Communications on Applied Mathematics and Computation >

2022 , Vol. 4 >Issue 1: 60 - 83

DOI: https://doi.org/10.1007/s42967-020-00096-0

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

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  • 1 School of Mathematics, Jilin University, Jilin 130012, China;
    2 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA;
    3 Department of Mathematics, Statistics and Physics, Wichita State University, Wichita, KS 67260, USA;
    4 Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 70409, USA;
    5 Department of Mathematics, Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI 48824, USA

Received date: 2020-06-30

  Revised date: 2020-09-11

  Online published: 2022-03-01

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Abstract

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 efciency. 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.

Key words： Multiresolution; Sparse grid; Ultra-weak discontinuous Galerkin method; Schrödinger equation; Adaptivity

Cite this article

Zhanjing Tao, Juntao Huang, Yuan Liu, Wei Guo, Yingda Cheng . An Adaptive Multiresolution Ultra-weak Discontinuous Galerkin Method for Nonlinear Schrödinger Equations[J]. Communications on Applied Mathematics and Computation, 2022 , 4(1) : 60 -83 . DOI: 10.1007/s42967-020-00096-0

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