Work

A gradient flow model for the Gross-Pitaevskii problem: mathematical and numerical analysis

Year: 2026

Type: article

Abstract: This paper concerns the mathematical and numerical analysis of the L 2 normalized gradient flow model for the Gross-Pitaevskii eigenvalue problem, which has been widely used to design the numerical schemes for the computation of the ground state of the Bose-Einstein condensate. We first provide the mathematical analysis for the model, including the well-posedness and the asymptotic behavior of the solution. Then we propose a normalized implicit-explicit fully discrete numerical scheme for the gradient flow model, and give some numerical analysis for the scheme, including the well-posedness and optimal convergence of the approximation. Some numerical experiments are provided to validate the theory.

Source: ESAIM Mathematical Modelling and Numerical Analysis

DOI: 10.1051/m2an/2026034

Authors: Tianyang Chu, Xiaoying Dai, Jing Wu, Aihui Zhou

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funder: National Natural Science Foundation of China