Analysis of the dipole simulation method for two-dimensional Dirichlet problems in Jordan regions with analytic boundaries
type: Item
instance of: scholarly article
title: Analysis of the dipole simulation method for two-dimensional Dirichlet problems in Jordan regions with analytic boundaries
zbMATH Open document ID: 1355.65170
author: Koya Sakakibara
published in: BIT
publication date: 2016-12-21T00:00:00Z
review text: The main aim of the paper is to introduce ways in which to arrange the dipole points and collocation points as well as to define the dipole moments in order to guarantee the stability and exponential convergence of the dipole simulation method (DSM). In order to take into account more general domains than the disk the author introduces the notion of peripheral conformal mapping from an annulus to a neighborhood of the domain boundary. Two numerical experiments are carried out. In the first one the domain is a disk and in the second one the domain is the interior simply-connected region surrounded by the curve defined by a polynomial. In each numerical experiment, the author considers two types of boundary data: a harmonic polynomial and a logarithmic potential. The numerical outcomes confirm the convergence theorem.
Mathematics Subject Classification ID: 65N80
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J08
zbMATH DE Number: 6667568
zbMATH Keywords: Laplace equation
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Jordan domain
zbMATH Keywords: analytic boundaries
zbMATH Keywords: dipole simulation method
zbMATH Keywords: method of fundamental solutions
zbMATH Keywords: charge simulation method
zbMATH Keywords: numerical experiments
zbMATH Keywords: convergence
zbMATH Keywords: stability
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
full work available at URL: s10543-016-0605-1
OpenAlex ID: W2261264844
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DOI: 10.1007/S10543-016-0605-1
description: scientific article; zbMATH DE number 6667568