A High-Efficient Algorithm for Parabolic Problems with Time-Dependent Coefficients
| Autor: | Hongling Hu, Xiangqi Wang, Chuanmiao Chen |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Mathematical optimization
Quadric Efficient algorithm Applied Mathematics Mechanical Engineering 05 social sciences Function (mathematics) Parabolic cylinder function 030204 cardiovascular system & hematology 03 medical and health sciences Matrix (mathematics) 0302 clinical medicine Conjugate gradient method 0502 economics and business Applied mathematics Initial value problem 050211 marketing Linear combination Mathematics |
| Zdroj: | Advances in Applied Mathematics and Mechanics. 9:501-514 |
| ISSN: | 2075-1354 2070-0733 |
| DOI: | 10.4208/aamm.2015.m1281 |
| Popis: | A high-efficient algorithm to solve Crank-Nicolson scheme for variable coefficient parabolic problems is studied in this paper, which consists of the Function Time-Extrapolation Algorithm (FTEA) and Matrix Time-Extrapolation Algorithm (MTEA). First, FTEA takes a linear combination of previous l level solutions as good initial value of Un(see Time-extrapolation algorithm (TEA) for linear parabolic problems, J. Comput. Math., 32(2) (2014), pp. 183–194), so that Conjugate Gradient (CG)-iteration counts decrease to 1/3~1/4 of direct CG. Second, MTEA uses a linear combination of exact matrix values in level L, L+s, L+2s to predict matrix values in the following s–1 levels, and the coefficients of the linear combination is deduced by the quadric interpolation formula, then fully recalculate the matrix values at time level L+3s, and continue like this iteratively. Therefore, the number of computing the full matrix decreases by a factor 1/s. Last, the MTEA is analyzed in detail and the effectiveness of new method is verified by numerical experiments. |
| Databáze: | OpenAIRE |
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