Bands Matrix Parallel Computing Research Based On Heterogeneous Systems

Bands matrix parallel solving has been widely used in modern computer engineering techniques and it is also the important research field of basic science.Bands matrix parallel solving also has been an important device in many domains such as computer graphics,fluid mechanics,cubic spline curve,atmosphere mode and so on.This thesis is in the background of 973 project "the development and assessment of high-resolution climate model system".At present,with the resolution increases the global numerical weather prediction system GRAPES whose physical part can be efficient parallel implementation process but the dynamic framework part is difficult to efficiently run in parallel.Its computing power can hardly meet the the size of the matrix increasing,so computing power has become the key problem of global numerical weather prediction system GRAPES.In response to these issues this paper designs a MPI/Open MP parallel bands matrix Solver based on heterogeneous systems.The solver introduces the geometry multigrid algorithm which contains network grid rough,limit operator,plug value operator and GCR algorithm which is used as smooth method and solver method for the most coarse grid layer.To compare currently ILU algorithm combined GCR algorithm to solve GRAPES Helmholtz Equation with the solver designed in this paper,the solver which uses multigrid algorithm has good scalability and can achieve mass of parallel run,and cannot cause iteration times sharply increase with matrix scale increases which can caused by global model grid resolution increases.MPI multi-process point-to-point communication,protocols,radio communication and the cycle fusion of Open MP multi-threading provide the implementation platform for geometry multiple grid parallel computing algorithm and GCR parallel computing algorithm.This paper designed the optimization strategy of geometric multigrid mixture grid roughening from fine-mesh to coarse-mesh according to Helmholtz Equation the grid point data near pole in anisotropic and isotropic near the equator grid point data.The optimization strategy can effectively reduce the iteration times and time overhead.In this paper,the optimized GCR algorithm effectively reduce the cost of broadcast communication between MPI processes and the introduction of GPU accelerated computing effectively reduce the cost of computing time.In order to prove the effectiveness of this paper's work,through GRAPES hermhotz equation real data tested on the high performance computer cluster,the results show that the parallel computing scheme can effectively solve the speed bottleneck of GRAPES hermhotz equation.