An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrodinger equations

2020/07/03 by Zhanjing Tao, Juntao Huang, Tao, Zhanjing +7
Computer Science · Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2007.01471

arxiv created 2020/07/03 · arxiv updated 2020/07/06

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.

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