On boundary integral operators for the Laplace and the Helmholtz equations and their discretisations
type: Item
instance of: scholarly article
title: On boundary integral operators for the Laplace and the Helmholtz equations and their discretisations
zbMATH Open document ID: 0946.65123
DOI: 10.1016/S0955-7997(98)00055-1
author: Yanyan Li
published in: Engineering Analysis with Boundary Elements
publication date: 2000-10-26T00:00:00Z
review text: The author investigates the main boundary integral operators (single layer potential operator, double layer potential operator, Hilbert operator, hypersingular operator) that arise from certain boundary integral formulation of the interior, or exterior, Dirichlet, or Neumann boundary value problems for the Laplace and the Helmholtz equations in some circle. He presents all eigenvalues and the corresponding eigenfunctions explicitly. Moreover, for the simplest boundary element collocation discretization, the explicit matrix entries as well as the eigenvalues of the matrix and the corresponding eigenvectors are given. This information can be used for the construction of efficient preconditioners for other boundary element matrices.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1389927
zbMATH Keywords: Laplace equation
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: boundary integral formulations
zbMATH Keywords: boundary element methods
zbMATH Keywords: eigenvalues
zbMATH Keywords: eigenvectors
zbMATH Keywords: single layer potential operator
zbMATH Keywords: double layer potential operator
zbMATH Keywords: Hilbert operator
zbMATH Keywords: hypersingular operator
zbMATH Keywords: eigenfunctions
zbMATH Keywords: collocation
zbMATH Keywords: preconditioners
reviewed by: Ulrich Langer
MaRDI profile type: Publication
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full work available at URL: s0955-7997(98)00055-1
OpenAlex ID: W1972474423
description: scientific article; zbMATH DE number 1389927