Optimization of a global seventh-order dissipative compact finite-difference scheme by a genetic algorithm

doi:10.1007/s10483-018-2382-6

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (11): 1679-1690.doi: https://doi.org/10.1007/s10483-018-2382-6

• 论文 • 上一篇

Optimization of a global seventh-order dissipative compact finite-difference scheme by a genetic algorithm

Yu LIN¹, Yaming CHEN², Chuanfu XU^1,3, Xiaogang DENG²

1. College of Computer, National University of Defense Technology, Changsha 410073, China;
2. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China;
3. State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China

收稿日期:2018-01-22 修回日期:2018-05-07 出版日期:2018-11-01 发布日期:2018-11-01
通讯作者: Yaming CHEN E-mail:chenym-08@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11601517, 11502296, 61772542, and 61561146395) and the Basic Research Foundation of National University of Defense Technology (No. ZDYYJ-CYJ20140101)

Optimization of a global seventh-order dissipative compact finite-difference scheme by a genetic algorithm

Yu LIN¹, Yaming CHEN², Chuanfu XU^1,3, Xiaogang DENG²

1. College of Computer, National University of Defense Technology, Changsha 410073, China;
2. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China;
3. State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China

Received:2018-01-22 Revised:2018-05-07 Online:2018-11-01 Published:2018-11-01
Contact: Yaming CHEN E-mail:chenym-08@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11601517, 11502296, 61772542, and 61561146395) and the Basic Research Foundation of National University of Defense Technology (No. ZDYYJ-CYJ20140101)

摘要/Abstract

摘要： A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme.

关键词: reciprocal theorem method, basic solution, bending of thickrectangular plate, Reissner’s theory, genetic algorithm, dissipative compact, time stable, finite-difference scheme, high-order

Abstract: A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme.

Key words: reciprocal theorem method, basic solution, bending of thickrectangular plate, Reissner’s theory, genetic algorithm, high-order, finite-difference scheme, time stable, dissipative compact

中图分类号:

76M20
93D20

Yu LIN, Yaming CHEN, Chuanfu XU, Xiaogang DENG. Optimization of a global seventh-order dissipative compact finite-difference scheme by a genetic algorithm[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(11): 1679-1690.

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Optimization of a global seventh-order dissipative compact finite-difference scheme by a genetic algorithm

Optimization of a global seventh-order dissipative compact finite-difference scheme by a genetic algorithm

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