Analytical integrations of hypersingular kernel in 3D BEM problems

DOI10.1016/S0045-7825(00)00308-XzbMath0987.65128OpenAlexW1984708287MaRDI QIDQ5937168

Alberto Salvadori

Publication date: 12 July 2001

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0045-7825(00)00308-x

zbMATH Keywords

symmetric Galerkin boundary element methodhypersingular kernellinear shape functionspotential problem

Mathematics Subject Classification ID

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

Related Items (18)

Complex variables-based approach for analytical evaluation of boundary integral representations of three-dimensional acoustic scattering ⋮ The CPCT based CBIE and HBIE for potential problems in three dimensions ⋮ Implementation of CPCT based BIEs for 3D elasticity and its application in fracture mechanics ⋮ Oblique mid ocean ridge subduction modelling with the parallel fast multipole boundary element method ⋮ Regularization of divergent integrals: a comparison of the classical and generalized-functions approaches ⋮ Analytical Galerkin Boundary Integrals of Laplace Kernel Layer Potentials in \(\boldsymbol{\mathbb{R}^3}\) ⋮ Evaluation of free terms in hypersingular boundary integral equations ⋮ Asymptotic error expansions for hypersingular integrals ⋮ Displacement approach with external variables only for multi-domain analysis via symmetric BEM ⋮ Analytical integrations for the approximation of 3D hyperbolic scalar boundary integral equations ⋮ Complex variables boundary element analysis of three-dimensional crack problems ⋮ 3D Galerkin integration without Stokes' theorem ⋮ Semi-analytic integration of hypersingular Galerkin BIEs for three-dimensional potential problems ⋮ An adaptive model order reduction method for boundary element-based multi-frequency acoustic wave problems ⋮ Analytical integrations in 3D BEM for elliptic problems: Evaluation and implementation ⋮ Parallel and vectorized implementation of analytic evaluation of boundary integral operators ⋮ High order boundary and finite elements for 3D fracture propagation in brittle materials ⋮ On the BEM for acoustic wave problems

Uses Software

• Mathematica

Cites Work

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• Numerical integration of functions with boundary singularities
• Fast solution techniques for the symmetric boundary element method in linear elasticity
• How to deal with hypersingular integrals in the symmetric BEM
• Kernel Properties and Representations of Boundary Integral Operators
• A galerkin symmetric boundary-element method in elasticity: Formulation and implementation
• Numerical integration schemes for the BEM solution of hypersingular integral equations

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