Waveform Relaxation for Field/Circuit Coupled DAEs with Generalized Capacitances

TL;DR

This paper introduces a new convergence criterion for waveform relaxation methods applied to complex field/circuit coupled DAEs with generalized capacitances, supported by theoretical analysis and numerical validation.

Contribution

It provides a novel, sufficient topological convergence criterion for higher index coupled systems with generalized capacitances, enhancing stability analysis.

Findings

The criterion guarantees convergence for a broad class of coupled systems.

Numerical simulations confirm the theoretical convergence results.

Abstract

Field/circuit coupling is a common approach when a lumped representation of a certain electrotechnical device is not accurate enough. To exploit existing code and underlying properties of the coupled systems, cosimulation techniques such as waveform relaxation can be used. The coupled system is of differential-algebraic type, which can potentially lead to divergence. This paper presents a novel, sufficient topological convergence criterion for field/circuit coupled systems of higher index containing a generalized capacitance. Hereby, the criterion holds for a full range of field systems whose structure can be classified as a generalized capacitance. Finally, the theoretical results are supported by numerical simulations.