A new multiscale discontinuous Galerkin method for the one-dimensional stationary Schr\"{o}dinger equation

Bo Dong University of Massachusetts Dartmouth Chi-Wang Shu Brown University Wei Wang Florida International University

Numerical Analysis and Scientific Computing mathscidoc:1610.25021

Journal of Scientific Computing, 66, 321-345, 2016
In this paper, we develop and analyze a new multiscale discontinuous Galerkin (DG) method for one-dimensional stationary Schr\"{o}dinger equations with open boundary conditions \bo{which have highly oscillating solutions}. Our method uses a smaller finite element space than the WKB local DG (WKB-LDG) method while achieving the same order of accuracy with no resonance errors. We prove that the DG approximation converges optimally with respect to the mesh size $h$ in $L^2$ norm without the typical constraint \bo{that $h$ has to be smaller than the wave length}. Numerical experiments were carried out to verify the second order optimal convergence rate of the method and to demonstrate its ability to capture oscillating solutions on coarse meshes in the applications to Schr\"{o}dinger equations.
discontinuous Galerkin method, multiscale method, Schr\"{o}dinger equation
[ Download ] [ 2016-10-11 11:20:30 uploaded by chiwangshu ] [ 697 downloads ] [ 0 comments ]
@inproceedings{bo2016a,
  title={A new multiscale discontinuous Galerkin method for the one-dimensional stationary Schr\"{o}dinger equation},
  author={Bo Dong, Chi-Wang Shu, and Wei Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161011112030836931135},
  booktitle={Journal of Scientific Computing},
  volume={66},
  pages={321-345},
  year={2016},
}
Bo Dong, Chi-Wang Shu, and Wei Wang. A new multiscale discontinuous Galerkin method for the one-dimensional stationary Schr\"{o}dinger equation. 2016. Vol. 66. In Journal of Scientific Computing. pp.321-345. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161011112030836931135.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved