high performance computing on graphics processing units: hgpu.org

Hyperbolic conservation laws are important mathematical models for describing many phenomena in physics or engineering. The Finite Volume (FV) method and the Discontinuous Galerkin (DG) methods are two popular methods for solving conservation laws on computers. Those two methods are good candidates for parallel computing: a) they require a large amount of uniform and simple computations, b) they rely on explicit time-integration, c) they present regular and local data access pattern. In this paper, we present several FV and DG numerical simulations that we have realized with the OpenCL and MPI paradigms. First, we compare two optimized implementations of the FV method on a regular grid: an OpenCL implementation and a more traditional OpenMP implementation. We compare the efficiency of the approach on several CPU and GPU architectures of different brands. Then we give a short presentation of the DG method. Finally, we present how we have implemented this DG method in the OpenCL/MPI framework in order to achieve high efficiency. The implementation relies on a splitting of the DG mesh into sub-domains and sub-zones. Different kernels are compiled according to the zones properties. In addition, we rely on the OpenCL asynchronous task graph in order to overlap OpenCL computations, memory transfers and MPI communications.