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

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.