Block Matrix Preconditioner Method for the Electric Field Integral Equation (Efie) Formulation Based on Loop-Star Basis Functions

Abstract

Abstract-In this paper, electromagnetic scattering problems are analyzed using an electric field integral equation (EFIE) formulation that is based on loop-star basis functions so as to avoid low-frequency instability problems. Moreover, to improve the convergence rate of iterative methods, a block matrix preconditioner (BMP) is applied to the EFIE formulation based on loop star-basis functions. Because the matrix system resulting from the conventional method of moments is a dense matrix, a sparse matrix version of each block matrix is constructed, followed by the inversion of the resultant block sparse matrix using incomplete factorization. Numerical results show that the proposed BMP is efficient in terms of computation time and memory usage.

Simple and Efficient Preconditioner for Surface Integral Solution of Scattering from Multilayer Dielectric Bodies

“…More efficient preconditioners are proposed by making use of the approximate Schur complement [7]. Since (7) is not a 2 × 2 partitioned system [14,15], these preconditioners are difficult to be extended from homogeneous bodies to multilayer dielectric object.…”

A New Efie Method Based on Coulomb Gauge for the Low-Frequency Electromagnetic Analysis

“…As a quasi-Helmholtz decomposition and robust low-frequency solver, the loop-tree or loopstar decomposition [4][5][6][7][8] separates the surface current into solenoidal and irrotational parts to capture the inductance and capacitance physics, respectively. After frequency normalization, however, the matrix is still ill-conditioned giving rise to bad convergence especially for a dense mesh.…”