Efficient Analyzing EM Scattering of Objects Above a Lossy Half-Space by the Combined MLQR/MLSSM

A large dense complex linear system is obtained when solving an electromagnetic scattering of arbitrary shaped object located above a lossy half-space with the surface integral equation approach. To analyze the large dense complex linear system efficiently, the multilevel QR (MLQR) is used to accelerate the matrix-vector multiplication when the corresponding matrix equation is solved by a Krylov-subspace iterative method. Although the MLQR is more efficient than the direct solution, this paper presents a novel recompression technique to further reduce computation time and storage memory. The technique applies the multilevel simply sparse method (MLSSM) to the matrices of MLQR. Using the MLSSM, a sparser representation of the impedance matrix is obtained, and a more efficient matrix-vector multiplication is implemented. The combined MLQR/MLSSM is comparable to the MLQR and the adaptive cross-approximation/ singular value decomposition (ACA-SVD) in terms of computation time and memory requirement. Remarkably, the new formulation can reduce the computational time and memory by about one order of magnitude, with excellent accuracy.