An error estimator for real-time simulators based on model order reduction

Abstract

Model order reduction (MOR) is one of the most appealing choices for real-time simulation of non-linear solids. In this work a method is presented in which real time performance is achieved by means of the o -line solution of a (high dimensional) parametric problem that provides a sort of response surface or computational vademecum. This solution is then evaluated in real-time at feedback rates compatible with haptic devices, for instance (i.e., more than 1kHz). This high dimensional problem can be solved without the limitations imposed by the curse of dimensionality by employing Proper Generalized Decomposition (PGD) methods. Essentially, PGD assumes a separated representation for the essential eld of the problem. Here, an error estimator is proposed for this type of solutions that takes into account the non-linear character of the studied problems. This error estimator allows to compute the necessary number of modes employed to obtain an approximation to the solution within a prescribed error tolerance in a given quantity of interest.