Improvements in Wideband and Robust Lorenz Gauge Potential-Based Finite Element Methods

Many emerging electromagnetic (EM) technologies contain extremely multiscale features, making them difficult to model numerically. In these contexts, traditional finite element method (FEM) solvers tend to perform poorly due to the low-frequency breakdown effect. Unfortunately, common approaches to mitigate this sacrifice performance at high frequencies, leading to adverse behavior in a multiscale setting. Previously, a FEM based on the EM potentials in the generalized-Lorenz gauge has been proposed as a solution to these issues. However, this formulation was only demonstrated on a limited set of simple geometries at low frequencies and did not have its performance compared against other low-frequency stable methods. Here, we propose modifications to the potential-based FEM formulation to improve solution efficiency in the frequency and time domains. Further, we provide theoretical and numerical studies demonstrating why these potential-based methods are more robust in complex modeling scenarios than standard FEM or those incorporating tree-cotree splitting to address low-frequency breakdown. We also simulate highly-complex multiscale geometries relevant to superconducting circuit quantum computers that show the robustness of the potential-based method across a broad range of operating points. In addition to this, we also discuss how lumped ports and absorbing boundary conditions can be incorporated into these methods to continue expanding the features of these methods. In the future, this potential-based method can serve as a compelling option for simulations of complex EM systems, especially those containing nonlinear or multiphysics effects.