A partition of unity-based multiscale method

Abstract

In this paper we present an octree partition of unity method (OctPUM) developed in the context of a multiscale environment with an enrichment technique for the modeling of heterogeneous media in the presence of singularities such as cracks which overcome long-standing problems associated with the assumption of local periodicity in traditional asymptotic homogenization methods. In order to compute the microscopic fields near the crack edge within the macroscale computations, a structural enrichment-based homogenization method is introduced in which the approximation space of the OctPUM at the macroscopic scale is enriched by functions generated at the microscopic scale using the asymptotic homogenization technique.