Numerical simulation of acoustic waves propagation by finite element method based on optimized matrices

Based on the wave equation, scholars worldwide have proposed various methods for numerical simulation of seismic wave propagation in underground and surface media. The finite element method offers a unique advantage in accurately depicting the undulating surfaces and steep palaeoburial hills with its triangular mesh. However, its computational efficiency cannot meet our needs while lots of memories are occupied. To address this, we optimized and improved the critical Mass matrix and Stiffness matrix of spatial discretization of the acoustic wave equation. We first fully utilized the flexibility of triangles to fit different undulating terrains, then reorganized the numbering of triangle mesh nodes and elements to reduce the bandwidth of the matrices, and then used optimized matrices for solving. The Crank-Nicolson scheme was adopted for time discretization, and the Perfectly Matched Layer condition was utilized to eliminate false waves reflected from the boundary. The numerical experiments with simple and significant fluctuation models proved that this method can accelerate computational efficiency while ensuring computational accuracy.