Waveform relaxation for low frequency coupled field/circuit differential-algebraic models of index 2

TL;DR

This paper explores a waveform relaxation method for coupled low-frequency field and circuit models, focusing on index 2 differential-algebraic equations, with applications in superconducting magnet quench protection systems.

Contribution

It provides convergence criteria for FEM-based field models coupled with circuit DAEs of index 2, highlighting the impact of circuit topology on simulation convergence.

Findings

Convergence depends heavily on circuit topology.

Waveform relaxation shows promise for coupled DAE systems.

Benchmark results illustrate the method's effectiveness.

Abstract

Motivated by the task to design quench protection systems for superconducting magnets in particle accelerators we address a coupled field/circuit simulation based on a magneto-quasistatic field modeling. We investigate how a waveform relaxation of Gau{\ss}-Seidel type performs for a coupled simulation when circuit solving packages are used that describe the circuit by the modified nodal analysis. We present sufficient convergence criteria for the coupled simulation of FEM discretised field models and circuit models formed by a differential-algebraic equation (DAE) system of index 2. In particular, we demonstrate by a simple benchmark system the drastic influence of the circuit topology on the convergence behavior of the coupled simulation.