On Iterative Solutions for Numerical Collision Models

Vasileios Chatziioannou; Sebastian Schmutzhard; Stefan Bilbao
DAFx-2017 - Edinburgh
Nonlinear interactions between different parts of musical instruments present several challenges regarding the formulation of reliable and efficient numerical sound synthesis models. This paper focuses on a numerical collision model that incorporates impact damping. The proposed energy-based approach involves an iterative solver for the solution of the nonlinear system equations. In order to ensure the efficiency of the presented algorithm a bound is derived for the maximum number of iterations required for convergence. Numerical results demonstrate energy conservation as well as convergence within a small number of iterations, which is usually much lower than the predicted bound. Finally, an application to music acoustics, involving a clarinet simulation, shows that including a loss mechanism during collisions may have a significant effect on sound production.