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Preconditioned Krylov subspace methods for boundary element solution of the Helmholtz equation
Author(s) -
Amini S.,
Maines N. D.
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19980315)41:5<875::aid-nme313>3.0.co;2-9
Subject(s) - boundary element method , krylov subspace , mathematics , helmholtz equation , discretization , mathematical analysis , integral equation , helmholtz free energy , singular boundary method , boundary (topology) , finite element method , operator (biology) , generalized minimal residual method , boundary value problem , linear system , physics , biochemistry , chemistry , repressor , quantum mechanics , gene , transcription factor , thermodynamics
Discretization of boundary integral equations leads, in general, to fully populated complex valued non‐Hermitian systems of equations. In this paper we consider the efficient solution of these boundary element systems by preconditioned iterative methods of Krylov subspace type. We devise preconditioners based on the splitting of the boundary integral operators into smooth and non‐smooth parts and show these to be extremely efficient. The methods are applied to the boundary element solution of the Burton and Miller formulation of the exterior Helmholtz problem which includes the derivative of the double layer Helmholtz potential—a hypersingular operator. © 1998 John Wiley & Sons, Ltd.