Fast Direct Solution of Electromagnetic Scattering From Metallic Objects in a Planarly Layered Medium

In this article, a fast direct solver is proposed for complicated electromagnetic (EM) scattering problems in planarly layered medium (PLM). For an arbitrary metallic object straddling two or more layers of the PLM, surface integral equations (SIEs) based on the matrix-friendly (MF) layered medium Green's functions (LMGFs) are applied. When dealing with either slowly convergent problems or problems with multiple right-hand side excitations, a system matrix in the format of hierarchically off-diagonal low-rank (HODLR) is chosen, from which a fast matrix inverse can readily be computed. However, directly applying traditional HODLR for PLM cases suffers from fairly low compression rate, especially when large matrix blocks at coarse levels or objects straddling different layers are encountered. Consequently, a modified HODLR (MHODLR) structure involving reconstruction and recompression is further investigated, where key parameters are carefully studied in the context of PLM. Meanwhile, performance differences for PLM and free-space (FS) problems are thoroughly explored. Several numerical examples with increasing complexities are presented to validate the proposed LMGF-MHODLR as a promising fast direct solver for EM scattering problems in a lossless or lossy PLM background.