Quadrature of singular integrands over surfaces

zbMath1065.65048MaRDI QIDQ1772039

Kendall E. Atkinson

Publication date: 15 April 2005

Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/124801

zbMATH Keywords

convergencepotential theorytrapezoidal rulesingular integrandradiosity equationspherical integrationboundary integral equation methods

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Boundary element methods for boundary value problems involving PDEs (65N38) Integral representations, integral operators, integral equations methods in two dimensions (31A10)

Related Items (11)

A highly accurate boundary treatment for confined Stokes flow ⋮ Arbitrarily high-order trapezoidal rules for functions with fractional singularities in two dimensions ⋮ Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations ⋮ Numerical integration over smooth surfaces in \(\mathbb R^3\) via class \(\mathcal Y_m\) variable transformations. II: Singular integrands ⋮ Further extension of a class of periodizing variable transformations for numerical integration ⋮ A novel class of symmetric and nonsymmetric periodizing variable transformations for numerical integration ⋮ Analysis of Atkinson's variable transformation for numerical integration over smooth surfaces in \(\mathbb R^{3}\) ⋮ Multivariate quadrature of a singular integrand ⋮ Corrected trapezoidal rules for boundary integral equations in three dimensions ⋮ Application of class \(\mathcal I_{m}\) variable transformations to numerical integration over surfaces of spheres ⋮ Numerical integration over smooth surfaces in \(\mathbb R^3\) via class \(\mathcal I_{m}\) variable transformations. I: Smooth integrands

Uses Software

• LAPLAC

This page was built for publication: Quadrature of singular integrands over surfaces