Transformations for evaluating singular boundary element integrals

DOI10.1016/S0377-0427(02)00357-6zbMath1014.65019MaRDI QIDQ1860376

Peter R. Johnston, David L. Elliott

Publication date: 23 February 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

comparison of methodsnumerical examplesboundary element methodGaussian quadratureLaplace equationline integralsweakly singular integralsnonlinear coordinate transformationHadamard finite-part integrals

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Boundary element methods for boundary value problems involving PDEs (65N38)

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Cites Work

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• Direct computation of Cauchy principal value integrals in advanced boundary elements
• A Collocation Method for the Generalized Airfoil Equation for an Airfoil with a Flap
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• Application of sigmoidal transformations to weakly singular and near-singular boundary element integrals
• Numerical Solution of the Generalized Airfoil Equation for an Airfoil with a Flap
• Semi-sigmoidal transformations for evaluating weakly singular boundary element integrals
• Error estimation of quadrature rules for evaluating singular integrals in boundary element problems
• A bi‐cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods
• An asymptotic analysis of two algorithms for certain Hadamard finite-part integrals
• A generalisation of Telles' method for evaluating weakly singular boundary element integrals

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