Details
| Original language | English |
|---|---|
| Article number | 115831 |
| Pages (from-to) | 115831 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 446 |
| Early online date | 28 Feb 2024 |
| Publication status | Published - 15 Aug 2024 |
Abstract
Keywords
- Galerkin space–time, Interface coupling, Mandel's benchmark, Monolithic framework, Multirate, Volume coupling
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of Computational and Applied Mathematics, Vol. 446, 115831, 15.08.2024, p. 115831.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A monolithic space–time temporal multirate finite element framework for interface and volume coupled problems
AU - Roth, Julian
AU - Soszyńska, Martyna
AU - Richter, Thomas
AU - Wick, Thomas
N1 - Funding Information: JR acknowledges the funding of the German Research Foundation (DFG) within the framework of the International Research Training Group on Computational Mechanics Techniques in High Dimensions GRK 2657 under Grant Number 433082294 . MS and TR acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 314838170 , GRK 2297 MathCoRe. TW acknowledges support by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy within the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453). In addition, we thank Hendrik Fischer for fruitful discussions and comments, and Fleurianne Bertrand (TU Chemnitz) and Mary Wheeler (UT Austin) for some discussions on Mandel’s problem.
PY - 2024/8/15
Y1 - 2024/8/15
N2 - In this work, we propose and computationally investigate a monolithic space–time multirate scheme for coupled problems. The novelty lies in the monolithic formulation of the multirate approach as this requires a careful design of the functional framework, corresponding discretization, and implementation. Our method of choice is a tensor-product Galerkin space–time discretization. The developments are carried out for both prototype interface- and volume coupled problems such as coupled wave-heat-problems and a displacement equation coupled to Darcy flow in a poro-elastic medium. The latter is applied to the well-known Mandel’s benchmark and a three-dimensional footing problem. Detailed computational investigations and convergence analyses give evidence that our monolithic multirate framework performs well.
AB - In this work, we propose and computationally investigate a monolithic space–time multirate scheme for coupled problems. The novelty lies in the monolithic formulation of the multirate approach as this requires a careful design of the functional framework, corresponding discretization, and implementation. Our method of choice is a tensor-product Galerkin space–time discretization. The developments are carried out for both prototype interface- and volume coupled problems such as coupled wave-heat-problems and a displacement equation coupled to Darcy flow in a poro-elastic medium. The latter is applied to the well-known Mandel’s benchmark and a three-dimensional footing problem. Detailed computational investigations and convergence analyses give evidence that our monolithic multirate framework performs well.
KW - Galerkin space–time
KW - Interface coupling
KW - Mandel's benchmark
KW - Monolithic framework
KW - Multirate
KW - Volume coupling
UR - http://www.scopus.com/inward/record.url?scp=85186586798&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2307.12455
DO - 10.48550/arXiv.2307.12455
M3 - Article
VL - 446
SP - 115831
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0771-050X
M1 - 115831
ER -