Balanced truncation model reduction for 3D linear magneto-quasistatic field problems

TL;DR

This paper introduces a novel regularization and balanced truncation model reduction method for 3D magneto-quasistatic field problems, improving simulation efficiency while preserving stability and passivity.

Contribution

It presents a new regularization approach for singular DAEs and a Lyapunov-based balanced truncation method tailored for magneto-quasistatic problems, enhancing model reduction techniques.

Findings

The proposed method effectively reduces model complexity.

It preserves stability and passivity in reduced models.

Numerical experiments confirm improved performance.

Abstract

We consider linear magneto-quasistatic field equations which arise in simulation of low-frequency electromagnetic devices coupled to electrical circuits. A finite element discretization of such equations on 3D domains leads to a singular system of differential-algebraic equations. First, we study the structural properties of such a system and present a new regularization approach based on projecting out the singular state components. Furthermore, we present a Lyapunov-based balanced truncation model reduction method which preserves stability and passivity. By making use of the underlying structure of the problem, we develop an efficient model reduction algorithm. Numerical experiments demonstrate its performance on a test example.