Linear Subspace Reduction for Quasistatic Field Simulations to Accelerate Repeated Computations

The design of electrical machines and high-voltage devices requires the simulation of non-linear low frequency electromagnetic problems in time domain. Typically magneto- and electro-quasistatic problems in magnetic vector/electric scalar potential formulation lead after space discretization to differential-algebraic or ordinary differential equations, respectively. Therefore, huge systems of equations have to be solved in both cases. Typically a large number of degrees of freedom (DoF) is in domains with constant material parameters, i.e., linear subdomains, e.g., air or vacuum in exterior domains. In this paper, we present a method for low frequency simulations based on the proper orthogonal decomposition to reduce the DoF in these linear subspaces. The application of the method will be shown for a simple transformer model and within a global sensitivity analysis (uncertainty quantification) of the switching point in a non-linear resistive material used in a 11 kV standard insulator model.