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

作     者：Zhanjing Tao Juntao Huang Yuan Liu Wei Guo Yingda Cheng Zhanjing Tao;Juntao Huang;Yuan Liu;Wei Guo;Yingda Cheng

作者机构：School of MathematicsJilin UniversityJilin 130012China Department of MathematicsMichigan State UniversityEast LansingMI 48824USA Department of MathematicsStatistics and PhysicsWichita State UniversityWichitaKS 67260USA Department of Mathematics and StatisticsTexas Tech UniversityLubbockTX 70409USA Department of MathematicsDepartment of Computational MathematicsScience and EngineeringMichigan State UniversityEast LansingMI 48824USA 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2022年第4卷第1期

页      面：60-83页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Funding Y.Liu:Research supported in part by a grant from the Simons Foundation(426993,Yuan Liu) W.Guo:Research is supported by NSF grant DMS-1830838 Y.Cheng:Research is supported by NSF grants DMS-1453661 and DMS-1720023 Z.Tao:Research is supported by NSFC Grant 12001231 

主　　题：Multiresolution Sparse grid Ultra-weak discontinuous Galerkin method Schrödinger equation Adaptivity 

摘      要：This paper develops a high-order adaptive scheme for solving nonlinear Schrödinger *** solutions to such equations often exhibit solitary wave and local structures,which make adaptivity essential in improving the simulation *** scheme uses the ultra-weak discontinuous Galerkin(DG)formulation and belongs to the framework of adaptive multiresolution *** numerical experiments are presented to demon-strate the excellent capability of capturing the soliton waves and the blow-up phenomenon.