Unfitted extended finite elements for composite grids

We consider an Extended Finite Elements method to handle the case of composite independent unstructured grids that lead to unfitted meshes. In particular, we address the case of two overlapped meshes, a background and a foreground one, where the thickness of the latter is smaller than the elements of the background mesh. This situation may lead to elements split into several portions, thus generating polyhedral elements. We detail the corresponding discrete formulation for the Poisson problem with discontinuous coefficients. We also provide some technical details for the 3D implementation. Finally, we provide some numerical examples with the aim of showing the effectiveness of the proposed formulation.