非静力模式GRAPES的预条件技术研究

GRAPES是中国气象科学研究院研制的一个非静力格点模式，该模式以大气运动的全可压运动方程为基础，采用半隐半Lagrange方案。在模式积分中，每个时间步需要求解关于气压梯度力的三维离散Helmholtz方程，该方程组的求解在整个数值模拟时间中占70%左右，为加速求解过程，采用高效预条件技术是必然选择。将提出的多行双门槛不完全分解预条件与国内外常用的多种其他预条件技术进行了比较，同时，考查了针对不完全分解预条件的加性Schwarz与基于因子组合的两种并行化预条件技术，结果发现，多行双门槛不完全分解预条件优于包括ILUT在内的其他不完全分解预条件，且加性Schwarz略优于基于因子组合的并行预条件技术。

Study on preconditioning techniques for non-hydrostatic model GRAPES

GRAPES is a non-hydrostatic grid model developed by Chinese Academy of Meteorological Sciences,which is based on the full-compressible motion equations for atmosphere,and exploits the semi-implicit semi-Lagrange scheme.During the integration,a 3D Helmholtz equation should be solved at each time step.The time required to solve this kind of equation is about 70% of the whole time elapsed.To speedup the solution process,it is no way but to exploit high efficient preconditioning techniques.In the paper,there applies the so-called multi-rows dual-threshold incomplete factorization and some widely used preconditiong techniques,and two types of parallelization techniques,that is the classic additive Schwarz and the so-called factors-combination based technique.The numerical results show that multi-row dual-threshold incomplete factorization is superior to the other tested preconditioning techniques including the widely used ILUT.In addition,the classic additive Schwarz is slightly better than the factors-combination based technique.