Geometric-integration tools for the simulation of musical sounds (Q1756717)

The authors introduce a procedure for deriving numerical schemes for models of musical instruments. The approach relies on a combination of the variational semi-discretization by \textit{E. Celledoni} et al. [J. Comput. Phys. 231, No. 20, 6770--6789 (2012; Zbl 1284.65184)] and the symplectic Runge-Kutta methods. This technique automatically derives a semi-discrete scheme preserving the Hamiltonian structure. In this way, geometric integrators can be immediately applied without any additional steps. Following this procedure the authors derive a series of explicit integration algorithms for a simple model describing piano sounds as a representative example for virtual instruments.