Theoretical and Practical Aspects of Space-Time DG-SEM Implementations
(2023) In The SMAI Journal of computational mathematics 9. p.61-93- Abstract
- We discuss two approaches for the formulation and implementation of space-time discontinuous Galerkin spectral element methods (DG-SEM). In one, time is treated as an additional coordinate direction and a Galerkin procedure is applied to the entire problem. In the other, the method of lines is used with DG-SEM in space and the fully implicit Runge–Kutta method Lobatto IIIC in time. The two approaches are mathematically equivalent in the sense that they lead to the same discrete solution. However, in practice they differ in several important respects, including the terminology used to describe them, the structure of the resulting software, and the interaction with nonlinear solvers. Challenges and merits of the two approaches are discussed... (More)
- We discuss two approaches for the formulation and implementation of space-time discontinuous Galerkin spectral element methods (DG-SEM). In one, time is treated as an additional coordinate direction and a Galerkin procedure is applied to the entire problem. In the other, the method of lines is used with DG-SEM in space and the fully implicit Runge–Kutta method Lobatto IIIC in time. The two approaches are mathematically equivalent in the sense that they lead to the same discrete solution. However, in practice they differ in several important respects, including the terminology used to describe them, the structure of the resulting software, and the interaction with nonlinear solvers. Challenges and merits of the two approaches are discussed with the goal of providing the practitioner with sufficient consideration to choose which path to follow. Additionally, implementations of the two methods are provided as a starting point for further development. Numerical experiments validate the theoretical accuracy of these codes and demonstrate their utility, even for 4D problems. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/244d8e6b-9c16-4802-8c9a-1cac68e124cc
- author
- Versbach, Lea Miko LU ; Linders, Viktor LU ; Klöfkorn, Robert LU and Birken, Philipp LU
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Space-time, Discontinuous Galerkin, DG-SEM
- in
- The SMAI Journal of computational mathematics
- volume
- 9
- pages
- 61 - 93
- publisher
- Centre Mersenne
- external identifiers
-
- scopus:85164375799
- ISSN
- 2426-8399
- DOI
- 10.5802/smai-jcm.95
- language
- English
- LU publication?
- yes
- id
- 244d8e6b-9c16-4802-8c9a-1cac68e124cc
- date added to LUP
- 2023-08-19 15:22:03
- date last changed
- 2023-09-14 12:27:58
@article{244d8e6b-9c16-4802-8c9a-1cac68e124cc, abstract = {{We discuss two approaches for the formulation and implementation of space-time discontinuous Galerkin spectral element methods (DG-SEM). In one, time is treated as an additional coordinate direction and a Galerkin procedure is applied to the entire problem. In the other, the method of lines is used with DG-SEM in space and the fully implicit Runge–Kutta method Lobatto IIIC in time. The two approaches are mathematically equivalent in the sense that they lead to the same discrete solution. However, in practice they differ in several important respects, including the terminology used to describe them, the structure of the resulting software, and the interaction with nonlinear solvers. Challenges and merits of the two approaches are discussed with the goal of providing the practitioner with sufficient consideration to choose which path to follow. Additionally, implementations of the two methods are provided as a starting point for further development. Numerical experiments validate the theoretical accuracy of these codes and demonstrate their utility, even for 4D problems.}}, author = {{Versbach, Lea Miko and Linders, Viktor and Klöfkorn, Robert and Birken, Philipp}}, issn = {{2426-8399}}, keywords = {{Space-time; Discontinuous Galerkin; DG-SEM}}, language = {{eng}}, pages = {{61--93}}, publisher = {{Centre Mersenne}}, series = {{The SMAI Journal of computational mathematics}}, title = {{Theoretical and Practical Aspects of Space-Time DG-SEM Implementations}}, url = {{http://dx.doi.org/10.5802/smai-jcm.95}}, doi = {{10.5802/smai-jcm.95}}, volume = {{9}}, year = {{2023}}, }