Application of Symmetrization of Coefficient Matrix in the Wave Equation for Acoustoelastic Coupling

This paper mainly discusses the application of coefficient matrix symmetrization in the acoustic-elastic coupled wave equation. By performing matrix symmetrization transformation on the acoustic wave equation and the elastic wave equation, it is transformed into a form suitable for stability proof by using the energy method, and the SMF system is established. Based on this, a universal discrete framework is constructed by combining the SBP-SAT method, and PML/MPML is introduced to improve the wave absorption effect at artificial boundaries. The energy method is transformed to the frequency domain to prove the stability of the discrete system. This method can realize the SBP-SAT simulation of elastic wave-acoustic wave coupling in the 2 D case, simplify the derivation of the acoustic wave equation and the program compilation process. The simulation results show that it can solve different types of wave problems at a lower computational cost, and this method is expected to be extended to other wave equations.