A Finite Element Model Order Reduction Technique for Multiscale Electromagnetic Problems

A fast finite element method (FEM) is proposed for electromagnetic computation of recently developed hyperuniform disordered materials having multiscale geometry features. The main idea of our fast FEM is to construct a small dimensional local solution space to approximate the solution space of a multiscale subdomain that requires a large number of unknowns in the conventional FEM. The approximation efficiency is guaranteed by the fact that the multiscale subdomain is usually electrically small at its working frequency and is densely meshed due to the fine geometry and material features. To further reduce the size of the solution space, the interpolative decomposition approach is employed to adaptively choose the number of skeleton vectors for a given accuracy. The solution space is then used as basis functions for the multiscale subdomain instead of using conventional ones in the finite element analysis to reduce the total number of unknowns. We present some numerical examples to demonstrate the accuracy and efficiency of our method.