适用于混合网格的并行GMRES+LU-SGS方法  

Parallel GMRES+LU-SGS method for mixed grids

作　　者：康忠良[1] 阎超[1] 

机构地区：[1]北京航空航天大学国家计算流体力学实验室,北京100191

出　　处：《空气动力学学报》2013年第2期225-230,共6页Acta Aerodynamica Sinica

基　　金：国家重点基础研究发展计划资助项目(2009CB724104)

摘　　要：给出了一种适用于混合网格的并行无矩阵GMRES+LU-SGS隐式时间格式。首先采用LU-SGS方法迭代若干步以获得一个合适的初场,然后切换到GMRES方法在每一时间步内近似求解,并将LU-SGS方法作为其预处理器。为加速收敛,将CFL数随着残差的降低逐步放大;为减少存储量和计算量,通量Jacobian采用无矩阵处理。在保证与串行执行一致的前提下,采用基于共享内存的OpenMP方法实现了并行计算,并通过对网格的分组避免了内存争夺。算例验证表明,方法极大地提高了计算收敛效率,并行结果与串行结果完全一致,计算结果与实验结果吻合较好。A parallel matrix-free GMRES＋LU-SGS implicit scheme is presented based on mixed grids. LU-SGS method is employed at the beginning process to obtain a better initial solution,and then switched to GMRES method with LU-SGS as preconditioner. To improve convergence efficiency, the CFL number is in- creased cor-respondingly to the reduction of the residual. A matrix-free approach is applied to reduce compu- tational and memory cost. OpenMP method based on shared-memory system is used to achieve paralleliza- tion, and a special grids grouping method is applied to avoid memory contention. The numerical results dem- onstrated that the present methods can improve convergence efficiency greatly, produce exactly the same re- sult as single proces-sor case and show good agreement with experiments.

关 键 词：混合网格 并行计算 GMRES 隐式格式 OPENMP 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]