Fully discrete spectral boundary integral methods for Helmholtz problems on smooth closed surfaces in \(\mathbb R^3\)
type: Item
instance of: scholarly article
title: Fully discrete spectral boundary integral methods for Helmholtz problems on smooth closed surfaces in \(\mathbb R^3\)
zbMATH Open document ID: 1018.65139
author: I. G. Graham
author: Ian H. Sloan
published in: Numerische Mathematik
publication date: 2002-12-01T00:00:00Z
review text: The paper is concerned with linear boundary integral equations of the second kind with a weakly singular kernel of a form which includes both the single and the double layer potentials for the Helmholtz equation. The boundary of the underlying 3D-domain is assumed to be diffeomorphic to the unit sphere, so that after corresponding transformations the boundary integral equation is posed on the unit sphere. A spectral Galerkin method with spherical polynomial basis functions is proposed for this equation. The occurring double integrals consist of an inner integral with weakly singular integrand, and an outer one with smooth integrand. A semidiscrete version is considered where only the outer integral is approximated by a quadrature formula, and a fully discrete version where both integrals are approximated. The main part of the paper is devoted to a stability and convergence analysis of the fully discrete method.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1837038
zbMATH Keywords: linear boundary integral equations
zbMATH Keywords: weakly singular kernel
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: spectral Galerkin method
zbMATH Keywords: stability
zbMATH Keywords: convergence
reviewed by: Michael Plum
MaRDI profile type: Publication
full work available at URL: s002110100343
OpenAlex ID: W2042097096
DOI: 10.1007/S002110100343
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description: scientific article; zbMATH DE number 1837038