S-fraction Multiscale Finite-volume Method for Spectrally Accurate Wavefield Simulations

Abstract

We have developed a novel approach for discretizing the spatial operator in acoustic and elastic wave propagation simulations. We split the reference fine grid model into multiple subdomains (coarse cells). Their interaction with neighbors is determined by the Neumann-to-Dirichlet (NtD) map. We construct low-dimensional spectrally-accurate approximant of the NtD map for each cell using reduced order modeling (ROM) techniques and then sparsify the approximant via a transformation to Stieltjes continued fraction (S-fraction). These steps constitute off-line part of the approach which is embarassingly parallel and performed just once for the entire time-domain simulation for all sources. In the on-line part of the approach, the spatial operator obtained by conjugation of coarse cells is employed in a time-stepping scheme. Due to the low dimension and to S-fraction transformation of the coarse cells ROMs, the communication costs in the on-line part are significantly reduced. Properly chosen ROMs also allow the time step to approach the Nyquist limit, which is typically unattainable with traditional FDTD. Our approach allows spectrally accurate wavefield simulations in media with unlimited complexity (inhomogeneity, anisotropy) even on regular model-independent grids. Our method is a perfect fit for multi-CPU and multi-GPU computations. Numerical results show the advantages of our approach.