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 displa...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-04-01
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| Series: | Advanced Modeling and Simulation in Engineering Sciences |
| Online Access: | https://doi.org/10.1186/s40323-024-00262-6 |
| _version_ | 1797199235220766720 |
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| author | Hendrik Fischer Julian Roth Ludovic Chamoin Amélie Fau Mary Wheeler Thomas Wick |
| author_facet | Hendrik Fischer Julian Roth Ludovic Chamoin Amélie Fau Mary Wheeler Thomas Wick |
| author_sort | Hendrik Fischer |
| collection | DOAJ |
| description | 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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| format | Article |
| id | doaj.art-0832733b1beb4cfb843b36287b7b2cf1 |
| institution | Directory Open Access Journal |
| issn | 2213-7467 |
| language | English |
| last_indexed | 2024-04-24T07:12:32Z |
| publishDate | 2024-04-01 |
| publisher | SpringerOpen |
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| series | Advanced Modeling and Simulation in Engineering Sciences |
| spelling | doaj.art-0832733b1beb4cfb843b36287b7b2cf12024-04-21T11:25:11ZengSpringerOpenAdvanced Modeling and Simulation in Engineering Sciences2213-74672024-04-0111112710.1186/s40323-024-00262-6Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticityHendrik Fischer0Julian Roth1Ludovic Chamoin2Amélie Fau3Mary Wheeler4Thomas Wick5Leibniz Universität Hannover, Institut für Angewandte Mathematik, AG Wissenschaftliches RechnenLeibniz Universität Hannover, Institut für Angewandte Mathematik, AG Wissenschaftliches RechnenUniversité Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, LMPS, Laboratoire de Mécanique Paris-SaclayUniversité Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, LMPS, Laboratoire de Mécanique Paris-SaclayThe University of Texas at Austin, Oden InstituteLeibniz Universität Hannover, Institut für Angewandte Mathematik, AG Wissenschaftliches RechnenAbstract 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.https://doi.org/10.1186/s40323-024-00262-6 |
| spellingShingle | Hendrik Fischer Julian Roth Ludovic Chamoin Amélie Fau Mary Wheeler Thomas Wick Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity Advanced Modeling and Simulation in Engineering Sciences |
| title | Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity |
| title_full | Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity |
| title_fullStr | Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity |
| title_full_unstemmed | Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity |
| title_short | Adaptive space-time model order reduction with dual-weighted residual (MORe DWR) error control for poroelasticity |
| title_sort | adaptive space time model order reduction with dual weighted residual more dwr error control for poroelasticity |
| url | https://doi.org/10.1186/s40323-024-00262-6 |
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