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We consider linear magneto-quasistatic field equations which arise insimulation of low-frequency electromagnetic devices coupled to electricalcircuits. A finite element discretization of such equations on 3D domains leadsto a singular system of differential-algebraic equations. First, we study thestructural properties of such a system and present a new regularizationapproach based on projecting out the singular state components. Furthermore, wepresent a Lyapunov-based balanced truncation model reduction method whichpreserves stability and passivity. By making use of the underlying structure ofthe problem, we develop an efficient model reduction algorithm. Numericalexperiments demonstrate its performance on a test example.

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