A Study of the Two Helmholtz Solvers in the GRAPES Model Using GCR and GMRES

J4 ›› 2011, Vol. 33 ›› Issue (11): 65-70.

• 论文 • Previous Articles Next Articles

A Study of the Two Helmholtz Solvers in the GRAPES Model Using GCR and GMRES

SONG Junqiang1,WU Xiangjun1，2,ZHANG Lilun1,CHEN Dehui2,JIN Zhiyan2,HU Jianglin2,LI Xingliang2

(1.School of Computer Science,National University of Defense Technology,Changsha 410073;
2.Center for Numerical Weather Prediction,National Meteorological Center of CMA,Beijing 100081,China)

Received:2011-03-01 Revised:2011-06-28 Online:2011-11-25 Published:2011-11-25

Abstract

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)

SONG Junqiang1,WU Xiangjun1，2,ZHANG Lilun1,CHEN Dehui2,JIN Zhiyan2,HU Jiang. A Study of the Two Helmholtz Solvers in the GRAPES Model Using GCR and GMRES[J]. J4, 2011, 33(11): 65-70.

References

［1］薛纪善,陈德辉.数值预报系统GRAPES的科学设计和应用［M］. 北京:科学出版社,2008.
［2］杨学胜,陈嘉滨,胡江林,等.全球非静力半隐式半拉格朗日模式及其极区离散处理［J］.中国科学D辑,2007,37(9):12671272.
［3］Varga R S.矩阵迭代分析:第2版=Matrix Iterative Analysis(Second Edition)—影印版［M］.北京:科学出版社,2006.
［4］Saad Y.稀疏线性系统的迭代方法:第2版=Iterative Methods for Sparse Linear Systems(Second Edition)—影印版［M］.北京:科学出版社,2009.
［5］吴建平.稀疏线性代数方程组迭代法中的预处理技术研究：［博士学位论文］［D］.长沙：国防科学技术大学,2002.
［6］刘宇,曹建文.适用于GRAPES数值天气预报软件的ILU预条件子［J］.计算机工程与设计, 2008,29(3):731734.
［7］Balay S,Buschelman K,Eijkhout V,et al.PETSc Users Manual Revision 3.0.0［R］.Argonne National Laboratory,2008.
［8］HYPRE:High Performance Preconditioners［EB/OL］.［20090817］.http://www.llnl.gov/CASC/hypre.
［9］Saad Y,Schultz M H.A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems［J］.Journal on Scientific and Statical Computing,1986(7):856869.
［10］Liu Guoping,Zhao Wentao,Zhang Lilun.Parallel Helmholtz Solver for Chinese GRAPES Atmosphere Model Based on the PETSc Tools［C］∥Proc of International Symposium on Distributed Computing and Applications to Business,Engineering and Science,2007:287290.
［11］Jablonowski C,Lauritzen P H,Taylor M,et al. Idealized Test Cases for the Dynamical Cores of Atmospheric General Circulation Models［C］∥Proc of a Proposal for the NCAR ASP 2008 Summer Colloquium.
［12］张贺，林朝晖，曾庆存.IAP AGCM4动力框架的积分方案及模式检验［J］.大气科学，2009，33(6):12671285.

A Study of the Two Helmholtz Solvers in the GRAPES Model Using GCR and GMRES

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 0

Recommended Articles

Metrics

Comments