Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Hendrik Fischer
  • Julian Roth
  • Ludovic Chamoin
  • Amelie Fau
  • Mary F. Wheeler
  • Thomas Wick

External Research Organisations

  • Université Paris-Saclay
  • University of Texas at Austin
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Details

Original languageEnglish
Article number9
JournalAdvanced Modeling and Simulation in Engineering Sciences
Volume11
Issue number1
Publication statusPublished - 18 Apr 2024

Abstract

In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the Biot system which consists of vector-valued displacements (geomechanics) coupled to a Darcy flow pressure equation. The MORe DWR method introduces a goal-oriented adaptive incremental proper orthogonal decomposition (POD) based-reduced-order model (ROM). The error in the reduced goal functional is estimated during the simulation, and the POD basis is enriched on-the-fly if the estimate exceeds a given threshold. This results in a reduction of the total number of full-order-model solves for the simulation of the porous medium, a robust estimation of the quantity of interest and well-suited reduced bases for the problem at hand. We apply a space-time Galerkin discretization with Taylor-Hood elements in space and a discontinuous Galerkin method with piecewise constant functions in time. The latter is well-known to be similar to the backward Euler scheme. We demonstrate the efficiency of our method on the well-known two-dimensional Mandel benchmark and a three-dimensional footing problem.

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Cite this

Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity. / Fischer, Hendrik; Roth, Julian; Chamoin, Ludovic et al.
In: Advanced Modeling and Simulation in Engineering Sciences, Vol. 11, No. 1, 9, 18.04.2024.

Research output: Contribution to journalArticleResearchpeer review

Fischer, H, Roth, J, Chamoin, L, Fau, A, Wheeler, MF & Wick, T 2024, 'Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity', Advanced Modeling and Simulation in Engineering Sciences, vol. 11, no. 1, 9. https://doi.org/10.48550/ARXIV.2311.08907, https://doi.org/10.1186/s40323-024-00262-6
Fischer, H., Roth, J., Chamoin, L., Fau, A., Wheeler, M. F., & Wick, T. (2024). Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity. Advanced Modeling and Simulation in Engineering Sciences, 11(1), Article 9. https://doi.org/10.48550/ARXIV.2311.08907, https://doi.org/10.1186/s40323-024-00262-6
Fischer H, Roth J, Chamoin L, Fau A, Wheeler MF, Wick T. Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity. Advanced Modeling and Simulation in Engineering Sciences. 2024 Apr 18;11(1):9. doi: 10.48550/ARXIV.2311.08907, 10.1186/s40323-024-00262-6
Fischer, Hendrik ; Roth, Julian ; Chamoin, Ludovic et al. / Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity. In: Advanced Modeling and Simulation in Engineering Sciences. 2024 ; Vol. 11, No. 1.
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abstract = "In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the Biot system which consists of vector-valued displacements (geomechanics) coupled to a Darcy flow pressure equation. The MORe DWR method introduces a goal-oriented adaptive incremental proper orthogonal decomposition (POD) based-reduced-order model (ROM). The error in the reduced goal functional is estimated during the simulation, and the POD basis is enriched on-the-fly if the estimate exceeds a given threshold. This results in a reduction of the total number of full-order-model solves for the simulation of the porous medium, a robust estimation of the quantity of interest and well-suited reduced bases for the problem at hand. We apply a space-time Galerkin discretization with Taylor-Hood elements in space and a discontinuous Galerkin method with piecewise constant functions in time. The latter is well-known to be similar to the backward Euler scheme. We demonstrate the efficiency of our method on the well-known two-dimensional Mandel benchmark and a three-dimensional footing problem.",
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