基于区域分解法的地下水有限元并行数值模拟

地下水系统概念的出现对地下水模拟技术、地下水决策支持管理提出了新的要求，比如地下水系统中同时包含包气带模型和饱和带模型，或在饱和带中同时出现孔隙介质模型和裂隙介质模型，更可能在建造地下水模型的同时必须结合考虑地表水模型，所有的这些顾虑和可能均会使模型复杂化，且不说用目前流行的数值方法难于求解，就算能求解也势必造成计算工作量的剧增，这就需要借助高性能计算机来担任这项工作．相对于代价高昂的共享内存多处理器技术，基于分布式模型的机群计算技术为此项工作的实现提供了可能．讨论了如何利用机群计算技术，实现地下水有限元并行数值模拟．从地下水有限元模型的并行求解可能、基于区域分解法的并行算法、并行编程以及并行计算的实现各方面着手，系统地阐述了地下水有限元并行模拟的关键技术，并将该方法应用于一个理想的地下水溶质运移模型中，取得了成功．还讨论了方法的应用前景，包括利用机群计算技术实现对整个流域的地下水进行准实时模拟，为地下水调度提供决策依据．

Parallel Computing Based on Domain Decomposition Method for Groundwater Numerical Simulation with Finite Element Method

The research of groundwater system has made the simulation of groundwater more and more complicated. For example, aeration zone and saturation zone, porous media and fractured media, groundwater and surface water could be included together in a model of the groundwater system. In order to solve the problems of numerical simulation and decision support for the complicated groundwater system, the computing performance of computers must be high enough. Symmetrical Multiple Processors (SPM) and Cluster are the most universal high-performance computing technologies. The cluster technology based on the distributed computing is more popular for solving the practical problems. Supported by the special software, the computers in the network can work together to solve the problems. Besides accelerating the speed of computing, the technology of cluster also takes full advantage of the hardware resource and reduces the investments. In this paper, a parallel computing for groundwater numerical simulation with cluster technology is discussed. The key technologies for the groundwater parallel modeling with finite element method are given, which are the possibilities of parallel computing, the parallel algorithm by domain decomposition method, the parallel programming and the implementation of the parallel computing. An ideal groundwater solute transport model is successfully set up with the overlapping domain decomposition method. Compared with ASM (Analytic Solution Method) and FEM (Finite Element Method), the computing results of parallel FEM is credible. Furthermore, compared with the stand-alone, the speeds of parallel computing are enhanced at the acceleration of 1.53. Finally, the application prospects of this method are analyzed. Because of the higher performance and the lower investment, it could be applied to the groundwater simulation and decision-making for the whole valley such as the Yangtse river delta area.