THE NUMERICAL COMPUTATION OF HYPERSINGULAR INTEGRALS AND ITS APPLICATION IN BEM

The boundary element methods sometimes lead to hypersingular integral equations. In this paper some numerical methods for computing hypersingular integrals, such as the method using series expansion of the kernel, the method of subtracting the singularity, the method by regularization, the indirect method, and the Newton-Cotes integration rules, are reviewed. Then, for the generalized Newton-Cotes integration formulas, by using geometric meshes near the singularity, a much better convergence rate is obtained. These methods can be applied in the boundary element methods.