On Iterative Solutions for Numerical Collision Models
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.