A wavelet algorithm for the solution of the double layer potential equation over polygonal boundaries
type: Item
instance of: scholarly article
title: A wavelet algorithm for the solution of the double layer potential equation over polygonal boundaries
zbMATH Open document ID: 0838.65111
published in: Journal of Integral Equations and Applications
publication date: 1995-10-23T00:00:00Z
review text: A piecewise linear collocation method for the solution of the double layer potential equation corresponding to Laplace's equation over polygonal domains is considered. For this collocation, a fast wavelet algorithms is defined which requires no more than \(O(N [\log N]^8)\) arithmetic operations and a storage capacity of \(O(N [\log N])\) numbers. A similar algorithm for piecewise cubic splines is also described. Some numerical results are presented to confirm the effectiveness of the algorithm. The convergence rate \(O (N^{-2} [\log N]^6)\) for the piecewise linear wavelet algorithm is also shown.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 31A30
zbMATH DE Number: 808208
zbMATH Keywords: collocation method
zbMATH Keywords: double layer potential equation
zbMATH Keywords: Laplace's equation
zbMATH Keywords: fast wavelet algorithms
zbMATH Keywords: algorithm
zbMATH Keywords: piecewise cubic splines
zbMATH Keywords: numerical results
zbMATH Keywords: convergence
author: Andreas Rathsfeld
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181075850
OpenAlex ID: W2054364143
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DOI: 10.1216/JIEA/1181075850
description: scientific article; zbMATH DE number 808208