While these techniques are widely used and understood, they work primarily with a model of the abstract sound produced by an instrument or object, not a model of the instrument or object itself. A more recent approach is physical modeling- based audio synthesis, where the audio waveforms are generated using detailed numerical simulation of physical objects or instruments.
There are various approaches to physical modeling sound synthesis. One such approach, studied extensively by Stefan Bilbao,1 uses the finite difference approximation to simulate the vibrations of plates and membranes. The finite difference simulation produces realistic and dynamic sounds (examples can be found at http://unixlab.sfsu.edu/~whsu/FDGPU). Realtime finite difference-based simulations of large models are typically too computationally-intensive to run on CPUs. In our work, we have implemented finite difference simulations in realtime on GPUs.