Transient wave propagation in inhomogeneous media with enriched overlapping triangular elements. (September 2020) - Chai, Yingbin; Bathe, Klaus-Jürgen
Highlights: We study and use overlapping finite elements in transient wave propagation dynamics. The Bathe time integration is used for solutions in inhomogeneous media. The total dispersion error is split into the spatial error and temporal error. We analyze the errors and show monotonic convergence to exact solutions. Abstract: We study and use overlapping triangular finite elements enriched by trigonometric functions and implicit time integration to solve transient wave propagations in inhomogeneous media. We show explicitly that the total dispersion error of the calculated solutions can be split into two parts, the spatial error and temporal error. The study of the spatial dispersion error shows the effectiveness of the enriched overlapping finite elements compared to the traditional finite elements and the overlapping finite elements without enrichment. The study of the temporal error of the Bathe time integration scheme shows monotonic convergence to zero with decreasing time step size. The result is that we see monotonic convergence to exact solutions as the mesh of enriched overlapping finite elements is refined and the time step is decreased. We demonstrate the effectiveness of using the proposed scheme in the solution of waves traveling in inhomogeneous media at different speeds, where reflected and transmitted waves are predicted accurately by "simply" using a fine enough mesh and small enough time step.