Design And Implement Of Parallel Numerical Computing On Massive Parallel Processor Dawning1000

Any challenging problem in the scientific computing can not be implemented without the support of computer. The demand of human to the performance of computer is unlimited. Scientific research areas such as model construction energy resource detecting, meteorology forecast and research of basic theory require extremely high computing capability. These important computing problems relate to irregular architecture, uneven compound material, nonlinear dynamics and some other complicated mathematics and physical knowledge. The successful development of parallel computer makes it possible to solve such problems involving extremely massive computations of high precision, which is impossible to use conventional computing method on PC. Typical parallel computers made in China are Dawning series, Yinghe series and Shengzhou series.Dawning1000 is domestic-made MPP system. Since it employs the architecture of distributing memory, each of its processor can only access its local memory directly. The processors can communicate with each other using the method of message passing. This thesis mainly studies the problem of design and implement of parallel numerical algorithm on Dawning1000. The main result of the research work includes three parts. First, we present the systematic methods of parallelizing sequential numerical algorithms on MPP, which includes task parallelism and data parallelism. In the method of data parallelism, we also give two rules of data partition and techniques of loop reconstruction. Second, based on the rules and methods mentioned above, we design MPP parallel algorithms for numerical algebra computations including matrix multiplication, transposition, inversion, decomposition, linear system solving, eigenvalue computation and problems on digital signal processing. Performance analysis is also given for each parallel algorithm designed. All of those algorithms have been tested in the Dawning1000 installed in the NATIONAL HIGH PERFORMANCE COMPUTING CENTER (HEFEI), USTC. The parallel programs are coded using MPI(C banding), and these source codes form the software packs of numerical computing on Dawning1000. Third, we present a method to optimize the number of processors so as to reach the shortest computing time. In the parallel computation for a fix-sized problem in MPP, sometimesincreasing the number of processors does not reduce the computation time, on the contrary, the computation time could be prolonged. By analyzing the communication delay in the parallel computation, we present a method to optimize the number pf processors so as to reach the shortest computing time. The correctness of our method has been verified by testing on the problems of matrix multiplication and Gauss-Seidel iteration in Dawn-1000. At last, we summarize our research work in the past three years and give some conclusions on massive parallel numerical computing on Dawning1000.