Removing the Courant-Friedrichs-Lewy stability criterion of the explicit time-domain very high degree spectral-element method with eigenvalue perturbation

The explicit time-domain spectral-element method (SEM) for synthesizing seismograms has gained tremendous credibility within the seismological community at all scales. Although recent introduction of nonperiodic homogenization addressed spatial meshing difficulty mechanical discontinuities, Courant-Friedrichs-Lewy (CFL) stability criterion strictly constrains maximum time step, which still puts a great burden on numerical simulation. In SEM, source instability using step beyond is that some unstable eigenvalues updated matrix are larger than what can be accurately simulated. We have succeeded in removing CFL condition SEM by combining forward dispersion-transform method, eigenvalue perturbation, and inverse method. Our theoretical analyses experiments homogeneous, moderate, strong heterogeneous models show this combination simulate waveforms with steps several times size limit even toward Nyquist especially efficient very high degree abundantly saves iteration without suffering from time-dispersion error. It demonstrates potential application prospect situations such as full-waveform inversion require multiple simulations same model.