Local proper generalized decomposition

Local model order reduction methods provide better results than global ones to problems with intricate manifold solution structure. A posteriori methods (e.g. Proper Orthogonal Decomposition) have been many times applied locally, but a priori methods (e.g. Proper Generalized Decomposition) have the difficulty of determining the manifold structure of the solution in a previous way. We propose three strategies for estimating the appropriate size of the local sub-domains where afterwards local PGD (l-PGD) is applied. It can be seen as a sort of a priori manifold learning or non-linear dimensionality reduction technique. Finally, three examples support the work