Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients

doi:10.1088/1674-1056/24/9/090204

中国物理B ›› 2015, Vol. 24 ›› Issue (9): 90204-090204.doi: 10.1088/1674-1056/24/9/090204

Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients

董灏^a, 聂玉峰^a, 崔俊芝^b, 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

收稿日期:2015-03-15 修回日期:2015-04-22 出版日期:2015-09-05 发布日期:2015-09-05
基金资助:
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.

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

Received:2015-03-15 Revised:2015-04-22 Online:2015-09-05 Published:2015-09-05
Contact: Nie Yu-Feng E-mail:yfnie@nwpu.edu.cn
Supported by:
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.

摘要/Abstract

摘要： 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.

关键词: hyperbolic-parabolic equations, rapidly oscillating coefficients, second-order two-scale numerical method, Newmark scheme

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.

Key words: hyperbolic-parabolic equations, rapidly oscillating coefficients, second-order two-scale numerical method, Newmark scheme

中图分类号: (Partial differential equations)

02.30.Jr

02.60.Cb (Numerical simulation; solution of equations)

董灏, 聂玉峰, 崔俊芝, 武亚涛. Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients[J]. 中国物理B, 2015, 24(9): 90204-090204.

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[J]. Chin. Phys. B, 2015, 24(9): 90204-090204.

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Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients

Second-order two-scale analysis and numerical algorithms for the hyperbolic-parabolic equations with rapidly oscillating coefficients

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