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

doi:10.1007/s42967-020-00096-0

Abstract

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

CLC Number:

65M60

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.

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