Project Details
Projekt
Numerical approximation of the Gross-Pitaevskii equation via vortex tracking (C05)
Subject Area
Mathematics
Term
since 2022
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 442047500
Gross-Pitaevskii equations play a central role in various models of condensed matter physics. A dominating feature is the occurrence of quantized vortices that effectively evolve according to a Hamilton-ODE system. The project aims at placing the well-developed analytical theory of this singular limit in a computational framework that allows to prove accuracy and efficiency of numerical approximations throughout the vortex regime ε ≪ 1. Equipped with these simulation tools, we expect to gain new analytical insights, for example on complex periodic solutions of the Gross-Pitaevskii equation.
DFG Programme
Collaborative Research Centres
Subproject of
SFB 1481:
Sparsity and Singular Structures
Applicant Institution
Rheinisch-Westfälische Technische Hochschule Aachen
Project Heads
Professor Dr. Christof Erich Melcher; Professor Dr. Benjamin Stamm
