Separated representation of the finite element solution of nonlinear magnetostatic problem based on non-intrusive Proper Generalized Decomposition

Abstract

The Proper Generalized Decomposition has shown its efficiency to solve parameterized problems in nonlinear system events when it is combined with the Discrete Empirical Interpolation Method. Nevertheless, the solution of finite element model with the Proper Generalized Decomposition framework requires to have access to matrices and vectors of the discretized problem, which makes the method highly intrusive. In this context, based on a set of finite element solutions for a set of input parameters, a surrogate model can be developed applying a non-intrusive Proper Generalized Decomposition approach. The proposed non-intrusive approach is based on a canonical decomposition of the finite element solutions combined with an interpolation method. We then obtain a surrogate model approximating the finite element solutions for a wide range of parameters. The surrogate model, given its evaluation speed, can be used for real-time applications. In this paper, the proposed non-intrusive Proper Generalized Decomposition approach is employed to approximate a nonlinear magnetostatic problem and is applied to a single phase standard transformer and to a three-phase inductance.