Gradient Flow Finite Element Discretisations with Energy-Based hp-Adaptivity for the Gross-Pitaevskii Equation with Angular Momentum Rotation
Type: article
Abstract: This article deals with the stationary Gross-Pitaevskii non-linear eigenvalue problem in the presence of a rotating magnetic field that is used to model macroscopic quantum effects such as Bose-Einstein condensates (BECs). In this regime, the ground-state wave-function can exhibit an a priori unknown number of quantum vortices at unknown locations, which necessitates the exploitation of adaptive numerical strategies. To this end, we consider the conforming finite element method and introduce a combination of a Sobolev gradient descent that respects the energy-topology of the problem to solve the non-linearity and an -adaptive strategy that is solely based on energy decay rather than a posteriori error estimators for the refinement process. Numerical results demonstrate that the hp-adaptive strategy is highly efficient in terms of accuracy to compute the ground-state wave function and energy for several test problems where we observe exponential convergence.
DOI: 10.48620/93132
Authors: Heid, Pascal, Houston, Paul, Stamm, Benjamin, Wihler, Thomas P.
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7115719726
Cites:
Cited by:
Related to: