An iterative substructuring method for the \(p\)-version of the boundary element method for hypersingular integral operators in three dimensions
type: Item
instance of: scholarly article
title: An iterative substructuring method for the \(p\)-version of the boundary element method for hypersingular integral operators in three dimensions
zbMATH Open document ID: 0914.65114
author: Norbert Heuer
published in: Numerische Mathematik
publication date: 1999-06-07T00:00:00Z
review text: The aim of this paper is to investigate preconditioners for the stiffness matrix of a linear system, which provide good bounds for the spectral condition number \(k\). The study of the preconditioners is based on domain decomposition. As a model problem the weak form of the hypersingular integral equation \[ \langle Du,v\rangle _{L^{2}(\Gamma)}=\langle f,v\rangle _{L^{2}(\Gamma)} \] is considered on the plane rectangular screen \(\Gamma \subset \mathbb{R}^{3}\) where \(f\in \widetilde{H}^{-1/2}(\Gamma)\) is a given function. Here \(D\) is the hypersingular integral operator \[ Du(x)=\frac{1}{4\pi } \frac{\partial }{\partial n_{x}}\oint\limits_{\Gamma }u(y) \frac{\partial }{\partial n_{y}} \frac{1}{| x-y| }dS_{y},\;x\in \Gamma \] which is a continuous and positive definite mapping from \(\widetilde{H} ^{1/2}(\Gamma)\) onto \(\widetilde{H}^{-1/2}(\Gamma).\) In the last section some numerical experiments are presented with three different preconditioners defined during the paper for the \(p\)-version of the boundary element method.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1187547
zbMATH Keywords: boundary element method
zbMATH Keywords: hypersingular integral equation
zbMATH Keywords: domain decomposition
zbMATH Keywords: iterative substructuring method
zbMATH Keywords: preconditioners
zbMATH Keywords: spectral condition number
zbMATH Keywords: numerical experiments
reviewed by: Ariadna Lucia Pletea
MaRDI profile type: Publication
full work available at URL: s002110050344
OpenAlex ID: W2055779721
DOI: 10.1007/S002110050344
description: scientific article; zbMATH DE number 1187547