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Direct evaluation of hypersingular integrals in 2D BEM. (English) Zbl 0743.65013
Numerical techniques for boundary element methods, Proc. 7th GAMM-Semin., Kiel/Ger. 1991, Notes Numer. Fluid Mech. 33, 23-34 (1992).
[For the entire collection see Zbl 0741.00061.]
The paper deals with hypersingular boundary integral equations. The limiting process is “translated” in terms of intrinsic coordinates. Suitable expansions allow all singular integrals to be evaluated analytically, and the limits to be carried out exactly. As an example, the standard boundary integral equation for the harmonic function on a two-dimensional domain is treated.

65D32 Numerical quadrature and cubature formulas
65N38 Boundary element methods for boundary value problems involving PDEs
41A55 Approximate quadratures
30E20 Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane