GRAPES is a new generation of numerical weather prediction system developed and used by Chinese researchers. As the accuracy requirement of weather prediction system is increasing, the grid resolution of the global model is greatly increasing; therefore, the computing power becomes one of the important factors restricting the performance of the numerical weather prediction system. In order to solve the problem, the paper introduces the geometric multi-grid solution to solve the GRAPES Helmholtz equation. The core idea of multi-grid solution is to eliminate the swing component of the residual by iterative algorithm and eliminate the smooth components of the residuals by using the coarse grid interpolation to correct the fine grid solution. This paper designs a parallel solution for GRAPES multi-grid, including grid coarsening operation, smooth operation, and the coarsest grid accurate solution operation. Finally, the actual data with the resolution of 1 is tested, achieving the better acceleration effect. At the same time, the analysis and explanations of the test results have some useful conclusions.
KEYWORDS
GRAPES, multi-grid, parallel solution
INTRODUCTIONIn daily life, the application of weather prediction is becoming more important, such as the disaster prevention and mitigation in agricultural production, the take-off and landing arrangement of civil aircraft, the rocket launching in space activities and the early warning of natural disasters, and so on; the weather prediction relates to all aspects of people's lives. GRAPES is a new generation of numerical weather prediction system developed by China Meteorological Bureau; the global numerical prediction model is its core component. 1-3 With the increasing prediction accuracy requirements, the resolution of GRAPES grid increases, so computing power becomes a bottleneck to constrain GRAPES.The core of global numerical prediction model is the solution of Helmholtz equation. 4 When the resolution increases, the dimension of the equation matrix increases sharply, and the overhead of computing resources increases. Multi-grid solving technique 5,6 is a matrix solution proposed by former Soviet scientists, which has been widely used in science and engineering. The multi-grid method is theoretically proved to be an optimal solution for linear elliptic problem at least; its computational complexity is proportional to the number of the grid nodes, and the convergence rate is independent of the grid size. 7 Therefore, the multi-grid solving technique can adapt to the increment of GRAPES grid resolution and the matrix equation size.This paper designs a parallel solution to solving the GRAPES Helmholtz equation by using the multi-grid method. It reduces the calculation time of multi-grid smooth operation and speeds up the convergence by using fine grid coarsening method, restriction operator, interpolation operator, and implementation strategy of parallel computation using MPI in GRAPES. Meanwhile, an optimization strategy of hybrid grid coarsening is designed aimed to...