一类偏微分方程的并行多分裂迭代算法  

Parallel Multisplitting Iterative Algorithm for a Certain Partial Differential Equations

作　　者：任铭[1] 景元萍[1] 

机构地区：[1]洛阳理工学院数理部,河南洛阳471023

出　　处：《洛阳理工学院学报（自然科学版）》2011年第1期85-88,共4页Journal of Luoyang Institute of Science and Technology：Natural Science Edition

摘　　要：许多工程和物理应用问题的求解通常都归结为求微分方程数值解。考虑到传统的偏微分方程求解算法仅适应于串行机以及单机性能无法满足大规模科学与工程问题的计算需求,针对一类偏微分方程,提出了相应的并行差分格式和并行多分裂迭代求解算法,通过编程将其与红-黑排序、共轭梯度法的加速比和并行效率进行比较,验证了多分裂迭代法在求解偏微分方程中易于实现并行,且具有良好的可扩展性。Many researches of engineering and physical application often fall into the numerical solutions to differential equations. In consideration of the fact that the traditional partial differential equations algorithm only suits to the serial machine and the single machine performance can＇t satisfy the large scale computing needs in the process of dealing with the science and engineering issues, this article has come up with the corresponding parallel difference scheme and parallel multisplitting iterative algorithm for a certain differential equations, which has been compared with Red-Black ordering and conjugate gradient method through designed programs and verified that multisplitting method is easier to realize parallel and has better scalability.

关 键 词：并行差分格式 并行多分裂 红黑排序 共轭梯度法 

分 类 号：O175[理学—数学]