Helmholtz Solving and Performance Optimization in Global/Regional Assimilation and Prediction System

Despite efficient parallelism in the solution of physical parameterization in the Global/Regional Assimilation and Prediction System (GRAPES), the Helmholtz equation in the dynamic core, with the increase of resolution, can hardly achieve sufficient parallelism in the solving process due to a large amount of communication and irregular access. In this paper, optimizing the Helmholtz equation solution for better performance and higher efficiency has been an urgent task. An optimization scheme for the parallel solution of the Helmholtz equation is proposed in this paper. Specifically, the geometrical multigrid optimization strategy is designed by taking advantage of the data anisotropy of grid points near the pole and the isotropy of those near memory equator in the Helmholtz equation, and the Incomplete LU (ILU) decomposition preconditioner is adopted to speed up the convergence of the improved Generalized Conjugate Residual (GCR), which effectively reduces the number of iterations and the computation time. The overall solving performance of the Helmholtz equation is improved by thread-level parallelism, vectorization, and reuse of data in the cache. The experimental results show that the proposed optimization scheme can effectively eliminate the bottleneck of the Helmholtz equation as regards the solving speed. Considering the test results on a 10-node two-way server, the solution of the Helmholtz equation, compared with the original serial version, is accelerated by $\mathrm{100}\mathrm{\times }$, with one-third of iterations reduced.