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 -