Numerical evaluation of singular and finite-part integrals on curved surfaces using symbolic manipulation
type: Item
instance of: scholarly article
title: Numerical evaluation of singular and finite-part integrals on curved surfaces using symbolic manipulation
zbMATH Open document ID: 0770.65008
DOI: 10.1007/BF02238933
author: Ralf Kieser
author: Christoph Schwab
author: W. L. Wendland
published in: Computing
publication date: 1993-04-01T00:00:00Z
review text: This paper considers a class of integrals that arise with the boundary element method in three dimensions. This method reduces a three- dimensional partial differential equation problem to a two-dimensional surface integration problem. The simplification in the numerical problem due to the decrease in dimension is offset by an increase in difficulty because the resulting surface integrals over boundary patches can be weakly, Cauchy or hypersingular. The authors first show how to regularize the problem by reducing the finite part integrals to sums of weakly singular integrals. Some of the integrals in the sums involve derivatives of certain expansion functions. The authors describe how to evaluate these derivatives symbolically. Then they show how Duffy's transformation can be used to reduce the strength of the corner singularities in the final set of integrals so that all integrals can be evaluated numerically with Gauss rules. The authors analyse the convergence of this process and present numerical examples that demonstrate the validity of their analysis and overall efficiency of their methods.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 30E20
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 150546
zbMATH Keywords: Cauchy singular integral
zbMATH Keywords: singular surface integrals
zbMATH Keywords: boundary element methods
zbMATH Keywords: tensor product Gaussian quadrature
zbMATH Keywords: numerical cubature
zbMATH Keywords: weakly singular
zbMATH Keywords: Hadamard finite part integrals
zbMATH Keywords: symbolic manipulation
reviewed by: A. Genz
describes a project that uses: Maple
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 150546