对抛物方程使用新显格式的区域分解算法  

DOMAIN DECOMPOSITION ALGORITHM USING NEW EXPLICIT SCHEME FOR THE PARABOLIC EQUATION

作　　者：盛志强[1] 刘兴平[2] 崔霞[2] 

机构地区：[1]中国工程物理研究院研究生部,北京2101信箱100088 [2]北京应用物理与计算数学研究所计算物理实验室,北京8009信箱100088

出　　处：《数值计算与计算机应用》2005年第4期249-261,共13页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(No.60373015)资助项目.

摘　　要：我们提出了两个具有改进稳定性限制条件的新显格式．与经典显格式相比,稳定性限制条 件分别对两维抛物问题放宽了4倍,对一维问题放宽了2倍,同时它的精度与经典全隐格式 的相同．然后,我们通过在内边界点使用大步长的这种新显格式,在内点使用全隐格式,设计 了一个有限差分区域分解算法,稳定性限制条件分别对一维抛物问题放宽了2m2倍,对二维 问题放宽了4m2倍．从而我们能使用一个大的时间步长,这使我们在并行求解抛物问题时能 节省大量的计算量．In this paper we present two new explicit schemes which have improved stability condition. The stability bound is increased by 4 times for the two dimensional parabolic problem and 2 times for the one dimensional parabolic problem compared with the classical single-point explicit scheme respectively. At the same time the accuracy of this new scheme is the same as that of the full implicit scheme. Then we design a finite difference domain decomposition procedure by using this new scheme with a larger spacing at interface points and the fully implicit scheme at interior points, the stability bound is released by 2m^2 for the one dimensional parabolic problem and 4m^2 for the two dimensional parabolic problem respectively. Hence we can use a larger time step, which can save a lot of computational works for the parallel solution of the parabolic problem.

关 键 词：区域分解 抛物方程 显格式 并行计算 有限差分 

分 类 号：O241.82[理学—计算数学] O175.26[理学—数学]