The numerical computation of hypersingular integrals and its application in BEM
The paper reviews some numerical methods for computing hypersingular integrals occurring in the boundary element method (BEM), such as the method using series expansions of the kernel, singularity subtraction, the method by regularization, the indirect method, and Newton-Cotes integration formulas. Using geometric meshes near the singularity, convergence rates are obtained for some generalized trapezoidal and Simpson rules. Numerical results confirm the effectiveness of this approach.
scientific article; zbMATH DE number 625970