Energy preserving scheme for non linear systems of wave equations. Application to piano strings.

Juliette Chabassier 1 Patrick Joly 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : The linear wave equation does not describe the com- plexity of the piano strings vibration enough for physics based sound synthesis. The nonlinear cou- pling between transversal and longitudinal modes has to be taken into account, as does the "geometrically exact" model. This system of equations can be clas- sified among a general energy preserving class of sys- tems. We present an implicit, centered, second order accurate, numerical scheme that preserves a discrete energy, leading to unconditional stability of the nu- merical scheme. The complete model takes into ac- count the bridge coupling the strings, and the ham- mer non linear attack on the strings.
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Juliette Chabassier, Patrick Joly. Energy preserving scheme for non linear systems of wave equations. Application to piano strings.. WAVES 2009 : The 9th International Conference on Mathematical and Numerical Aspects of Wawes Propagation, Jun 2009, Pau, France. pp.00. ⟨hal-00688959⟩

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