An Adaptive Multiresolution Ultra-weak Discontinuous Galerkin Method for Nonlinear Schrödinger Equations

被引：0
作者：
Zhanjing Tao
Juntao Huang
Yuan Liu
Wei Guo
Yingda Cheng
机构：
[1] Jilin University,School of Mathematics
[2] Michigan State University,Department of Mathematics
[3] Wichita State University,Department of Mathematics, Statistics and Physics
[4] Texas Tech University,Department of Mathematics and Statistics
[5] Michigan State University,Department of Mathematics, Department of Computational Mathematics, Science and Engineering
来源：
Communications on Applied Mathematics and Computation | 2022年 / 4卷
关键词：
Multiresolution; Sparse grid; Ultra-weak discontinuous Galerkin method; Schrödinger equation; Adaptivity; 65M60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper develops a high-order adaptive scheme for solving nonlinear Schrödinger equations. The solutions to such equations often exhibit solitary wave and local structures, which make 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.
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页码：60 / 83
页数：23
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