Multiscale asymptotic expansions and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients

Authors:
Qiao-Li Dong;Li-Qun Cao
Affiliations:
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

In this paper, we discuss the multiscale analysis and numerical algorithms for the wave equations of second order with rapidly oscillating coefficients. The formal multiscale asymptotic expansions of the solutions for these problems in four specific cases are presented. Higher order corrector methods are constructed and associated explicit convergence rates are obtained in some cases. A multiscale numerical method and a symplectic geometric scheme are introduced. Finally, some numerical results and unsolved problems are presented, and these numerical results support strongly the convergence theorem of this paper.