热物性反问题高效并行算法研究
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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。
The Temperature Sensitivity of Parameter (TSP) is an important science research project in the invert heat conduct research to find new efficient parallel algorithms. And for develop efficient parallel algorithm is the depth of the authors' research group for many years.
This research describes the progress of the temperature sensitivity, studies non-uniform grid virtual boundary prediction on parallel algorithm, parallel computing based on two-level non-uniform grid VBF parallel algorithm. The Thermal parameters sensitivity analysis of initial boundary value problems sensitive initial boundary value problem is taking into account, Considered the expression of multiple parameters corresponding to the parallel computing method of sensitivity initial boundary value problems, the calculation results show that:for different parameters, calculation of sensitivity values are not the same. The efficient parallel algorithm of temperature parameter sensitivity is build. Finally,this article used8node processors for parallel computing, and the efficiency of parallel computing is85%.
The main innovation points of this dissertation are:
(1) The parallel algorithm with virtual boundary forecast based on two-grid non-uniform grids.
On the double grid, the different steps of the non-uniform grid are given. On the region of virtual boundary value, establish forecast method of boundary function, the results of this algorithm show higher efficiency than the method of solving the direct iterative method that used to solve the sub-region, the computing time is about direct iterative method is about2/3.
(2) Inverse heat conduction problem is used to establish the initial boundary value problem of temperature sensitivity parameter,and to cstablish the parallel computing model. According to the temperature on the sensitivity definition, establishes the initial boundary value problem of sensitivity, constructs the region splitting parallel computing model, for single and multiple parameters inverse heat conduction problem parameter sensitivity were calculated, be sensitive with the change of time and space data.
(3) The fast domain splitting varied step parallel algorithm based on temperature parameter sensitivity data. According to the data of the sensitivity for different parameters, this research find the temperature parameter sensitivity is different. Therefore, a different step length parallel algorithm is obtained based on the polynomial coefficients.
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。
The Temperature Sensitivity of Parameter (TSP) is an important science research project in the invert heat conduct research to find new efficient parallel algorithms. And for develop efficient parallel algorithm is the depth of the authors' research group for many years.
This research describes the progress of the temperature sensitivity, studies non-uniform grid virtual boundary prediction on parallel algorithm, parallel computing based on two-level non-uniform grid VBF parallel algorithm. The Thermal parameters sensitivity analysis of initial boundary value problems sensitive initial boundary value problem is taking into account, Considered the expression of multiple parameters corresponding to the parallel computing method of sensitivity initial boundary value problems, the calculation results show that:for different parameters, calculation of sensitivity values are not the same. The efficient parallel algorithm of temperature parameter sensitivity is build. Finally,this article used8node processors for parallel computing, and the efficiency of parallel computing is85%.
The main innovation points of this dissertation are:
(1) The parallel algorithm with virtual boundary forecast based on two-grid non-uniform grids.
On the double grid, the different steps of the non-uniform grid are given. On the region of virtual boundary value, establish forecast method of boundary function, the results of this algorithm show higher efficiency than the method of solving the direct iterative method that used to solve the sub-region, the computing time is about direct iterative method is about2/3.
(2) Inverse heat conduction problem is used to establish the initial boundary value problem of temperature sensitivity parameter,and to cstablish the parallel computing model. According to the temperature on the sensitivity definition, establishes the initial boundary value problem of sensitivity, constructs the region splitting parallel computing model, for single and multiple parameters inverse heat conduction problem parameter sensitivity were calculated, be sensitive with the change of time and space data.
(3) The fast domain splitting varied step parallel algorithm based on temperature parameter sensitivity data. According to the data of the sensitivity for different parameters, this research find the temperature parameter sensitivity is different. Therefore, a different step length parallel algorithm is obtained based on the polynomial coefficients.
引文
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