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

verfasst von: Hendrik Fischer, Julian Roth, Ludovic Chamoin, Amelie Fau, Mary F. Wheeler, Thomas Wick
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.
Organisationseinheit(en): Institut für Angewandte Mathematik
Internationales GRK 2657: Methoden der Numerischen Mechanik in höheren Dimensionen
Institut für Baumechanik und Numerische Mechanik
Externe Organisation(en): Universität Paris-Saclay
University of Texas at Austin
Typ: Artikel
Journal: Advanced Modeling and Simulation in Engineering Sciences
Band: 11
Publikationsdatum: 18.04.2024
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Ingenieurwesen (sonstige), Angewandte Mathematik, Angewandte Informatik, Modellierung und Simulation
Elektronische Version(en): https://doi.org/10.48550/ARXIV.2311.08907 (Zugang: Offen)
https://doi.org/10.1186/s40323-024-00262-6 (Zugang: Offen)

BibTeX

@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",
journal = "Advanced Modeling and Simulation in Engineering Sciences",
issn = "2213-7467",
publisher = "Springer Open",
number = "1",
}