An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrodinger equations
Numerical Analysis
2020-07-06 v1 Numerical Analysis
Abstract
This paper develops a high order adaptive scheme for solving nonlinear Schrodinger equations. The solutions to such equations often exhibit solitary wave and local structures, which makes adaptivity essential in improving the simulation efficiency. Our scheme uses the ultra-weak discontinuous Galerkin (DG) formulation and belongs to the framework of adaptive multiresolution schemes. Various numerical experiments are presented to demonstrate the excellent capability of capturing the soliton waves and the blow-up phenomenon.
Cite
@article{arxiv.2007.01471,
title = {An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrodinger equations},
author = {Zhanjing Tao and Juntao Huang and Yuan Liu and Wei Guo and Yingda Cheng},
journal= {arXiv preprint arXiv:2007.01471},
year = {2020}
}