2025/07/24 by Herles, Leon, Mally, Mario, Ostrowski, Jörg +2
#Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #Numerical Analysis (math.NA) #and Science (cs.CE)
paper · doi:10.48550/arxiv.2507.18235
Simulating electromagnetic fields across broad frequency ranges is challenging due to numerical instabilities at low frequencies. This work extends a stabilized two-step formulation of Maxwell's equations to the time-domain. Using a Galerkin discretization in space, we apply two different time-discretization schemes that are tailored to the first- and second-order in time partial differential equations of the two-step solution procedure used here. To address the low-frequency instability, we incorporate a generalized tree-cotree gauge that removes the singularity of the curl-curl operator, ensuring robustness even in the static limit. Numerical results on academic and application-oriented 3D problems confirm stability, accuracy, and the method's applicability to nonlinear, temperature-dependent materials.