Details
| Original language | English |
|---|---|
| Article number | 9 |
| Journal | Advanced Modeling and Simulation in Engineering Sciences |
| Volume | 11 |
| Issue number | 1 |
| Publication status | Published - 18 Apr 2024 |
Abstract
ASJC Scopus subject areas
- Engineering(all)
- Engineering (miscellaneous)
- Mathematics(all)
- Applied Mathematics
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Modelling and Simulation
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In: Advanced Modeling and Simulation in Engineering Sciences, Vol. 11, No. 1, 9, 18.04.2024.
Research output: Contribution to journal › Article › Research › peer review
}
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 -