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arXiv · 1510.07023

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

Duan Chen·Wei Cai·Brian Zinser·Min Hyung Cho
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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.

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Duan Chen, Wei Cai, Brian Zinser, Min Hyung Cho. 2015-10-23. Accurate and Efficient Nystrom Volume Integral Equation Method for the Maxwell equations for Multiple 3-D Scatterers. https://doi.org/10.1016/j.jcp.2016.05.042

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