A Simple and Effective Strategy for Accurate and Efficient Wave Propagation Analysis Using Spectral Elements

This article presents a numerical study of wave propagation problems, emphasizing the balance between high-frequency filtering and computational efficiency. Simple yet effective explicit time schemes optimized for the spectral element method are proposed and evaluated in terms of accuracy and performance. Spurious high-frequency modes arising from spatial discretization, particularly under discontinuous loading, are mitigated by leveraging the intrinsic numerical dissipation of low-order explicit schemes. When combined with higher-order spectral elements, this approach achieves superior accuracy compared with conventional methods. A central contribution is the introduction of an effective CFL number, CFL * , derived from the bifurcation point of the spectral radius, providing a practical criterion for selecting time steps that introduce targeted damping into the highest frequencies. Numerical results for two-dimensional Lamb’s problems confirm that the proposed framework significantly enhances robustness, accuracy, and efficiency by suppressing non-physical oscillations while maintaining physical fidelity.