A Two-Step Formulation of Maxwell's Equations Using Generalized Tree-Cotree Gauges for Low-Frequency-Stability

TL;DR

This paper introduces a novel low-frequency stabilization method for Maxwell's equations using a two-step formulation with generalized tree-cotree gauges, improving stability and divergence control in computational electromagnetics.

Contribution

It proposes a new stabilization approach combining frequency scaling and tree-cotree decomposition within a two-step Maxwell's formulation, enhancing low-frequency stability.

Findings

Effective stabilization demonstrated through computational examples.

Divergence of magnetic potential remains consistent with potential decoupling.

Two variants of the method show improved low-frequency performance.

Abstract

This paper presents a new low-frequency stabilization for a two-step formulation solving the full set of Maxwell's equations. The formulation is based on a electric scalar and magnetic vector potential equation using the electroquasistatic problem as gauge condition. The proposed stabilization technique consists of an adequate frequency scaling for the electroquasistatic problem, and a tree-cotree decomposition of the magnetic vector potential such that its divergence remains consistent with the partial decoupling of the magnetic and electric potentials. The paper discusses two variants and demonstrates the effectiveness by a few computational examples.