A general framework for high precision computation of singular integrals in Galerkin SIE formulations

The direct evaluation method was originally introduced in computational electromagnetics as a semi-analytical method for high precision computation of singular Galerkin inner products arising in surface integral equation formulations over planar triangular tesselations. Recently, the basic philosophy of the direct evaluation method was utilized for the development of fully numerical schemes. Here, we describe how these novel algorithms could lead to a general framework for accommodating, without significant retooling, a considerably wider repertoire of applications including weakly singular and strongly singular integrals with high-order basis/testing functions over curved surfaces and possibly with Green´s functions expressed in spectral integral form, as well as singular integrals arising in shape derivatives of sensitivity analysis.