Laplace's equation and the Dirichlet-Neumann map in multiply connected domains
type: Item
instance of: scholarly article
title: Laplace's equation and the Dirichlet-Neumann map in multiply connected domains
zbMATH Open document ID: 0769.65085
author: G. B. McFadden
author: Anne Greenbaum
author: Leslie Greengard
published in: Journal of Computational Physics
publication date: 1993-06-29T00:00:00Z
review text: The authors investigate a new integral equation method for the solution of the Dirichlet problem in multiply connected domains. This new formulation is combined with the fast multipole method to produce an algorithm capable of solving the Laplace equation in domains with hundreds of distinct boundary components. The asymptotic CPU time requirements of the authors' scheme are of order \(O(N+M)\) in the unpreconditioned mode and of order \(O(N+M^ 3)\) in the preconditioned mode, where \(N\) is the total number of points in the boundary condition and \(M\) is the number of distinct boundary components. Some numerical results are given.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 220638
zbMATH Keywords: boundary elements
zbMATH Keywords: preconditioning
zbMATH Keywords: superalgebraic convergence rates
zbMATH Keywords: interior and exterior problems
zbMATH Keywords: iterative method
zbMATH Keywords: GMRES
zbMATH Keywords: integral equation method
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: multiply connected domains
zbMATH Keywords: fast multipole method
zbMATH Keywords: algorithm
zbMATH Keywords: Laplace equation
zbMATH Keywords: asymptotic CPU time
zbMATH Keywords: numerical results
reviewed by: Karel Najzar
MaRDI profile type: Publication
full work available at URL: jcph.1993.1073
OpenAlex ID: W2013776667
DOI: 10.1006/JCPH.1993.1073
description: scientific article; zbMATH DE number 220638