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In this paper, we propose a potential-based integral equation solver for low-frequency electromagnetic (EM) problems. In this formulation, the scalar potential ( \Phi ) equation is solved in tandem with the vector potential ( \textbf {A} ) equation. The resulting system is immune to low-frequency catastrophe and accurate in capturing the electrostatic and magnetostatic physics. The fast convergence of the new \textbf {A}$ - $\Phi $ system, which is a typical symmetric saddle point problem, is made possible through the design of an appropriate left constraint preconditioner. Numerical examples validate the efficiency and stability of the novel formulation in solving both EM scattering and circuit problems over a wide frequency range up to very low frequencies. [ABSTRACT FROM PUBLISHER]

Conventional electric field integral equation-based theory is susceptible to the spurious internal resonance problem when the characteristic modes (CMs) of closed perfectly conducting objects are computed iteratively. In this paper, we present a combined field integral equation-based theory to remove the difficulty of internal resonances in CMs analysis. The electric and magnetic field integral operators are shown to share a common set of nontrivial characteristic pairs (values and modes), leading to a generalized eigenvalue problem which is immune to the internal resonance corruption. Numerical results are presented to validate the proposed formulation. This work may offer efficient solutions to CM analysis which involves electrically large closed surfaces. [ABSTRACT FROM PUBLISHER]

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]

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]

Large-scale characteristic mode analysis (CMA) poses challenges in computational electromagnetics as it calls for efficient solutions of large dense generalized eigenvalue problems. In this paper, we consider two applications that involve large-scale CMA, and demonstrate that fast multipole algorithms (FMAs) can be easily incorporated into the implicitly restarted Arnoldi method (IRAM) for eigenanalysis after simple modifications. The first application performs CMA for large platforms made by closed perfectly conducting surfaces. Multilevel FMA (MLFMA) is embedded into a combined field integral equation-based theory of characteristic mode (TCM). The second application addresses multiscale modeling of small but geometrically complicated objects, which possess fine subwavelength structures. An augmented electric field integral equation-based TCM is formulated, and low-frequency (LF-)FMA is adopted to accelerate the required matrix–vector products. [ABSTRACT FROM AUTHOR]