A general purpose open software for evaluating singular Galerkin inner products in SIE formulations

Abstract

Summary form only given. 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 tessellations. 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 Greens functions expressed in spectral integral form, as well as singular integrals arising in shape derivatives of sensitivity analysis. The complete set of codes used in this work is available as free, open-source software.