| 三维双曲型方程初边值问题的块三对角可扩展并行求解算法 |
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| 引用本文： | 张衡,张武,苏变萍.三维双曲型方程初边值问题的块三对角可扩展并行求解算法[J].石河子大学学报,2009,27(6):785-788. |
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| 作者姓名： | 张衡 张武 苏变萍 |
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| 作者单位： | [1]石河子大学师范学院数学系,石河子832003 [2]上海大学计算机工程与科学学院,上海200072 [3]西安建筑科技大学理学院,西安710055 |
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| 基金项目： | 哈尔滨工业大学校科研和教改项目 |
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| 摘 要： | 对三维双曲型方程带Dirichlet边界条件初边值问题的离散系统用块三对角可扩展并行算法求解，提出了保证精度和最优并行效率的分治策略。使用此方法在上海大学超级计算机“自强3000”上进行了数值实验，实验的结果与理论分析一致；在保证精度的前提下，得到线性加速比，并行效率达到90％以上。
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| 关 键 词： | 块三对角线性方程组 块对角占优 差分格式 分治策略 |
A Scalable Parallel Algorithm of Block Tridiagonal Systems for the 3 D-Hyperbolic Equation Initial Boundary Value Problem |
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| ZHANG Heng,ZHANG Wu,SU Bianping.A Scalable Parallel Algorithm of Block Tridiagonal Systems for the 3 D-Hyperbolic Equation Initial Boundary Value Problem[J].Journal of Shihezi University(Natural Science),2009,27(6):785-788. |
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| Authors: | ZHANG Heng ZHANG Wu SU Bianping |
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| Institution: | ZHANG Heng, ZHANG Wu, SU Bianping (1 Department of Mathematics,Normal College,Shihezi University,Shihezi 832003,China; 2 School of Computer Engineering and Science, Shanghai University, Shanghai 200072, China; 3 School of Sciences,Xi＇an University of Architecture and Technology, Xi＇an 710055 ,China) |
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| Abstract: | A scalable parallel algorithm of block tridiagonal systems for solving the initial boundary value problem of 3D-hyperbolic equation with the Dirichlet boundary condition is discussed. The divided - and - conquer strategy to ensure the accuracy and best parallel efficiency are developed. The method proposed in this paper has been implemented on the super computer＂ZiQiang 3000＂ of Shanghai University, and the numerical results match closely with the theoretical analysis. With the given accuracy, the line speedup is obtained, and the parallel implementation efficiency over 90% is reached. |
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| Keywords: | block tridiagonal systems block diagonal dominant difference scheme divided-and-conquer strategy |
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