Summary
A general direct method for the evaluation of hypersingular integrals in the BEM is presented with reference to two-dimensional problems. It is first shown that there are no special problems in the derivation of hypersingular boundary integral equations (HBIE’s), that is, in taking the singular point on the boundary. No unbounded quantities ultimately arise if the limiting process is properly performed. In the second part, the limit is expressed in terms of intrinsic coordinates. This is maybe the most critical step since the effects of the mapping must be accounted for. Then, the use of suitable expansions allows all singular integration to be performed analytically, even if curved higher-order boundary elements are employed. The original hypersingular integral is thus shown to be equivalent to some simple computable terms.
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© 1992 Springer Fachmedien Wiesbaden
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Guiggiani, M. (1992). Direct Evaluation of Hypersingular Integrals in 2D BEM. In: Hackbusch, W. (eds) Numerical Techniques for Boundary Element Methods. Notes on Numerical Fluid Mechanics (NNFM), vol 33 7. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14005-4_3
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DOI: https://doi.org/10.1007/978-3-663-14005-4_3
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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