A discontinuous Galerkin finite-element method of seismic modeling in complex media using GPUs

The discontinuous Galerkin finite-element method (DGFEM), which is a high-order finite element method adapting to complex surface conditions, has attracted extensive attention. Based on triangular unstructured meshes and local Lax-Friedrichs flux, the matrix forms of DGFEM calculation using elastic, viscoelastic, and poroelastic wave equations are established, and the general calculation format for single wave field components is developed, which improves the scalability of DGFEM programming. Based on this format, the procedure to construct a universal CUDA kernel is developed, which can be easily extended for more complex media and 3D cases, and the CPU+GPU parallel computing framework of 2D DGFEM is established. The results of a theoretical model and a complex mountain model reveal that the general calculation format and CUDA kernels constructed in this paper can accurately simulate P-waves, S-waves, and slow P-waves described by using acoustic, elastic, viscoelastic, and poroelastic wave equations. Compared to single-core CPU simulation, the speedup ratio of 2D DGFEM elastic-wave GPU calculation is about 100 on the average. Meanwhile, the simulation time for elastic, viscoelastic, and poroelastic waves is approximately 1.7, 2.3, and 3.0 times that of acoustic wave simulation, respectively. This result can be used to guide multi-process load balancing in the simulation of complex coupled media.