This project is concerned with a preliminary exploration of numerical techniques for sound synthesis based on the simulation of acoustical systems (generally intended to represent musical instruments). Most methods used to date in so-called "physical modeling" are really only quasi physical, and rely on signal processing constructs (such as delay lines and oscillators) rather than on the mainstream simulation body of techniques.
This project, then, is concerned with exploring two families of such methods, namely spectral/pseudospectral methods, which have the well-known property of generating extremely accurate solutions under some conditions, and energy-conserving methods, which are highly useful in the context of strongly nonlinear instrument modeling. The systems under study span the full range of musical instrument types, from strings and bars to plates and membranes.
The main results were conclusive. While spectral methods are well-known for calculating solutions of extremely high accuracy, this property is only useful over a limited range of frequencies; accuracy drops off noticeably in the higher range. As such, these methods, though interesting, are of little use in synthesis, as the distortion produced is audible---indeed, simple methods, while formally less accurate, possess much better properties over the entire range of frequencies. In short, the concept of "wideband" accuracy of numerical methods has been developed, and is now used by the group in designing new methods.
Energy-conserving methods, on the other hand, turn out to be critically important in the case of simulation of highly nonlinear musical acoustic systems such as cymbals and gongs. Such methods were developed in the case of flat plates and curved shells; the energy conservation property allows operation at a reasonable audio rate without the danger of instability, and also serves as a theoretical tool for proving numerical stability.