A general algorithm for the numerical solution of hypersingular boundary integral equations. (English) Zbl 0765.73072

The limiting process that leads to the formulation of hypersingular boundary integral equations is first discussed in detail. In the second part, a new general method for the evaluation of hypersingular surface integrals in the boundary element method (BEM) is presented. The proposed method can be systematically applied in any BEM analysis, either with open or closed surfaces, and with curved boundary elements of any kind and order (of course, provided the density function meets necessary regularity requirements at each collocation point). The algorithm operates in the parameter plane of intrinsic coordinates and allows any hypersingular integral in the BEM to be directly transformed into a sum of a double and a one-dimensional regular integrals. Since all singular integrations are performed analytically, standard quadrature formulae can be used.


74S15 Boundary element methods applied to problems in solid mechanics
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