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Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients |
Dong Hao (董灏)a, Nie Yu-Feng (聂玉峰)a, Cui Jun-Zhi (崔俊芝)b, Wu Ya-Tao (武亚涛)a |
a School of Science, Northwestern Polytechnical University, Xi'an 710129, China; b Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China |
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Abstract We study the hyperbolic-parabolic equations with rapidly oscillating coefficients. The formal second-order two-scale asymptotic expansion solutions are constructed by the multiscale asymptotic analysis. In addition, we theoretically explain the importance of the second-order two-scale solution by the error analysis in the pointwise sense. The associated explicit convergence rates are also obtained. Then a second-order two-scale numerical method based on the Newmark scheme is presented to solve the equations. Finally, some numerical examples are used to verify the effectiveness and efficiency of the multiscale numerical algorithm we proposed.
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Received: 15 March 2015
Revised: 22 April 2015
Accepted manuscript online:
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PACS:
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02.30.Jr
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(Partial differential equations)
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02.60.Cb
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(Numerical simulation; solution of equations)
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Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11471262), the National Basic Research Program of China (Grant No. 2012CB025904), and the State Key Laboratory of Science and Engineering Computing and the Center for High Performance Computing of Northwestern Polytechnical University, China. |
Corresponding Authors:
Nie Yu-Feng
E-mail: yfnie@nwpu.edu.cn
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Cite this article:
Dong Hao (董灏), Nie Yu-Feng (聂玉峰), Cui Jun-Zhi (崔俊芝), Wu Ya-Tao (武亚涛) Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients 2015 Chin. Phys. B 24 090204
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[1] |
Wu Y T, Nie Y F and Yang Z H 2014 CMES-Computer Modeling in Engineering & Sciences 4 297
|
[2] |
Cui J Z 2001 Proceedings on Computational Mechanics in Science and Engineering, Peking University Press, December 5-8, 2001, Guangzhou, China, p. 33
|
[3] |
Yang Z Q, Cui J Z and Li B W 2014 Chin. Phys. B 23 030203
|
[4] |
Su F, Cui J Z, Xu Z and Dong Q L 2010 Finite Elements in Analysis and Design 46 320
|
[5] |
Cao L Q, Cui J Z and Luo J L 2003 Journal of Computational and Applied Mathematics 157 1
|
[6] |
Dong Q L and Cao L Q 2014 Applied Mathematics and Computation 232 872
|
[7] |
Dong Q L and Cao L Q 2009 Applied Numerical Mathematics 59 3008
|
[8] |
Cao L Q 2005 Numerische Mathematik 103 11
|
[9] |
Cao L Q, Cui J Z and Zhu D C 2002 SIAM Journal on Numerical Analysis 40 543
|
[10] |
Cao L Q and Cui J Z 2004 Numerische Mathematik 96 525
|
[11] |
Yang Z H, Chen Y, Yang Z Q and Ma Q 2014 Chin. Phys. B 23 076501
|
[12] |
Migórski S 1996 Universitatis Iagellonicae Acta Matematica 33 59
|
[13] |
Nguetseng G, Nnang H and Svanstedt N 2010 Journal Of Function Spaces And Applications 8 17
|
[14] |
Lu L Q and Li S J 2014 Journal of Mathematical Analysis and Applications 418 64
|
[15] |
Zhang S 2007 Thermodynamic Analysis of Periodic MultiPhase Materials by Spatial and Temporal Multiscale Method (Ph. D. Dissertation) (Dalian: Dalian University of Technology) (in Chinese)
|
[16] |
Timofte C 2010 AIP Conference Proceedings 1301 543
|
[17] |
Hubert N 2012 Nonlinear Differential Equations and Applications NoDEA 19 539
|
[18] |
Narazaki T 2004 J. Math. Soc 56 585
|
[19] |
Radu P, Todorova G and Yordanov B 2010 Trans. Amer. Math. Soc 362 2279
|
[20] |
Todorova G and Yordanov B 2009 J. Differential Equations 246 4497
|
[21] |
Zhang X and Wang T S 2007 Computational Dynamics (Beijing: Tsinghua University press) (in Chinese) pp. 162-167
|
[22] |
Bensoussan A, Lions J L and Papanicolaou G 1978 Asymptotic Analysis of Periodic Structures (Amsterdam: North-Holland Publishing Company) pp. 537-545
|
[23] |
Oleinik O A, Shamaev A S and Yosifian G A 1992 Mathematical Problems in Elasticity and Homogenization (Amsterdam: North-Holland Publishing Company) pp. 13-23
|
[24] |
Cioranescu D and Donato P 1999 An Introduction to Homogenization (New York: Oxford University Press) pp. 125-137, 222-238
|
[25] |
Braess D 2007 Finite Elements Theory, Fast Solvers, and Applications in Elasticity Theory (Cambridge: Cambridge University Press)
|
[26] |
Lin Q and Zhu Q D 1994 The Preprocessing snd Preprocessing for the Finite Element Method (Shanghai: Shanghai Scientific & Technical Publishers) (in Chinese) pp. 57-65
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