[1] Liu Qingfu, Zhong Weijun,. Parallel EOI algorithm with different insertion schemes [J]. Journal of Southeast University (English Edition), 2003, 19 (3): 283-288. [doi:10.3969/j.issn.1003-7985.2003.03.016]
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Parallel EOI algorithm with different insertion schemes(
)
一类相异嵌入格式的嵌套迭代并行算法
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 19
- Issue:
- 2003 3
- Page:
- 283-288
- Research Field:
- Mathematics, Physics, Mechanics
- Publishing date:
- 2003-09-30
Info
- Title:
- Parallel EOI algorithm with different insertion schemes
- 一类相异嵌入格式的嵌套迭代并行算法
- Author(s):
- Liu Qingfu; Zhong Weijun
- College of Economics and Management, Southeast University, Nanjing 210096, China
- Keywords:
- diffusion equation; different insertion scheme; convergent rate; property of gradual-approach convergence
- PACS:
- O241.28
- DOI:
- 10.3969/j.issn.1003-7985.2003.03.016
- Abstract:
- A parallel embedding overlapped iterative(EOI)algorithm about classic implicit equations with asymmetric Saul’yev schemes(CIS-EOI)to solve one-dimensional diffusion equations is discussed to improve the properties of the segment classic implicit iterative(SCII)algorithm. The structure of CIS-EOI method is given and the stability of scheme and convergence of iteration are proved by matrix method. The property of gradual-approach convergence is also discussed. It has been shown that the convergent rate is faster and the property of gradual-approach convergence also becomes better with the increasing of the net point in subsystems than with the SCII algorithm. The simulation examples show that the parallel iterative algorithm with a different insertion scheme CIS-EOI is more effective.
- 为改善并行迭代算法SCII的收敛速度和渐近收敛性质, 本文给出了求解一维扩散方程的一类相异嵌入格式的嵌套迭代并行算法CIS-EOI.论述了CIS-EOI 算法的基本构造, 并用矩阵理论证明了格式的稳定性;讨论了迭代收敛性和渐近收敛性质.CIS-EOI算法不仅加快了迭代法的收敛速度、改善了网格加密时的渐近收敛性质, 还提高了精确度, 比单纯采用SCII算法要好.文中数值例子表明相异嵌入格式的嵌套迭代并行算法CIS-EOI 是有效的.
References:
[1] Liu Qingfu. Parallel iterative algorithms for solving the implicit difference equations [J]. Guizhou Science, 2002, 6(2):29-37.(in Chinese)
[2] Chen Jin, Zhang Baolin. Massively parallel algorithm for parabolic equation: one dimensional problem [J]. Computational Physics Sinica, 1994, 4(5): 372-382.
[3] Zhang Baolin, Gu Tongxiang, Mo Zeyao. Principles and methods of numerical parallel computation[M]. Beijing: National Defence Industry Press, 1999.212-216.(in Chinese)
[4] Chen Jin, Zhang Baolin. A Class of alternation block crank-nicolson method [J]. Intern J Computer Math, 1992, 45(5): 89-112.
[5] Hu Jiagan. The estimates of =M-1N=∞1 and the optimally scaled matrix [J]. Journal of Computational Mathematics, 1984, 2(6):122-129.
[6] Zhang Baolin, Su Xiumin. Parallel algorithms for solving the implicit difference equations [J]. Computational Physics Sinica, 1992, 9(3):250-256.(in Chinese)
[7] Zhang Baolin. One finite difference methods for solving initial-boundary value problems in parallel [J]. Comm on Appl Math and Comput, 1996, 6(1): 53-65.
Memo
- Memo:
- Biographies: Liu Qingfu(1973—), male, graduate; Zhong Weijun(corresponding author), male, doctor, professor, zhong.wj@public1.ptt.js.cn.