Dispersion Analysis of Triangle‐Based Finite Element Method for Acoustic and Elastic Wave Simulations

Abstract

AbstractAcoustic and elastic wave equations are discretized by finite element method with triangles and central difference scheme in space and time, respectively. The generalized eigenvalue problems are constructed to analyze the numerical dispersion of the finite element method. Three types of mass finite element method, which are consistent finite element method (CFEM), lumped finite element method (LFEM) and mixed finite element method (MFEM), are implemented to the numerical scheme, and the numerical dispersion is under a comprehensive study. Then, the MFEM is adopted to investigate the behavior of numerical anisotropy in terms of four typical triangle meshes. Comparing the numerical dispersion and anisotropy behavior when MFEM uses different interpolation orders, one can easily find that numerical error decreases as the interpolation order increases. Specifically, the numerical dispersion and anisotropy are negligible when third‐order interpolation is used. Finally, controlling the other impact factors, the dispersive properties of elastic wave propagation in elastic medium with various velocity ratios are analyzed, and the results of numerical dissipation are presented at the end of this paper.