Numerical dispersion in the thin-layer method

The thin-layer method (TLM) is an effective numerical tool for the analysis of wave motions in laminated media. In a nutshell, the TLM combines the finite element method in the direction of layering together with analytical solutions for the remaining directions. This partial discretization introduces some numerical dispersion in the TLM, the degree of which depends on the refinement of the model. In this paper, we first characterize this numerical dispersion for both anti-plane (SH) and in-plane (SV–P) body waves in an unbounded medium. We then develop optimal tuning factors, with the aid of which the numerical dispersion error is minimized and the accuracy of the solution improved. Finally, we verify the effectiveness of the tuning factors by comparing the numerical results obtained with the TLM against the exact results of canonical models for guided waves in plates, and for Love and for Rayleigh waves in semi-infinite media.