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Time-Extrapolation Algorithm (TEA) for Linear Parabolic Problem

Time-Extrapolation Algorithm (TEA) for Linear Parabolic Problem
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Year:    2014

Journal of Computational Mathematics, Vol. 32 (2014), Iss. 2 : pp. 183–194

Abstract

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) is greatly reduced. Numerical experiments compare the efficiency of Direct Conjugate Gradient Method (DCG) and Extrapolation Cascadic Multigrid Method (EXCMG). Last, we propose a Time-Extrapolation 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1310-FE1

Journal of Computational Mathematics, Vol. 32 (2014), Iss. 2 : pp. 183–194

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    12

Keywords:    Parabolic problem Crank-Nicolson scheme Error estimates Time-extrapolation algorithm CG-iteration.

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