An efficient Nystr¨om scheme for solving volume integral equations

Abstract

An efficient Nystr¨om scheme is developed for solving three-dimensional (3D) electromagnetic (EM) problems by volume integral equations (VIEs). Although the surface integral equations (SIEs) are preferred whenever available, the VIEs are important and indispensable in the integral equation methods when the problems involve inho-mogeneous media. Currently, the VIEs are usually solved by the method of moments (MoM) and the Nystr¨om method as a good alternative for the MoM has not receive sufficient attention in the VIEs. In this work, we present an efficient Nystr¨om scheme for 3D VIEs based on a robust local correction method. The local correction method first interpolates the unknown function based on the quadrature points in the tetrahedral elements with self or near interactions, and then derives the solutions of the resulting hypersingular integrals from singularity subtraction in the Cauchy-principle-value (CPV) sense. Numerical examples for EM scattering by 3D penetrable objects are used to demonstrate the scheme.