Hypersingular kernel integration in 3D Galerkin boundary element method

Authors:
A. Aimi;M. Diligenti
Affiliations:
Department of Mathematics, University of Parma, Italy;Department of Mathematics, University of Parma, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 3
Cited 5

On the h-, p-and h-p versions of the boundary element method-numerical results

Computer Methods in Applied Mechanics and Engineering
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Numerical integration of functions with boundary singularities

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Numerical solution of integral equations by means of the Sinc collocation method based on the double exponential transformation

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Semi-analytic integration of hypersingular Galerkin BIEs for three-dimensional potential problems

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Numerical solution of integral equations by means of the Sinc collocation method based on the double exponential transformation

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Semi-analytic treatment of the three-dimensional Poisson equation via a Galerkin BIE method

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Neumann exterior wave propagation problems: computational aspects of 3D energetic Galerkin BEM

Computational Mechanics

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Abstract

We consider Cauchy singular and Hypersingular boundary integral equations associated with 3D potential problems defined on polygonal domains, whose solutions are approximated with a Galerkin boundary element method, related to a given triangulation of the boundary. In particular, for constant and linear shape functions, the most frequently used basis functions, we give explicit results of the analytical inner integrations and suggest suitable quadrature schemes to evaluate the outer integrals required to form the Galerkin matrix elements. These numerical indications are given after an analysis of the singularities arising in the whole integration process, which is valid also for shape functions of higher degrees.