Simplecticity of Coupled System of the Wave Equation and the Elastic Equation

Abstract

Abstract. In this paper, we investigate the symplecticity of a coupled system of the wave equation and the elastic equation as a model for simulations of a string and a bridge of a piano. Because simulations of acoustical phenomena often face difficulties due to long term simulations, numerical schemes with a good energetic behavior are preferable. As such, the symplectic integrators are promising; however, to apply these integrators, the system must be symplectic. In this paper, we prove that the semi-discretized coupled system is certainly symplectic under a natural assumption. We also performed numerical experiments, thereby confirming the theoretical result.