Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media

Ching-Shan Chou The Ohio State University Chi-Wang Shu Brown University Yulong Xing University of Tennessee

Numerical Analysis and Scientific Computing mathscidoc:1610.25040

Journal of Computational Physics, 272, 88-107, 2014
Solving wave propagation problems within heterogeneous media has been of great interest and has a wide range of applications in physics and engineering. The design of numerical methods for such general wave propagation problems is challenging because the energy conserving property has to be incorporated in the numerical algorithms in order to minimize the phase or shape errors after long time integration. In this paper, we focus on multi-dimensional wave problems and consider linear second-order wave equation in heterogeneous media. We develop and analyze an LDG method, in which numerical fluxes are carefully designed to maintain the energy preserving property and accuracy. Compatible high order energy conserving time integrators are also proposed. The optimal error estimates and the energy conserving property are proved for the semi-discrete methods. Our numerical experiments demonstrate optimal rates of convergence, and show that the errors of the numerical solutions do not grow significantly in time due to the energy conserving property.
wave propagation, local discontinuous Galerkin method, energy conservation, optimal error estimate, heterogeneous media
[ Download ] [ 2016-10-12 04:28:04 uploaded by chiwangshu ] [ 849 downloads ] [ 0 comments ]
@inproceedings{ching-shan2014optimal,
  title={Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media},
  author={Ching-Shan Chou, Chi-Wang Shu, and Yulong Xing},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012042804090722158},
  booktitle={Journal of Computational Physics},
  volume={272},
  pages={88-107},
  year={2014},
}
Ching-Shan Chou, Chi-Wang Shu, and Yulong Xing. Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media. 2014. Vol. 272. In Journal of Computational Physics. pp.88-107. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012042804090722158.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved