A volume-element-free scheme for solving volume integral equations

Solving inhomogeneous problems by integral equation approach relies on the solution of volume integral equations (VIEs) and usually tetrahedral elements in geometrical discretization are required to match arbitrary shapes. However, tetrahedral discretization is expensive since special commercial software is required even for a very simple geometry. In this work, we propose a volume-element-free scheme (VEFS) for solving the VIEs based on the transformation of volume integral into boundary integral through the Green-Gauss theorem. The scheme is simple to implement and the commercial software for discretization is not needed. The numerical example for electromagnetic (EM) scattering by a dielectric sphere is presented to illustrate the scheme.