Accelerating The Discontinuous Galerkin Cell-Vertex Scheme (Dg-Cvs) Solver On Cpu-Gpu Heterogeneous Systems

Dg-Cvs (Discontinuous Galerkin Cell-Vertex Scheme) is an efficient, accurate and robust numerical solver for general hyperbolic conservation laws. It can solve a broad range of conservation laws such as the shallow water equation and Magnetohydrodynamics equations. Dg-Cvs is a Riemann-Solver-free high order space-time method for arbitrary space conservation laws. It fuses the discontinuous Galerkin (dg) method and the conservation element/solution element (ce/se) method to take advantage of the best features of both methods. Thanks to the ce/se method, the time derivative of the solution is treated as an independent unknown, which is amendable to gpu\u27s parallel execution. In this thesis, we use a cpu-gpu heterogeneous processor to accelerate Dg-Cvs to demonstrate that complex scientific applications can benefit from a heterogeneous computing system. There are challenges that such scientific program poses on the gpu architecture such as thread divergence and low kernel occupancy. We developed optimizations to address these concerns. Our proposed optimizations include thread remapping to minimize thread divergence and register pressure reduction to increase kernel occupancy. Our experiment results show that Dg-Cvs on gpu outperforms cpu by up to 57\% before optimization and 145\% afterwards. We also use Dg-Cvs as a real world application to explore the possibility of using shared virtual memory (svm) for tighter collaboration between cpu and gpu. However, svm did not help improve the performance due to the overhead of address translation and atomic operations. We developed a microbenchmark to better understand the performance impact of svm