Reduced basis method for the Stokes equations in decomposable domains using greedy optimization

Abstract

In this paper we present a method for the solution of Stokes parametrized equations in domain composed by an arbitrary number of predefined shapes. The novelty of the proposed approach is the possibility to use the set of precomputed bases to solve Stokes equations in very different computational domains, defined by combining one or more reference geometries. In order to define a set of basis functions that can be used for an enlarged number of possible geometrical configurations, the method requires the use of artificial parameter functions. Due to this assumption, the selection of the set of the basis functions is performed through an optimization greedy algorithm, that represents an alternative technique to the classical greedy approach.