Multidimensional (MD) physical systems are usually given in terms of partial differential equations (PDEs). Similar to one-dimensional systems, they can also be described by transfer function models (TFMs). In addition to including initial and boundary conditions as well as excitation functions exactly, the TFM can also be discretized in a simple way. This leads to suitable implementations for digital signal processors. Therefore it is possible to implement physics based digital sound synthesis algorithms derived from TFMs in real-time. This paper extends the recently presented solution for vibrating strings with one spatial dimension to two-dimensional drum models.

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The Functional Transformation Method (FTM) provides a frequency domain based analytic solution of arbitrary linear partial differential equation. For wave field simulations however, its application was so far restricted to simple geometries as the FTM involves a search for the eigenmodes of the model. Recently so called block based modeling algorithms were introduced, that follow a divide-and-conquer approach. A complex geometry is split into several simple elementary blocks. These blocks are solved and discretized separately, while their connection is realized in the discrete system during run-time. In this paper a 2D wave field simulation program based on block based modeling is demonstrated. Elementary block models are solved with the FTM and can be connected together to create complex 2D geometries. The complete system benefits from the advantages of the FTM (e.g. dispersionfree simulations), while the complexity of the geometry fits the needs of typical CAD drawings.

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