Numerical integration scheme for singular integrals based on polar coordinates free from angular quasi-singularities

Abstract

Boundary element method formulations usually rely eventually on the calculation of weakly singular integrals, and hence robust and efficient algorithms for their evaluation are desirable. This paper proposes a numerical scheme based on a conformal polar transformation, four novel non-linear angular transformations, and a subdivision pattern which allows treating both triangular and quadrilateral elements in a common framework. It is shown that this scheme has small sensitivity to the location of the collocation point and the element aspect ratio and skewness because all sources of angular quasi-singularities have been removed by the non-linear transformations. The proposed methodology is compared against others where its robustness and efficacy is demonstrated.