Skip to main content

Research Repository

Advanced Search

Higher Order Composite DG approximations of Gross–Pitaevskii ground state: benchmark results and experiments

Engström, C.; Giani, S.; Grubišić, L.

Higher Order Composite DG approximations of Gross–Pitaevskii ground state: benchmark results and experiments Thumbnail


Authors

C. Engström

L. Grubišić



Abstract

Discontinuous Galerkin composite finite element methods (DGCFEM) are designed to tackle approximation problems on complicated domains. Partial differential equations posed on complicated domain are common when there are mesoscopic or local phenomena which need to be modeled at the same time as macropscopic phenomena. In this paper, an optical lattice will be used to illustrate the performance of the approximation algorithm for the ground state computation of a Gross-Pitaevskii equation, which is an eigenvalue problem with eigenvector nonlinearity. We will adapt the convergence results of Marcati and Maday 2018 to this particular class of discontinuous approximation spaces and benchmark the performance of the classic symmetric interior penalty hp-adaptive algorithm against the performance of the hp-DGCFEM.

Citation

Engström, C., Giani, S., & Grubišić, L. (2022). Higher Order Composite DG approximations of Gross–Pitaevskii ground state: benchmark results and experiments. Journal of Computational and Applied Mathematics, 400, Article 113652. https://doi.org/10.1016/j.cam.2021.113652

Journal Article Type Article
Acceptance Date May 8, 2021
Online Publication Date Jul 27, 2021
Publication Date Jan 15, 2022
Deposit Date May 11, 2021
Publicly Available Date Mar 29, 2024
Journal Journal of Computational and Applied Mathematics
Print ISSN 0377-0427
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 400
Article Number 113652
DOI https://doi.org/10.1016/j.cam.2021.113652

Files




You might also like



Downloadable Citations