Convergence of Low-Frequency EFIE-Based Systems With Weighted Right-Hand-Side Effect

This paper addresses the convergence of the electric-field integral equation (EFIE)-based matrix systems with the right-hand-side effect. The role of the right-hand-side excitation in determining the convergence rate of the iterative solvers is found to be important or even crucial at low frequencies. The weighted contributions from different singular vectors are decided by not only the corresponding singular values but also the right-hand side. Based on this understanding, we investigate the low-frequency stabilized form of both EFIE and Calderón multiplicative preconditioner EFIE (CMP-EFIE) on capacitive problems. For the parallel-plate capacitor excited by the delta-gap source, the singular vectors with small singular values cannot be excited, and the charge currents on the capacitive surface dominate. Thus, the stability of the EFIE-based system can be achieved at low frequencies. Detailed spectral analysis and convergent results are carried out in order to capture the physical nature of the problems.