Application of mixed modeling strategies for the simulation of the 2D wave equation for arbitrary geometries

For the simulation of multi-dimensional systems, currently so called block based methods are under investigation. A physical model is split into a number of blocks, each corresponding to a specific spatial region, which are modeled and realized separately. The correct interaction of these blocks is guaranteed by interaction laws, which can be derived from the assumption of a global model. In doing so, this paper presents an application of mixed modeling strategies for the 2D wave equation, where different blocks are realized with different methods. On the one hand the Finite Difference Time Domain (FDTD) approach can model arbitrary geometries, but suffers from numerical dispersion. The Functional Transformation Method (FTM) on the other hand, is completely free of numerical dispersion, but is restricted to simple geometries. Via a combination of both methods, it is possible to model arbitrary geometries, while large parts of the modeling region are realized free of dispersion with the FTM.