A monolithic space–time temporal multirate finite element framework for interface and volume coupled problems

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

Externe Organisationen

  • Universität Paris-Saclay
  • Otto-von-Guericke-Universität Magdeburg
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Details

OriginalspracheEnglisch
Aufsatznummer115831
Seiten (von - bis)115831
FachzeitschriftJournal of Computational and Applied Mathematics
Jahrgang446
Frühes Online-Datum28 Feb. 2024
PublikationsstatusVeröffentlicht - 15 Aug. 2024

Abstract

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.

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A monolithic space–time temporal multirate finite element framework for interface and volume coupled problems. / Roth, Julian; Soszyńska, Martyna; Richter, Thomas et al.
in: Journal of Computational and Applied Mathematics, Jahrgang 446, 115831, 15.08.2024, S. 115831.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Roth J, Soszyńska M, Richter T, Wick T. A monolithic space–time temporal multirate finite element framework for interface and volume coupled problems. Journal of Computational and Applied Mathematics. 2024 Aug 15;446:115831. 115831. Epub 2024 Feb 28. doi: 10.48550/arXiv.2307.12455, 10.1016/j.cam.2024.115831
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abstract = "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{\textquoteright}s benchmark and a three-dimensional footing problem. Detailed computational investigations and convergence analyses give evidence that our monolithic multirate framework performs well.",
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note = "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{\textquoteright}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{\textquoteright}s problem.",
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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.

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