A Two-Step Darwin Model Time Domain Formulation for Quasistatic Electromagnetic Field Calculations

TL;DR

This paper introduces a two-step computational method for quasistatic electromagnetic fields based on the Darwin model, improving numerical stability and efficiency in simulating inductive, resistive, and capacitive effects.

Contribution

A novel two-step algorithm for Darwin field models that separates scalar and vector potential computations, enhancing numerical stability and avoiding ill-conditioned monolithic formulations.

Findings

Numerical simulations confirm the validity of the two-step approach.

The method accurately captures inductive, resistive, and capacitive effects.

The approach improves computational stability over traditional monolithic methods.

Abstract

In the absence of wave propagation, transient electromagnetic fields are governed by a composite scalar/vector potential formulation for the quasistatic Darwin field model. Darwin-type field models are capable of capturing inductive, resistive, and capacitive effects. To avoid possibly non-symmetric and ill-conditioned fully discrete monolithic formulations, here, a Darwin field model is presented which results in a two-step algorithm, where the discrete representations of the electric scalar potential and the magnetic vector potential are computed consecutively. Numerical simulations show the validity of the presented approach.