Scattering From Quasi-Planar and Moderate Rough Surfaces: Efficient Method to Fill the EFIE-Galerkin MoM Impedance Matrix and to Solve the Linear System

First, an acceleration to compute the impedance matrix obtained from the electric field integral equation (EFIE) discretized by the Galerkin method of moments (MoM) with Rao–Wilton–Glisson basis functions is addressed. It is based on a far-field approximation and makes it possible to avoid looping on the source and observation triangles. Next, the impedance matrix is split into strong and weak interactions; the latter is compressed by expressing it from Toeplitz submatrices. Then, the linear system is efficiently solved by a bi-iterative scheme. For a given order, the least-squares QR (LSQR) algorithm is applied to solve the sparse linear system related to the strong interactions, while the matrix–vector products, related to the weak interactions, are accelerated by using FFTs. Numerical results of the field scattered by perfectly conducting paraboloid-shape object and Gaussian rough surface are shown.