Time-stepping beyond CFL: a locally one-dimensional scheme for acoustic wave propagation

In this abstract, we present a case study in the application of a time-stepping method, unconstrained by the CFL condition, for computational acoustic wave propagation in the context of full waveform inversion. The numerical scheme is a locally one-dimensional (LOD) variant of alternating dimension implicit (ADI) method. The LOD method has a maximum time step that is restricted only by the Nyquist sampling rate. The advantage over traditional explicit time-stepping methods occurs in the presence of high contrast media, low frequencies, and steep, narrow perfectly matched layers (PML). The main technical point of the note, from a numerical analysis perspective, is that the LOD scheme is adapted to the presence of a PML. A complexity study is presented and an application to full waveform inversion is shown.