Numerical integration in 3D Galerkin BEM solution of HBIes

We consider hypersingular boundary integral equations associated with 3D problems defined on polygonal domains, whose solutions are approximated with a Galerkin boundary element method, related to a given triangulation of the boundary. At first, for linear shape functions, the most frequently used b...

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Bibliographic Details
Published in:Computational mechanics 2002-04, Vol.28 (3-4), p.233-249
Main Authors: AIMI, A, DILIGENTI, M
Format: Article
Language:English
Subjects:
Basis functions
Boundary element method
Boundary integral method
Domains
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Galerkin method
Integral equations
Numerical integration
Physics
Shape functions
Singularities
Solid mechanics
Static elasticity
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Triangulation
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Summary:We consider hypersingular boundary integral equations associated with 3D problems defined on polygonal domains, whose solutions are approximated with a Galerkin boundary element method, related to a given triangulation of the boundary. At first, for linear shape functions, the most frequently used basis functions, we give explicit results of the analytical inner integrations. Then, after an analysis of the singularities arising in the whole integration process, we propose suitable quadrature schemes to evaluate integrals required to form the Galerkin matrix elements. Several numerical results are presented.
ISSN:0178-7675
1432-0924
DOI:10.1007/S00466-001-0284-9