Staff Only: item control page