Low-Frequency Stabilization of Dielectric Simulation Problems with Conductors and Insulators

TL;DR

This paper introduces stable formulations for dielectric simulation problems involving conductors and insulators, enabling accurate solutions at low frequencies and large time steps by addressing numerical instabilities related to system matrix condition numbers.

Contribution

The paper proposes new scaled formulations that improve numerical stability in dielectric simulations at low frequencies and large time steps.

Findings

Stable formulations enable reliable low-frequency and static simulations.

Numerical experiments confirm improved stability and accuracy.

Condition number issues are effectively mitigated.

Abstract

When simulating resistive-capacitive circuits or electroquasistatic problems where conductors and insulators coexist, one observes that large time steps or low frequencies lead to numerical instabilities, which are related to the condition number of the system matrix. Here, we propose several stable formulations by scaling the equation systems. This enables a reliable calculation of solutions for very low frequencies (even for the static case), or large time steps. Numerical experiments underline the findings.