A Potential-Based Integral Equation Method for Low-Frequency Electromagnetic Problems

In this paper, we propose a potential-based integral equation solver for low-frequency electromagnetic (EM) problems. In this formulation, the scalar potential (Φ) equation is solved in tandem with the vector potential (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 A-Φ 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.