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

Engström, C.; Giani, S.; Grubišić, L.

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: Jan 27, 2023
• 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