基于GPU并行计算及CUDA编程在环境工程中的应用研究

发布时间：2018-04-06 06:12

本文选题：地下水数值模拟　切入点：GMRES(m)　出处：《中国地质大学(北京)》2017年硕士论文

【摘要】：随着社会经济的快速发展,水资源供需矛盾日渐突出,由此产生了许多环境问题。地下水数值模拟技术对于研究环境中的地质问题具有十分重要的意义,不仅可以预测地下水位、合理开发规划利用地下水资源,还可以解决各种地质环境问题。地下水数值模拟描述了地下水的水位随着时间与空间的变化规律。随着地下水数值模拟研究深入,研究模型网格粒度越来越精细、时间跨度长以及研究尺度日益扩大,由此产生了海量数据。传统的串行模拟技术日渐不能满足这种高精度网格划分以及大规模地下水流动模型的模拟。并行技术通过对模拟过程中产生的海量数据进行有效的处理,可以缩短模拟时间来提高模拟系统的效率,对大规模的地下水流动模拟的研究提供了有力的保障。广义极小值残差法GMRES(m)不限定于矩阵的特性,对于一般的矩阵都具有很强的适应性,可以广泛的应用于大型线性方程组的求解应用中。选取高质量的预条件子与GMRES(m)算法相结合,可以有效的改善系数矩阵的谱范数,加快算法的收敛速度。本文基于GPU并行技术平台对GMRES(m)进行并行化处理,应用于地下水模拟系统中迭代求解步骤,实现地下水数值模拟系统对海量数据的高效处理。本文基于GPU并行技术在地下水数值模拟系统中的应用,最终完成了如下工作:(1)分析了GMRES(m)算法的并行性,基于CUDA的cuBLAS和cuSparse函数库进行GMRES(m)算法并行,应用于地下水数值模拟系统迭代求解中,加快线性方程组的求解速率。(2)选取jacobi与ILU0预条件子,分别与并行GMRES(m)算法结合,加快并行GMRES(m)算法在地下水数值模拟系统中迭代求解的收敛速度。(3)选取不同尺度的地下水数值模型测试基于GPU并行平台预处理GMRES(m)算法在地下水模拟系统中迭代求解速率。验证预处理GMRES(m)算法的并行高效性以及可靠性。
[Abstract]:With the rapid development of social economy, the contradiction between supply and demand of water resources is becoming more and more prominent, resulting in many environmental problems.Numerical simulation of groundwater is of great significance to the study of geological problems in the environment. It can not only predict the groundwater level, reasonably develop and utilize groundwater resources, but also solve various geological environmental problems.Numerical simulation of groundwater describes the variation of groundwater level with time and space.With the further study of groundwater numerical simulation, the mesh granularity of the model becomes more and more fine, the time span is long and the research scale is expanding day by day, resulting in a huge amount of data.The traditional serial simulation technology can not meet the needs of high precision mesh generation and large-scale groundwater flow simulation.Parallel technology can shorten the simulation time to improve the efficiency of the simulation system by effectively processing the massive data generated in the simulation process and provide a strong guarantee for the large-scale groundwater flow simulation research.The generalized minimal residual method (GMRES) is not limited to the properties of matrices and has strong adaptability to general matrices. It can be widely used in solving large linear equations.The combination of high quality preconditioners and GMRESm) algorithm can effectively improve the spectral norm of the coefficient matrix and speed up the convergence of the algorithm.In this paper, based on the GPU parallel technology platform, we parallelize the GMRESm) and apply it to the iterative solution of groundwater simulation system to realize the efficient processing of the massive data in the groundwater numerical simulation system.In this paper, based on the application of GPU parallel technology in groundwater numerical simulation system, the following work has been accomplished: 1) the parallelism of the GMRESm) algorithm is analyzed, and the cuBLAS and cuSparse function library of CUDA is used to parallel the GMRESMAM algorithm.In the iterative solution of groundwater numerical simulation system, the jacobi and ILU0 preconditioners are selected to accelerate the solving rate of linear equations, respectively, which are combined with the parallel GMRESm) algorithm.Speed up the convergence rate of iterative solution in groundwater numerical simulation system using parallel GMRESm) algorithm. Select different scales of groundwater numerical model to test the rate of iterative solution in groundwater simulation system based on GPU parallel platform preprocessing GMRESMAM) algorithm.The parallel efficiency and reliability of the preprocessing GMRESm) algorithm are verified.
【学位授予单位】：中国地质大学(北京)
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P641;TP338.6

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