Comparison of parametric model order reduction methods to solve magneto-quasistatic and electro-quasistatic problems

In this paper, we compare two parametric model order reduction methods, the multi-moment matching method and the interpolation of projection subspaces method for the magneto-quasistatic (MQS) and electro-quasistatic (EQS) problems derived from Maxwell’s equations and discretized with the Finite Element (FE) method. The two problems considered are both governed by the differential–algebraic equations. The material characteristic parameters as well as the geometry parameters have been considered. The applications are two realistic test cases: an EQS model of a transformer bushing under insulation defect uncertainty and a MQS model of a planar inductor with geometric and material variations. The result shows that both methods approximate well global quantities, such as the current or the voltage, as well as the local quantities like field distributions. The multi-moment matching method remains always faster in the online stage, since the reduced basis is not parameter dependent, requiring no reduced basis calculation. The multi-moment matching method requires an affine decomposition of the FE model, which is not easy to obtain when considering geometry parameters. A hybrid method is proposed and tested leading to more accurate results than the interpolation of projection subspaces method but much easier to implement than the multi-moment matching method.