Numerical integration of logarithmic and nearly logarithmic singularity in BEMs

DOI10.1016/S0307-904X(01)00021-XzbMath0994.65131MaRDI QIDQ1347894

V. Pereyra

Publication date: 15 May 2002

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

zbMATH Keywords

numerical examplesboundary element methodnumerical experimentsaccuracylogarithmic singularitysingular kernelsweak singularity

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Numerical quadrature and cubature formulas (65D32) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (14)

Calculation of three-dimensional nearly singular boundary element integrals for steady-state heat conduction ⋮ A novel semi-analytical algorithm of nearly singular integrals on higher order elements in two dimensional BEM ⋮ A new semi-analytic algorithm of nearly singular integrals on higher order element in 3D potential BEM ⋮ Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures ⋮ A meshless singular boundary method for three‐dimensional elasticity problems ⋮ Analytic formulations for calculating nearly singular integrals in two-dimensional BEM ⋮ Transformation methods for the numerical integration of three-dimensional singular functions ⋮ A practical examination of the errors arising in the direct collocation boundary element method for acoustic scattering ⋮ Unnamed Item ⋮ A three-dimensional, \(p\)-version BEM: high-order refinement leveraged through regularization ⋮ Hybrid nearly singular integration for isogeometric boundary element analysis of coatings and other thin 2D structures ⋮ Anisotropic heat conduction across an interface crack/defect filled with a thin interstitial medium ⋮ The iterated sinh transformation ⋮ Efficient and accurate implementation of \(hp\)-BEM for the Laplace operator in 2D

Cites Work

• On numerical cubatures of singular surface integrals in boundary element methods
• Numerical evaluation of singular and finite-part integrals on curved surfaces using symbolic manipulation
• On numerical cubatures of nearly singular surface integrals arising in BEM collocation
• A self‐adaptive co‐ordinate transformation for efficient numerical evaluation of general boundary element integrals
• Effective numerical treatment of boundary integral equations: A formulation for three‐dimensional elastostatics
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