Performance Analysis ofWave Field Simulation with theFunctional Transformation Method

摘要

The application of the Functional Transformation Method (FTM) for the simulation of acoustical wave fieldshas been recently extended to complex room geometries by the usage of so called "block-based" modelingtechniques. The complete model is split into several elementary blocks with simple geometry, which aresolved 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 isintroduced compared with an all-in-one FTM solution, and how accurate are the FTM simulations comparedwith classical methods (e.g. digital waveguide meshes). This paper offers an answer for both questions byproving, that the worst-case scenario of the proposed procedure, I.e. minimum size block models, is identicalto a waveguide mesh. The complete derivation is first performed for 1D models and then extended to 2Dwave fields, demonstrating the equivalence of minimum-size block-based FTM modeling and digital waveguidemeshes.