Direct Solution of Finite Element-Boundary Integral System for Electromagnetic Analysis in Half-Space

Abstract

An efficient direct solution scheme is presented to solve the finite element-boundary integral (FEBI) system for the analysis of open-region electromagnetic problems in half-space. Data-sparse representation based on hierarichal (H-) matrix is employed to construct the direct solution framework. The FEBI system matrix is first represented to be an H-matrix form, in which the FE submatrices are accurately represented by H-matrices, while the H-matrix approximations of the BI submatrices are constructed by the adaptive cross approximation algorithm combined with singular value decomposition recompression (ACA-SVD). Based on the data-sparse formatted algorithm, the lower and upper (LU) triangular factors of the FEBI system matrix can be computed and stores as H-matrix forms with low computational costs. The resulting method, refered to as the direct FEBI method (D-FEBI), is free of convergence problem and well-suited for multiple right-hand side (RHS) computations. The performance of the D-FEBI is examined by two examples of monostatic electromagnetic scattering above a lossy half-space.