Convergence and stability of the method of meshless fundamental solutions using an array of randomly distributed sources
type: Item
instance of: scholarly article
title: Convergence and stability of the method of meshless fundamental solutions using an array of randomly distributed sources
zbMATH Open document ID: 1057.65091
author: Peter Mitic
author: Youssef F. Rashed
published in: Engineering Analysis with Boundary Elements
publication date: 2004-09-23T00:00:00Z
review text: The authors consider the Laplace equation in two-dimensional simply connected bounded domain under the Dirichlet and Neumann conditions on parts of the boundary. They discuss applications of a variant of collocation method on the boundary which makes use of several external source functions. They write about a possibility to obtain an over-determined system but almost everywhere they consider only the case when the corresponding matrix is invertible and ``a solution is assured if rational or symbolic computation is used throughout''. Results dealing with convergence relate to the moving the sources ``a sufficient distance from the boundary''. But there are words about possible great round-off errors. Numerical examples with simple domains and a relatively small number of sources are discussed. Special attention is paid to the case of randomly distributed sources.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 2102403
zbMATH Keywords: Laplace equation
zbMATH Keywords: round-off errors
zbMATH Keywords: numerical examples
zbMATH Keywords: randomly distributed sources
zbMATH Keywords: method of fundamental solutions
zbMATH Keywords: meshless techniques
zbMATH Keywords: convergence
zbMATH Keywords: symbolic computation
zbMATH Keywords: Mathematica
zbMATH Keywords: indirect boundary element method
zbMATH Keywords: source collocation method
reviewed by: Evgeniĭ Dyakonov
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: j.enganabound.2003.07.005
OpenAlex ID: W2021198545
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DOI: 10.1016/J.ENGANABOUND.2003.07.005
description: scientific article; zbMATH DE number 2102403