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

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.