热物性反问题高效并行算法研究

发布时间：2018-03-26 22:31

本文选题：热物性反问题　切入点：虚边界预测　出处：《武汉理工大学》2013年博士论文

【摘要】：在热物性反问题中,温度对参数的敏感度(简称敏感度)是一个重要的并行计算算法研究的内容。对“敏感度”进行理论分析和计算,进而开发高效并行算法是作者所在课题组多年并行算法研究的深入工作。论文叙述了“敏感度”的研究现状和研究进展,研究了非均匀网格下虚边界预测(VBF)的并行算法,讨论了基于两重网格的非均匀网格VBF并行算法以及非均匀变步长并行计算方法,给出了热物性反问题中温度对参数的敏感度的初边值问题,以及多个参数表达的热物性系数对应的敏感度初边值问题,计算结果表明：对不同的参数,敏感度的函数值大小不同。由此建立了基于敏感度的非均匀网格虚边界预测反问题高效并行算法。本文用8个节点处理器进行了并行计算,并行计算效率为85%。本文的主要创新点是： (1)研究了基于两重网格非均匀步长的虚边界预测的并行算法。在粗细两重网格上,取步长不同的非均匀网格,在子区域虚拟边界上,建立边界函数值预测方法,算例表明该算法比直接对各子区域进行迭代求解的方法有更高的求解效率,计算时间大约为直接迭代求解的2/3左右。 (2)建立了热物性反问题中温度对参数的敏感度的初边值问题及并行计算数学模型。根据温度对参数的敏感度的定义,建立了敏感度的初边值问题,构造了区域分裂并行计算模型,对单参数和多参数的热物性反问题参数的敏感度进行了并行计算,得到敏感度随时间和空间变化的数据。 (3)构造了基于温度对参数敏感度的两重网格变步长虚边界预测的反问题高效并行算法。对敏感度计算数据进行分析,发现参数不同,温度的敏感度也不同。因而,提出了根据不同的参数,选取不同计算步长的并行算法。算例表明,在相同的精确度下,该算法比等步长算法减少40-65%的计算量。本文得到国家自然科学基金项目(项目编号：60173046,69773021)、中科院软件所计算机科学国家重点实验室开放课题基金(批准号：SYSKF1009)、湖北省自然科学基金面上项目(2005ABA227)的资助。
[Abstract]:In the inverse problem of thermal properties, the sensitivity of temperature to parameters (abbreviated as sensitivity) is an important part of parallel computing algorithm. Furthermore, the development of efficient parallel algorithms is the research work of the author's research group for many years. In this paper, the research status and progress of "sensitivity" are described, and the parallel algorithm of virtual boundary prediction (VBF) under non-uniform mesh is studied. In this paper, the VBF parallel algorithm based on double meshes and the nonuniform variable step size parallel computation method are discussed. The initial boundary value problem of temperature sensitivity to parameters in inverse thermal properties problem is given. And the sensitivity initial boundary value problem corresponding to the coefficient of thermal properties expressed by several parameters. The calculation results show that: for different parameters, The sensitivity function value is different, and an efficient parallel algorithm based on sensitivity is proposed for the inverse problem of non-uniform mesh virtual boundary prediction. In this paper, 8 node processors are used for parallel computation, and the parallel computing efficiency is 85. The main innovations of this paper are:. A parallel algorithm for virtual boundary prediction based on non-uniform step size of double mesh is studied. In this paper, a method for predicting the value of boundary function is established on the subregion virtual boundary by taking non-uniform mesh with different step size on the thick and thin double grid. The example shows that the algorithm is more efficient than the iterative method for solving each subregion directly. The computational time is about 2 / 3 of the direct iterative solution. (2) the initial-boundary value problem of the sensitivity of temperature to parameters and the mathematical model of parallel calculation are established. Based on the definition of the sensitivity of temperature to parameters, the initial boundary value problem of sensitivity is established, and a domain splitting parallel computing model is constructed. The sensitivity of the parameters of the inverse problem of thermal properties with single and multiple parameters is calculated in parallel. The sensitivity changes with time and space. (3) an efficient parallel inverse problem algorithm based on the sensitivity of temperature to parameters is proposed to predict the virtual boundary of double mesh with variable step size. By analyzing the sensitivity calculation data, it is found that the sensitivity of temperature is different with different parameters. Therefore, a parallel algorithm with different calculation steps is proposed according to different parameters. Compared with the equal step size algorithm, the algorithm reduces the computation cost by 40-65%. This paper is supported by the National Natural Science Foundation of China (Project No.:: 60173046 / 69773021), the Open Project Foundation of State key Laboratory of computer Science, Institute of Software, Chinese Academy of Sciences (Grant No.: SYSKF1009, Hubei Province Natural Science Foundation Project 2005ABA227).
【学位授予单位】：武汉理工大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TP338.6

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