大区域地下水模拟的预优并行GMRES(m)算法研究  

Study on Parallel GMRES(m) Algorithm Integrating with Preconditioners Applied to Large-scale Groundwater Flow Simulation

作　　者：黄林显[1] 邵景力[1] 崔亚莉[1] 程汤培[2] 李玲[1] 

机构地区：[1]中国地质大学水资源与环境学院,北京100083 [2]北京应用物理与计算数学研究所,北京100086

出　　处：《现代地质》2012年第3期614-619,共6页Geoscience

基　　金：国家重点基础研究发展计划项目("973"项目)(2010CB428804)

摘　　要：大区域研究区由于涉及范围大、水文地质参数复杂多变,一直是进行地下水数值模拟的热点和难点。针对大区域地下水模拟的特点,在MPI环境中对Krylov子空间GMRES(m)算法的并行性进行分析,提出基于区域分解法的并行实现策略,并对不同的预条件子的加速效果进行比较。数值实验结果表明:并行GMRES(m)算法在求解大区域三维地下水模型时可以显著的加快求解速度,且具有较好的可扩展性。另外,Jacobi预条件子与GMRES算法的组合具有更优的加速比和执行效率,是一种求解大型化、复杂化地下水水流问题的可行方案。Large-scale numerical simulation of groundwater flow is always being the hot issue and the main dif- ficulty in the field of groundwater simulation due to the large size of the study area and the complexity hydrogeo- logic parameters. According to the characteristics of the large-scale groundwater flow simulation, this study ana- lyzed the parallelism of GMRES algorithm of Krylov subspace in the MPI circumstance, and suggested parallel implementation strategies based on the domain decomposition method, and compared the different precondition- ing algorithms. The simulation result shows that the parallel GMRES（m） algorithm which has a high degree of expandability, could significantly speed up the computation when dealing with the large-scale groundwater mode- ling. Furthermore, the parallel GMRES （m） algorithm could obtain better speedup and efficiency when precon- ditioned with Jacobi method, which indicates that parallel GMRES （m） algorithm integrating with Jacobi precon- ditioner is a feasible solution for solving the complex problems of large-scale groundwater flow.

关 键 词：大区域地下水模拟 区域分解法 并行GMRES(m)算法 预条件技术 

分 类 号：P641.2[天文地球—地质矿产勘探]