A generalisation of Telles' method for evaluating weakly singular boundary element integrals

DOI10.1016/S0377-0427(00)00273-9zbMath0984.65123OpenAlexW2078911811MaRDI QIDQ5939870

David L. Elliott, Peter R. Johnston

Publication date: 2 January 2002

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(00)00273-9

zbMATH Keywords

comparisonnumerical examplesboundary element methoderror boundsGaussian quadratureLaplace equationcoordinate transformationGauss-Legendre quadratureline integralsweakly singular integrals

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (10)

Boundary element analysis of thin structures using a dual transformation method for weakly singular boundary integrals ⋮ Numerically exact integration of a family of axisymmetric finite elements ⋮ Error analysis for a sinh transformation used in evaluating nearly singular boundary element integrals ⋮ A practical examination of the errors arising in the direct collocation boundary element method for acoustic scattering ⋮ A modified non-linear transformation method for evaluating weakly singular boundary integrals. ⋮ A boundary element numerical scheme for the two-dimensional convection-diffusion equation ⋮ A boundary weak singularity elimination method for multilayer structures ⋮ A new transformation technique for evaluating nearly singular integrals ⋮ A non-linear co-ordinate transformation for accurate numerical evaluation of weakly singular integrals ⋮ Transformations for evaluating singular boundary element integrals

Cites Work

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• Remarks on methods for the computation of boundary-element integrals by co-ordinate transformation
• A self‐adaptive co‐ordinate transformation for efficient numerical evaluation of general boundary element integrals
• A Collocation Method for the Generalized Airfoil Equation for an Airfoil with a Flap
• 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
• Ignoring the Singularity in Approximate Integration
• A Unified Approach to Quadrature Rules with Asymptotic Estimates of Their Remainders

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