An iterative and multigrid solution of boundary integral equations
type: Item
instance of: scholarly article
title: An iterative and multigrid solution of boundary integral equations
zbMATH Open document ID: 0829.65129
DOI: 10.1016/0898-1221(95)00021-P
publication date: 1996-01-22T00:00:00Z
review text: The author considers the mixed boundary value problem (1) \(\Delta u = 0\) in \(\Omega \subset \mathbb{R}^2\), \(u = u_0\) on \(\Gamma_1\), \(\partial u/\partial n = \nu_0\) on \(\Gamma_2\) for the two-dimensional Laplace equation as some model problem. Instead of applying the boundary integral equation method (BIEM) to (1) directly, the author defines a sequence of pure Dirichlet and Neumann type subproblems in such a way that it remains consistent with the original problem (1). Now, the subproblems can be transformed to integral equations by BIEM in a standard way and can be discretized by the boundary element method. The author proves that the sequence of functions produced by the alternate solution of the Dirichlet and Neumann type subproblems converges rapidly to the solution of (1). The same is true for the discrete counterparts. The discrete subproblems can be solved very efficiently by multigrid techniques. The results of the numerical experiments reported confirm the efficiency of the proposed method.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 779206
zbMATH Keywords: iterative method
zbMATH Keywords: multigrid method
zbMATH Keywords: convergence
zbMATH Keywords: Laplace equation
zbMATH Keywords: boundary integral equation method
zbMATH Keywords: boundary element method
zbMATH Keywords: numerical experiments
author: C. Gaspar
reviewed by: Ulrich Langer
MaRDI profile type: Publication
cites work: Q3703469
cites work: Q3709786
cites work: Q3992982
cites work: Q3675465
cites work: Q3038509
cites work: Q3698230
cites work: Q3219912
cites work: Solution of potential problems using combinations of the regular and derivative boundary integral equations
cites work: Q5661106
cites work: Q3830482
full work available at URL: 0898-1221(95)00021-p
OpenAlex ID: W1990151013
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 779206