Abstarct: When simulatig partial differential equations in 2, 3 space dimention, it is important to use efficient implementation strategies, in particular with respect to memory usage. In the other hand, in many wave quation applications, only a small part of the computational domain is complex enough to motivate a more complex unstructured discretization, whewras quite large regions of the computational domain are sufficiently discretised with simple, Cartesian grids. For these reasons, hn this thesis, we present a hybrid approach, which combine the flexibility of the finite element method with the efficiency of the finite difference method.