Reserch On The Parallel Techniques Of Difference Equation Of The Governing Equation Of The Ocean Model

An important branch of modern natural science is marine and atmospheric science, which involves a lot of ocean-atmosphere coupling models; and these coupled models comprise of nonlinear partial differential equations that are solved numerically due to their difficulty for analytical solvability. Many equations of ocean-atmosphere models are solved by the serial numerical method. Higher requirements are put forward with improvements in the space and time resolution of ocean-atmosphere models, in which case, the serial algorithms of these models don’t meet the computational demands anymore. The high performance parallel computing technology brings opportunities to improve the efficiency of these models; more and more serial ocean-atmosphere models are changing into parallel versions.The finite difference method of the governing equation of the ocean model is divided into explicit and implicit scheme. The selection of a difference scheme is related to the stability and convergence of the governing equation, and is related to the selection of parallel technique in the parallelization of ocean model. This paper will focus on the parallelization of the semi-implicit, explicit and implicit scheme, and take the specific ocean models for examples, and then give the general parallel technique of the corresponding difference scheme of ocean model.In this paper, the main work is as follows:1 The semi-implicit scheme is one of the most commonly used schemes in the discretization of governing equation of ocean model. Aimed at the characteristic (The characteristic of the semi-implicit is that the calculation is simple and the given result is achieved with less computational time step) of the semi-implict, taking the MASNUM for an example, this paper develops a parallel algorithm based on domain decomposition. In order to adapt to parallel computers of various environment, this paper develops three versions of parallel MASNUM:the OpenMP version, the MPI version and the MPI-OpenMP version. These three versions are tested on three platforms; and the result reveals that these versions can get higher speedup and efficiency as the number of processors increase, which can meet the requirement of business forecast to a certain extent.2 The explicit scheme is another one of the most commonly used schemes in the discretization of governing equation of ocean model. The characteristic of explicit schema is that calculation is simple, and that the value of the given grid point of ocean model depends on the grid point at the previous time step. Aimed at characteristics of the explicit scheme and taking the GRGO for an example, this paper proposes a parallel technology based on overlapping domain decomposition for ocean model. This technology doesn’t need a lot of changes of the original ocean model; and only using MPI basic functions can parallelize the original ocean model. Relative to redevelop the parallel system, the parallel technology can quickly transform the original model of the serial solutions into parallel solution; and the parallel version of the ocean model can get higher speedup, which meets the requirements of the speed of the experiment.3 The implicit scheme is another one of the most commonly used schemes in the discretization of governing equation of ocean model besides explicit scheme; and the characteristic of implicit scheme is that the given result is achieved with less computation time step. Aimed at the characteristic of tridiagonal linear system produced from implicit scheme (The ADI, back-Euler, Crank-Nicolson scheme and so on), this paper develops a dual-level parallel algorithm, the first level is based PDD (Parallel Diagonal Dominant), the second level is based on Parallel Partition algorithm or PPT (Parallel Partition LU algorithm). The dual-level parallel algorithm can make use of the merits of the PDD algorithm that can get a higher speedup and the Parallel Partition algorithm or PPT algorithm that can doesn’t have accuracy lose, i.e., the dual-level parallel algorithm can get higher speedup and higher accuracy.