Sparse Matrix Canonical Grid Method for Three-Dimension Rough Surface

Abstract

This paper developed SMCG (sparse matrix canonical grid) method with vector RWG basis function for PMCHW integral equations. According to the strength of the electromagnetic interaction between discrete elements, the dense impedance matrix is decomposed into a sparse matrix for the strong interaction and flat-surface matrices for the weak interaction. Then the SMFSIA (Sparse Matrix Flat Surface Iterative Approach) is used to solve the linear equations with CG (conjugate gradient) method. The strong interaction matrix multiplies with a column vector fast, taking advantage of the sparse matrix. If the rough surface is spilt by canonical grid, flat-surface matrices are BTTB (Block-Toeplitz Toeplitz-Blocked) matrices, so that the product can be obtained by using 2D-FFT (two dimensional fast Fourier transform). Some examples show that SMCG method and the conventional method of moment (MoM) method are in good agreement. The analysis of time complexity and memory requirement indicates that The SMCG method can greatly speed up the solution without taking too much extra memory. For scattering computation of electrically large rough surface, the SMCG method has obvious advantages over the conventional Mom method.