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

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Hendrik Fischer
  • Julian Roth
  • Ludovic Chamoin
  • Amelie Fau
  • Mary F. Wheeler
  • Thomas Wick
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Aufsatznummer9
FachzeitschriftAdvanced Modeling and Simulation in Engineering Sciences
Jahrgang11
Ausgabenummer1
PublikationsstatusVeröffentlicht - 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.

ASJC Scopus Sachgebiete

Zitieren

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, Jahrgang 11, Nr. 1, 9, 18.04.2024.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-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, Jg. 11, Nr. 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), Artikel 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 ; Jahrgang 11, Nr. 1.
Download
@article{26e91193c7fe4156b40684604b2ddbf5,
title = "Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity",
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.",
author = "Hendrik Fischer and Julian Roth and Ludovic Chamoin and Amelie Fau and Wheeler, {Mary F.} and Thomas Wick",
note = "Open Access funding enabled and organized by Projekt DEAL.",
year = "2024",
month = apr,
day = "18",
doi = "10.48550/ARXIV.2311.08907",
language = "English",
volume = "11",
number = "1",

}

Download

TY - JOUR

T1 - Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity

AU - Fischer, Hendrik

AU - Roth, Julian

AU - Chamoin, Ludovic

AU - Fau, Amelie

AU - Wheeler, Mary F.

AU - Wick, Thomas

N1 - Open Access funding enabled and organized by Projekt DEAL.

PY - 2024/4/18

Y1 - 2024/4/18

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85190661716&partnerID=8YFLogxK

U2 - 10.48550/ARXIV.2311.08907

DO - 10.48550/ARXIV.2311.08907

M3 - Article

VL - 11

JO - Advanced Modeling and Simulation in Engineering Sciences

JF - Advanced Modeling and Simulation in Engineering Sciences

IS - 1

M1 - 9

ER -

Von denselben Autoren