Abstract:

GRAPES（Global and Regional Assimilation and PrEdiction System）is a new generation of NWP model in CMA (China Meteorological Administration) for the operational implementation. After the discretization of computing equations for GRAPES's model, the first calculation becomes the solution of the Helmholtz equations which is the kernel computing of the dynamic framework. The running time for solving the Helmholtz equations is more than onethird of the total cost for GRAPESglobal mode at 0.5ox0.5o horizontal resolution with 38 vertical levels, and for the higher resolution model, the timecost is an exponential growth. The generalized conjugate residual method is employed to solve the 3D Helmholtz equation in the version of the GRAPES mode currently, as a contrast, another method which is based on GMRES（generalized minimal residual method）of PETSc(Portable, Extensible Toolkit for Scientific computation) is used here. The computation shows that the GMRES method with high precision can improve the forecast accuracy and has much better scalability for largescale parallel computing.

Key words: GRAPES；Helmholtz equation；GCR(Generalized Conjugate Residual method)；GMRES(Generalized Minimal RESidual method)