MPI- and CUDA- implementations of modal finite difference method for P-SV wave propagation modeling

Among different discretization approaches, Finite Difference Method (FDM) is widely used for acoustic and elastic full-wave form modeling. An inevitable deficit of the technique, however, is its sever requirement to computational resources. A promising solution is parallelization, where the problem is broken into several segments, and the calculations are distributed over different processors. For the present FD routines, however, such parallelization technique inevitably needs domain-decomposition and inter-core data exchange, due to the coupling of the governing equations. In this study, a new FD-based procedure for seismic wave modeling, named as ‘Modal Finite Difference Method (MFDM)” is introduced, which deals with the simulation in the decoupled modal space; thus, neither domain-decomposition nor inter-core data exchange is anymore required, which greatly simplifies parallelization for both MPI- and CUDA implementations over CPUs and GPUs. With MFDM, it is also possible to simply cut off less-significant modes and run the routine for just the important ones, which will effectively reduce computation and storage costs. The efficiency of the proposed MFDM is shown by some numerical examples.