Harris, Paul 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 0377-0427Full text not available from this repository.
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|
|Depositing User:||editor cmis|
|Date Deposited:||21 May 2007|
|Last Modified:||19 Mar 2015 16:18|
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