Efficient 3D Simulation of Wave Propagation with the Functional Transformation Method
نویسندگان
چکیده
The functional transformation method (FTM) is a elegant mathematical approach for the solution of partial differential equations (PDEs) and has been so far successfully applied in digital sound synthesis for the simulation of string and percussion (drums for instance) instruments. Based on suitable integral transformations, the problem is solved analytically in both, time and space frequency domain. Discretization and inverse transformation yields a discrete algorithm, implementable in any computer hardware. In this paper the FTM is used for the simulation of three-dimensional (3D) wave propagation. With the help of a multi-dimensional fast Fourier transform (FFT), the complete wave field can be evaluated and visualized very efficiently. A program is demonstrated which simulates a 90m room with an audio bandwidth of 5kHz at 5 images per second on current PC-hardware. The algorithm is compared with classical simulation techniques both in computational complexity and accuracy.
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