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We propose a broadband multilevel fast multipole algorithm using hybridization of the plane wave and the multipole expansions of Green’s function in the analysis of 3-D electromagnetic problems. In the proposed method, the diagonal plane-wave expansion is used for low order harmonics, which captures most of the propagating spectrums, while the dense multipole expansion is used for high order harmonics, which captures most of the evanescent spectrums. By analyzing the errors and choosing the numbers of harmonics accordingly in the plane wave and the multipole expansions, the method is free of low-frequency breakdown and remains accurate at arbitrarily low frequencies, which is similar to the dense fast multipole algorithm (FMA). Meanwhile, the method reduces to the conventional diagonal FMA as the frequency increases. Therefore, it can be regarded as the generalization of the conventional dense and diagonal FMAs. Numerical studies in this paper show that very high accuracies can be achieved using the method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]