Low-rank based FEM-MoM method for analyzing electromagnetic scattering problems in half-space

摘要

An efficient low-rank based matrix algorithm is presented for the FEM-MoM method to analyze electromagnetic scattering from complex objects in half-space. A fast low-rank lower and upper (LU) triangular factorization algorithm is firstly developed to solve the inverse of FEM system matrix in FEM-MoM, which reduces the computational costs to be almost linear. A domain decomposition technique is employed to further accelerate the low-rank LU factorization. Then, a multilevel UV method is introduced to generate hierarchical low-rank representations for the MoM matrices, which accelerates the matrix-vector products of the MoM in FEM-MoM. Since the multilevel UV method is purely algebraic and kernel-independent, it is well suited for dealing with multi-scale objects and complex half-space Green's function. The proposed FEM-MoM method is completely based on low-rank matrix algorithm, which exhibits high computational accuracy and efficiency. Numerical example of electromagnetic scattering in lossy half-space demonstrates the effectiveness of the proposed method.