Reduction of a Finite Element Parametric Model using Adaptive POD Methods – Application to uncertainty quantification

Abstract

Model Order Reduction (MOR) methods enable reduction of the computation time when dealing with parametrized numerical models. Among these methods, the Proper Orthogonal Decomposition (POD) method seems to be a good candidate because of its simplicity and its accuracy. In the literature, the offline/online approach is generally applied but is not always required especially if the study focuses on the device without any coupling with others. In this paper, we propose a method to construct adaptively the reduced model while its utilization which limits the evaluations of the full model when appropriate. A stochastic magnetostatic example with 14 uncertain parameters is studied by applying the Monte Carlo simulation method to illustrate the proposed procedure. In that case, it appears that the complexity of this method does not depend on the number of input parameters and so is not affected by the curse of dimensionality.