Numerical evaluation of arbitrary singular domain integrals based on radial integration method

In this paper, a new approach is presented for the numerical evaluation of arbitrary singular domain integrals based on the radial integration method. The transformation from domain integrals to boundary integrals and the analytical elimination of singularities can be accomplished by expressing the non-singular part of the integration kernels as polynomials of the distance r and using the intrinsic features of the radial integral. In the proposed method, singularities involved in the domain integrals are explicitly transformed to the boundary integrals, so no singularities exist at internal points. Some numerical examples are provided to verify the correctness and robustness of the presented method.