Higher Order Composite DG approximations of Gross–Pitaevskii ground state : Benchmark results and experiments
(2022) In Journal of Computational and Applied Mathematics 400.- 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 modelled at the same time as macroscopic 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... (More)
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 modelled at the same time as macroscopic 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.
(Less)
- author
- Engström, C. LU ; Giani, S. and Grubišić, L.
- publishing date
- 2022-01-15
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Composite finite elements, Discontinuous Galerkin finite element approximations, Gross–Pitaevskii eigenvalue problem
- in
- Journal of Computational and Applied Mathematics
- volume
- 400
- article number
- 113652
- publisher
- Elsevier
- external identifiers
-
- scopus:85111523654
- ISSN
- 0377-0427
- DOI
- 10.1016/j.cam.2021.113652
- language
- English
- LU publication?
- no
- additional info
- Funding Information: The work of L.G. has been supported by the Croatian Science Foundation grant IP-2019-04-6268 . We gratefully acknowledge the support. Publisher Copyright: © 2021 Elsevier B.V.
- id
- fc504bac-e23e-49ad-bbac-9925d901f6c7
- date added to LUP
- 2023-03-24 11:04:09
- date last changed
- 2023-03-24 13:27:18
@article{fc504bac-e23e-49ad-bbac-9925d901f6c7,
abstract = {{<p>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 modelled at the same time as macroscopic 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.</p>}},
author = {{Engström, C. and Giani, S. and Grubišić, L.}},
issn = {{0377-0427}},
keywords = {{Composite finite elements; Discontinuous Galerkin finite element approximations; Gross–Pitaevskii eigenvalue problem}},
language = {{eng}},
month = {{01}},
publisher = {{Elsevier}},
series = {{Journal of Computational and Applied Mathematics}},
title = {{Higher Order Composite DG approximations of Gross–Pitaevskii ground state : Benchmark results and experiments}},
url = {{http://dx.doi.org/10.1016/j.cam.2021.113652}},
doi = {{10.1016/j.cam.2021.113652}},
volume = {{400}},
year = {{2022}},
}