Numerical Simulation Method of Acoustic Wave Propagation Based on Semi-Symplectic Theory

Abstract

An acoustic wave propagation simulating method based on semi-symplectic theory is developed. The acoustic wave equations with n degree of freedom in space domain of Lagrange System which are obtained in FEM are converted to equations with 2n degree of freedom in Hamiltonian System with the Legendre’s Transformation. These equations are then integrated with the Precision Integration algorithm in time domain. The algorithm is employed to simulate the acoustical wave propagation in two dimensional medium. We demonstrate the remarkable stability of the presented algorithm by comparison of the results of the FEM and that of the Semi-Sympectic Theory under different time steps. The results presented in this paper show that the proposed algorithm is effective, accurate, and not sensitive to time step.