A local multiple proper generalized decomposition based on the partition of unity

Abstract

It is well known that model order reduction techniques that project the solution of the problem at hand onto alow-dimensional subspace present difficulties when this solution lies on a non-linear manifold. To overcomethese difficulties—notably, an undesirable augment in the number of requiredmodesin the solution—severalsolutions have been suggested. Among them we can cite the use of non-linear dimensionality reductiontechniques or, alternatively, the employ of local linear reduced order approaches. These last approachesusually present the difficulty of ensuring continuity between these local models. Here, a new method ispresented that ensures this continuity by resorting to the paradigm of the partition of unity, while employing Proper Generalized Decompositions at each local patch.