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Accurate numerical integration of singular boundary element kernels over boundaries with curvature
Author(s) -
Lean Meng H.,
Wexler A.
Publication year - 1985
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620210203
Subject(s) - boundary element method , singular boundary method , mathematics , boundary knot method , gaussian quadrature , numerical integration , singular integral , mathematical analysis , boundary (topology) , curvature , boundary value problem , finite element method , geometry , integral equation , nyström method , physics , thermodynamics
Use of the Green function, for the solution of boundary‐value problems, frequently results in singular integral equations. Algorithms are presented for the accurate and efficient treatment of singular kernels frequently encountered in the boundary element method (BEM). They are based upon the use of appropriately weighted Gaussian quadrature formulae, together with numerical geometrical transformations of the region of integration. The use of high‐order subdomain expansion functions, for interpolation over nonplanar elements, allows boundary curvature to be accommodated. In particular, the handling of Green functions with logarithmic and r −1 behaviour are detailed. Volume integrals, with r −2 singularity, are outlined. Operations are performed on a simplex, thus resulting in generality and ease of automation. This scheme has been incorporated into boundary element method software and successfully applied to a variety of problems.