Two-dimensional block based physical modeling with the functional transformation method

The functional transformation method (FTM) is a mathematical founded method for the solution of multi-dimensional initial boundary value problems. It is based on suitable problem-specific integral transformations, that yield a transfer function model (TFM) in both space and time frequency domain. This TFM can be discretized and, after inverse transformation, realized on computer hardware. The boundary conditions are so far inherently included in the solution. Slight changes in type or form always require a complete reanalysis. Therefore in this paper a new block-based approach for two-dimensional regions is presented, where the complete model is subdivided into smaller regions. These smaller models are solved independently with the FTM and are merged again in the discrete system. The complete procedure is demonstrated and illustrated with the two-dimensional wave equation.