A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media

Tsz Shun Eric CHUNG Chi Yeung Lam Jianliang Qian

Numerical Analysis and Scientific Computing mathscidoc:1910.43561

Journal of Computational Physics, 348, 660-682, 2017.11
The numerical approximation of high-frequency wave propagation in inhomogeneous media is a challenging problem. In particular, computing high-frequency solutions by direct simulations requires several points per wavelength for stability and usually requires many points per wavelength for a satisfactory accuracy. In this paper, we propose a new method for the acoustic wave equation in inhomogeneous media in the time domain to achieve superior accuracy and stability without using a large number of unknowns. The method is based on a discontinuous Galerkin discretization together with carefully chosen basis functions. To obtain the basis functions, we use the idea from geometrical optics and construct the basis functions by using the leading order term in the asymptotic expansion. Also, we use a wavefront tracking method and a dimension reduction procedure to obtain dominant rays in each cell. We show
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@inproceedings{tsz2017a,
  title={A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media},
  author={Tsz Shun Eric CHUNG, Chi Yeung Lam, and Jianliang Qian},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020202352797207090},
  booktitle={Journal of Computational Physics},
  volume={348},
  pages={660-682},
  year={2017},
}
Tsz Shun Eric CHUNG, Chi Yeung Lam, and Jianliang Qian. A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media. 2017. Vol. 348. In Journal of Computational Physics. pp.660-682. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020202352797207090.
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