Analytical Formula for the Magnetic-to-Electric Field Coupling of Magnetization in the Partial Element Equivalent Circuit Method

In this paper, the analytical formula for the magnetic-to-electric field coupling of time-varying magnetization is presented in the framework of the partial element equivalent circuit (PEEC) method with a Manhattan-type tessellation. In the virtue of the results presented in a previous work, the proposed formula allows obtaining a quasi-magnetostatic PEEC solver in which all the matrix entries can be computed analytically. This ensures a significant speedup of the resulting PEEC solver if compared to the one where the evaluation of the integral was performed numerically. The numerical results confirm the accuracy and robustness of the proposed formula and the expected significant speedups. Detailed pseudocodes are provided to make the results easily reproducible.