Numerical evaluation of singular and finite-part integrals on curved surfaces using symbolic manipulation

DOI10.1007/BF02238933zbMath0770.65008MaRDI QIDQ1206802

Ralf Kieser, Christoph Schwab, Wolfgang L. Wendland

Publication date: 1 April 1993

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

boundary element methodssymbolic manipulationweakly singularCauchy singular integralHadamard finite part integralsnumerical cubaturesingular surface integralstensor product Gaussian quadrature

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (12)

Variable order composite quadrature of singular and nearly singular integrals ⋮ Numerical integration of logarithmic and nearly logarithmic singularity in BEMs ⋮ Regularization of divergent integrals: a comparison of the classical and generalized-functions approaches ⋮ On numerical cubatures of singular surface integrals in boundary element methods ⋮ Numerical calculation of weakly singular surface integrals ⋮ A semi-analytical algorithm for the evaluation of the nearly singular integrals in three-dimensional boundary element methods ⋮ Hierarchical quadrature for singular integrals ⋮ Hypersingular kernel integration in 3D Galerkin boundary element method ⋮ Adaptive integration techniques for almost singular functions in the boundary element method ⋮ Quadrature methods for 2D and 3D problems ⋮ Asymptotic expansions for two-dimensional hypersingular integrals ⋮ On numerical cubatures of nearly singular surface integrals arising in BEM collocation

Uses Software

• Maple

Cites Work

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• On numerical cubatures of singular surface integrals in boundary element methods
• The numerical evaluation of principal value integrals by finite-part integration
• An Analysis of Quadrature Errors in Second-Kind Boundary Integral Methods
• Strong ellipticity of boundary integral operators.
• Quadrature Over a Pyramid or Cube of Integrands with a Singularity at a Vertex
• A General Algorithm for Multidimensional Cauchy Principal Value Integrals in the Boundary Element Method
• Kernel Properties and Representations of Boundary Integral Operators
• A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations
• New Error Coefficients for Estimating Quadrature Errors for Analytic Functions

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