Evaluating the singular integrals arising in MPIE formulations with a double-exponential algorithm

Novel generalized Cartesian product rules for the computation of weakly singular integrals, arising in the mixed potential integral equation formulations are presented in this paper. The key feature of the proposed integration schemes lies in the incorporation of the double exponential quadrature rule, originally developed by Takahasi and Mori in the mid-seventies for the integration of functions with singularities at the endpoints of the associated integration interval.