Arlequin based PGD domain decomposition

Abstract

Problems defined in fully or partially separable domains can be solved by considering a space separated representation of the unknown fields. Thus three-dimensional problems can be solved from the solution of some one-dimensional problems in the case of fully separated representations involving the three space coordinates or as a sequence of 2D and 1D problems in the case of partially separated representations (plates, shells or extruded geometries). When the domains become more complex, sometimes they can be simplified by using appropriate mappings. When it is not possible or such a transformation becomes too complex, the use of domain decomposition could facilitate the use of separated representations. However, domain coupling in the context of space separated representations have never been analyzed. In this paper we propose a domain decomposition strategy based on the use of space separated representations and the Arlequin coupling strategy. First we consider separated representations of the physical space that will be then extended to address parametric solutions.