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Optimal transformations of the integration variables in computation of singular integrals in BEM. (English) Zbl 0962.74073
Summary: The paper deals with numerical integrations of singular integrals in BEMs. It is shown that, from the point of view of numerical integrations, the only serious problem which can arise is due to weakly singular and nearly singular integrals. We pay attention to the study of numerical integrations of nearly singular integrals by using transformations of integration variables. Theoretical considerations and numerical experiments are performed for integrals occurring in two-dimensional BEM formulations. The use of optimal transformation is confronted with the optimization of a polynomial transformation.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
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