Accurate and Efficient Nystrom Volume Integral Equation Method for the Maxwell equations for Multiple 3-D Scatterers

TL;DR

This paper introduces a highly accurate and efficient Nyström volume integral equation method for solving Maxwell's equations involving multiple 3-D scatterers, utilizing advanced numerical techniques for singular integral computation.

Contribution

The paper presents a novel Nyström VIE method with explicit correction integrals and tensor-product quadrature for accurate Maxwell simulations involving many complex 3-D objects.

Findings

High accuracy with minimal collocation points

Demonstrated p-convergence in electromagnetic scattering calculations

Validated efficiency and precision through numerical examples

Abstract

In this paper, we develop an accurate and efficient Nystr\"{o}m volume integral equation (VIE) method for the Maxwell equations for large number of 3-D scatterers. The Cauchy Principal Values that arise from the VIE are computed accurately using a finite size exclusion volume together with explicit correction integrals consisting of removable singularities. Also, the hyper-singular integrals are computed using interpolated quadrature formulae with tensor-product quadrature nodes for several objects, such as cubes and spheres, that are frequently encountered in the design of meta-materials . The resulting Nystr\"{o}m VIE method is shown to have high accuracy with a minimum number of collocation points and demonstrate $p$-convergence for computing the electromagnetic scattering of these objects. Numerical calculations of multiple scatterers of cubic and spherical shapes validate the efficiency and accuracy of the proposed method.