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

作　　者：董灏 聂玉峰 崔俊芝 武亚涛 

机构地区：[1]School of Science,Northwestern Polytechnical University [2]Academy of Mathematics and Systems Science,Chinese Academy of Sciences

出　　处：《Chinese Physics B》2015年第9期40-53,共14页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant No.11471262);the National Basic Research Program of China(Grant No.2012CB025904);the State Key Laboratory of Science and Engineering Computing and the Center for High Performance Computing of Northwestern Polytechnical University,China

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.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 

分 类 号：O175.28[理学—数学]