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

TL;DR

This paper introduces an adaptive multiresolution ultra-weak discontinuous Galerkin method tailored for nonlinear Schrödinger equations, effectively capturing complex wave phenomena and improving computational efficiency.

Contribution

It presents a novel high-order adaptive scheme combining ultra-weak DG formulation with multiresolution adaptivity for nonlinear Schrödinger equations.

Findings

Successfully captures soliton waves

Effectively models blow-up phenomena

Demonstrates high accuracy and efficiency

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.