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

Yu LIN, Yaming CHEN, Chuanfu XU, Xiaogang DENG

doi:10.1007/s10483-018-2382-6

Applied Mathematics and Mechanics >

2018 , Vol. 39 >Issue 11: 1679 - 1690

DOI: https://doi.org/10.1007/s10483-018-2382-6

Articles

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

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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 date: 2018-01-22

Revised date: 2018-05-07

Online published: 2018-11-01

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)

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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

Cite this article

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, 2018 , 39(11) : 1679 -1690 . DOI: 10.1007/s10483-018-2382-6

References

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