Accurate and Efficient Singularity Treatment in Integral Equation Discontinuous Galerkin Method

A novel approach based on the singularity cancellation (SC) is proposed to accurately and efficiently evaluate the singular integrals arising in the integral equation discontinuous Galerkin (IEDG) method. Since IEDG employs the half-RWG basis function to discretize the 3-D integral equations, the operation of using Green's identity to convert the strongly singular integrals into the weakly singular ones gives rise to 3-D integrals along with 4-D integrals. Thus, the well-developed SC methods based on Duffy's transformation for the 4-D integrals arising in the traditional Galerkin method cannot be directly applied to IEDG. To solve this problem, a new scheme is developed to cancel out the singularities of the 3-D integrals in IEDG. The accuracy and efficiency of the proposed method are validated and demonstrated by several numerical results.