Asynchronous OpenCL/MPI Numerical Simulations of Conservation Laws

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) method are two popular methods for solving conservation laws on computers. 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 present how we have implemented the DG method in the OpenCL/MPI framework in order to achieve high efficiency. The implementation relies on a splitting of the DG mesh into subdomains and subzones. Different kernels are compiled according to the zone properties. In addition, we rely on the OpenCL asynchronous task graph in order to overlap OpenCL computations, memory transfers and MPI communications.