Performance Analysis of Wave Field Simulation with the Functional Transformation Method

The application of the Functional Transformation Method (FTM) for the simulation of acoustical wave fields has been recently extended to complex room geometries by the usage of so called “block-based” modeling techniques. The complete model is split into several elementary blocks with simple geometry, which are solved separately with the FTM and reconnected in the discrete system with Wave Digital Filter (WDF) principles. Concerning the performance of this algorithm, two questions arise: how much additional error is introduced compared with an all-in-one FTM solution, and how accurate are the FTM simulations compared with classical methods (e.g. digital waveguide meshes). This paper offers an answer for both questions by proving, that the worst-case scenario of the proposed procedure, i.e. minimum size block models, is identical to a waveguide mesh. The complete derivation is first performed for 1D models and then extended to 2D wave fields, demonstrating the equivalence of minimum-size block-based FTMmodeling and digital waveguide meshes.