TIME-EXTRAPOLATION ALGORITHM (TEA) FOR LINEAR PARABOLIC PROBLEMS *
TIME-EXTRAPOLATION ALGORITHM (TEA) FOR LINEAR PARABOLIC PROBLEMS *
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DOI：
10.4208/jcm.1310-fe1
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发表时间：
2014-03
影响因子：
0.9
通讯作者：
Chuanmiao Chen;Hongling Hu;K. Pan
中科院分区：
文献类型：
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作者：
Chuanmiao Chen;Hongling Hu;K. Pan
讨论了抛物线问题准均匀网格上Crank-Nicolson格式的快速解。首先，为了降低解的正则性要求，证明了一些新的误差估计。其次，我们分析了抛物型离散格式的两个特点，发现多重网格法（MG）的效率大大降低。数值实验比较了直接共轭梯度法（DCG）和外推级联多重网格法（EXCMG）的效率。最后，我们提出了一种时间外推算法（TEA），它将先前几级解的线性组合作为良好的初始值来加快收敛速度。对一些典型的外推公式进行了数值比较。我们发现，在一定的精度要求下，3阶7级外推公式的CG迭代次数约为DCG的1/3。由于TEA算法与空间维度无关，因此对于准均匀网格仍然有效。由于只需要最精细的网格，因此所提出的方法被认为对于非线性抛物线问题非常有效。
The fast solutions of Crank-Nicolson scheme on quasi-uniform mesh for parabolic problems are discussed. First, to decrease regularity requirements of solutions, some new error estimates are proved. Second, we analyze the two characteristics of parabolic discrete scheme, and find that the efficiency of Multigrid Method (MG) isgreatly reduced. Numerical experiments compare the efficiency of Direct Conjugate Gradient Method (DCG) and Extrapolation Cascadic Multigrid Method (EXCMG). Last, we propose a TimeExtrapolation Algorithm (TEA), which takes a linear combination of previous several level solutions as good initial values to accelerate the rate of convergence. Some typical extrapolation formulas are compared numerically. And we find that under certain accuracy requirement, the CG iteration count for the 3-order and 7-level extrapolation formula is about 1/3 of that of DCG’s. Since the TEA algorithm is independent of the space dimension, it is still valid for quasi-uniform meshes. As only the finest grid is needed, the proposed method is regarded very effective for nonlinear parabolic problems.