Solving algorithm and parallel optimization of Helmholtz equation in GRAPES model

Abstract

GRAPES is a new generation of Numerical Weather Prediction (NWP) system developed and currently used by Chinese Meteorology Administration (CMA). The core calculation of GRAPES model is the solution of the Helmholtz equation. With the improvement of the resolution of the model, the amount of computation increases exponentially, which requires high computational efficiency. Based on the 1° resolution data of the GRAPES global model, this paper uses the Generalized Conjugate Residual Method (GCR) and generalized minimum residual method (GMRES) to solve the Helmholtz equation. ILU preprocessing is used to accelerate the convergence of the algorithm. MPI and MPI + OpenMP parallel are used to solve and optimize the algorithm. The results are verified and the performance is analyzed. Experimental results show that preprocessing can reduce the number of iterations required for convergence. For GCR and GMRES, the performance of MPI + OpenMP hybrid parallel is 37% and 5% higher than MPI parallel computing, respectively.