Reduction of a Finite-Element Parametric Model Using Adaptive POD Methods—Application to Uncertainty Quantification

Model order reduction methods enable reduction of the computation time when dealing with parametrized numerical models. Among these methods, the proper orthogonal decomposition 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 adaptively construct the reduced model while it limits the evaluation 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.