A Coarse-Grained Integral Equation Method for Multiscale Electromagnetic Analysis

Nowadays, increasing demands are placed on enhancements of the model fidelity in electromagnetic (EM) analysis. One major difficulty comes from the multiscale nature of the high-definition geometry, in which the spatial scales differ by orders of magnitude. It often leads to strongly nonuniform discretizations, and a large, dense, and ill-conditioned matrix equation to solve. The work investigates an adaptive coarse-graining domain decomposition method for the integral equation-based solution of large, complex EM problems. A parallel and multilevel skeletonization approach is employed to construct effective coarse-grid basis functions locally per subdomain. The benefits of the work include a well-preconditioned system, an effective matrix compression, and the reduced computational costs. The numerical results validate the hypothesis and demonstrate a considerable reduction in the computational complexity for multiscale problems of interest.