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An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrödinger equations
Tao, Zhanjing Huang, Juntao Liu, Yuan Guo, Wei Cheng, Yingda
Tao, Zhanjing
Huang, Juntao
Liu, Yuan
Guo, Wei
Cheng, Yingda
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Adobe PDF, 4.29 MB
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2021-01-25
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Preprint
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Keywords
Multiresolution,Sparse grid,Ultra-weak discontinuous Galerkin method,Schrödinger equation,Adaptivity
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Citation
Tao, Z., Huang, J., Liu, Y. et al. An Adaptive Multiresolution Ultra-weak Discontinuous Galerkin Method for Nonlinear Schrödinger Equations. Commun. Appl. Math. Comput. 4, 60–83 (2022). https://doi.org/10.1007/s42967-020-00096-0
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 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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Preprint from available from arXiv. Also available from publisher.
Publisher
Springer
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Communications on Applied Mathematics and Computation;Volume 4
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2661-8893