Summary We consider model reduction for magneto‐quasistatic field equations in the vector potential formulation. A finite element discretization of such equations leads to large‐scale differential‐algebraic equations of special structure. For model reduction of linear systems, we employ a balanced truncation approach, whereas nonlinear systems are reduced using a proper orthogonal decomposition method combined with a discrete empirical interpolation technique. We will exploit the special block structure of the underlying problem to improve the performance of the model reduction algorithms. Furthermore, we discuss an efficient evaluation of the Jacobi matrix required in nonlinear time integration of the reduced models. Copyright © 2017 John Wiley & Sons, Ltd.

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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 differentialalgebraic 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.