A monolithic space-time temporal multirate finite element framework for interface and volume coupled problems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929255421575168 |
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| author | Roth, Julian Soszyńska, Martyna Richter, Thomas Wick, Thomas |
| author_facet | Roth, Julian Soszyńska, Martyna Richter, Thomas Wick, Thomas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12455 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A monolithic space-time temporal multirate finite element framework for interface and volume coupled problems Roth, Julian Soszyńska, Martyna Richter, Thomas Wick, Thomas Numerical Analysis 65M50, 65M60, 74J05, 76S05 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. |
| title | A monolithic space-time temporal multirate finite element framework for interface and volume coupled problems |
| topic | Numerical Analysis 65M50, 65M60, 74J05, 76S05 |
| url | https://arxiv.org/abs/2307.12455 |