Fast Time-Domain Analysis of Darwin Model of Maxwell’s Equations Using Arnoldi-Based Model Order Reduction

Abstract

The quasi-static approximation that considers inductive–capacitive–resistive effects is referred to as the Darwin model of Maxwell’s equation. However, numerical analysis of the Darwin model is computationally expensive on account of large ill-conditioned equations. In this article, we proposed a new model order reduction technique for the Darwin model of Maxwell’s equations to drastically reduce the computational cost. In this method, four symmetric non-gauged equations were solved to obtain the basis vectors and avoid solving the non-symmetric equations. The reduced-order model (ROM) was obtained through congruent transformation, and time-domain analysis was performed using the time-difference method. We observed that the symmetric ROM was superior to the asymmetric ROM, in terms of accuracy and stability of the time-domain analysis.