Proper Generalized Decomposition computational methods on a benchmark problem: introducing a new strategy based on Constitutive Relation Error minimization

Background Nowadays, numerical simulations constitute a common tool in science and engineering activities. It is especially used for prediction and decision making, or simply for a better understanding of physical phenomena. However, in order to give an accurate representation of the real world, a large set of parameters and nonlinearities may need to be introduced in the mathematical models involved in the simulation, leading to important and often overwhelming computational effort. This results in a huge number of degrees of freedom, a drawback for such complex models, so that they cannot be tackled with classical brute force methods. Therefore, alternative numerical approaches are required, such as model reduction methods. These methods exploit the fact that the response of complex models can often be approximated with a reasonable accuracy by the response of a surrogate model, seen as the projection of the initial one on a lower dimensional Abstract