摘要
在许多实际计算中,由于对时间步长稳定性的要求,辐射热传导方程的计算通常采用隐式格式．隐式格式难以直接在并行机上实施,显式差分格式尽管易于在并行机上实施,但它的稳定性条件苛刻．在计算问题规模相当大时,例如需要具有数百、数千甚至上万台处理器的大型并行计算机进行计算时,数据的强相关与全局通讯等问题成为制约实现高性能计算的突出的瓶颈问题．因此,改造现有的隐式格式,研究适应于大型并行计算机的并行计算方法是目前大型科学与工程计算中迫切需要解决的具有挑战性的问题．本文简要介绍基于界面修正的迭代并行计算格式的构造及基本性质．所提出的并行格式的构造方法是将预测-校正技术应用于分区子区域的内边界,且与子区域内部的迭代求解相结合,讨论了这些并行格式的稳定性、收敛性与并行度等性质．
In practical simulation, due to the requirement to the time step length, implicit schemes are often chosen for radiation heat conduct equation. Implicit schemes are hard to parallelize, while explicit schemes are easy to implement on parallel computer in spite of its strict stability constraints. When the problem requires hundreds, thousands even tens of thousands of CPUs to compute together, the strong coupling and the global communication become the bottleneck of high performance computing. It has become a challenging problem in large scale scientific and engineering computation to reformulate exist implicit schemes and develop parallel computational methods for large scale parallel computers. In this paper, the construction and basic properties of iterative parallel schemes are introduced. The proposed parallel schemes apply the predication and correction techniques to the inner interface of subdomains. The techniques are combined to the itera- tive solution procedure of the subdomain problem. The stability, convergence and parallelism are studied.
出处
《数值计算与计算机应用》
CSCD
2006年第1期67-80,共14页
Journal on Numerical Methods and Computer Applications
基金
国家重点基础研究发展计划(973计划)(2005CB321703)国家自然科学基金(10476002
60533020)资助
关键词
热传导方程
并行差分方法
迭代法
界面修正
Heat equation, parallel difference scheme, iterative methods, interface correction
