Embedded solids of any dimensions in the extended finite element method

First, we propose a new methodology to enforce Dirichlet boundary conditions in the X-FEM, available for every combination of the space and boundary dimensions. Second, we introduce a new algorithm to define a reduced function space over an embedded solid of arbitrary dimension. The combination of both algorithms allows to treat any embedding i.e. 1, 2 and 3D problems embedded in 2 or 3D background meshes.