Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity
This paper explores an iterative approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order models. One of the main challenges in addressing coupled multi-physics prob...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-02-01
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| Series: | Results in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037423000766 |
| _version_ | 1797260335703392256 |
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| author | Francesco Ballarin Sanghyun Lee Son-Young Yi |
| author_facet | Francesco Ballarin Sanghyun Lee Son-Young Yi |
| author_sort | Francesco Ballarin |
| collection | DOAJ |
| description | This paper explores an iterative approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order models. One of the main challenges in addressing coupled multi-physics problems is the complexity and computational expenses involved. In this study, we introduce a decoupled iterative solution approach, integrated with reduced order modeling, aimed at augmenting the efficiency of the computational algorithm. The iterative technique we employ builds upon the established fixed-stress splitting scheme that has been extensively investigated for Biot’s poroelasticity. By leveraging solutions derived from this coupled iterative scheme, the reduced order model employs an additional Galerkin projection onto a reduced basis space formed by a small number of modes obtained through proper orthogonal decomposition. The effectiveness of the proposed algorithm is demonstrated through numerical experiments, showcasing its computational prowess. |
| first_indexed | 2024-03-08T16:32:11Z |
| format | Article |
| id | doaj.art-4ecb9e88299445baaa1998c353faaa1d |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-04-24T23:23:42Z |
| publishDate | 2024-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-4ecb9e88299445baaa1998c353faaa1d2024-03-16T05:09:08ZengElsevierResults in Applied Mathematics2590-03742024-02-0121100430Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticityFrancesco Ballarin0Sanghyun Lee1Son-Young Yi2Department of Mathematics and Physics, Università Cattolica del Sacro Cuore, 25133 Brescia, Italy; Corresponding author.Department of Mathematics, Florida State University, Tallahassee, FL 32304, USADepartment of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USAThis paper explores an iterative approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order models. One of the main challenges in addressing coupled multi-physics problems is the complexity and computational expenses involved. In this study, we introduce a decoupled iterative solution approach, integrated with reduced order modeling, aimed at augmenting the efficiency of the computational algorithm. The iterative technique we employ builds upon the established fixed-stress splitting scheme that has been extensively investigated for Biot’s poroelasticity. By leveraging solutions derived from this coupled iterative scheme, the reduced order model employs an additional Galerkin projection onto a reduced basis space formed by a small number of modes obtained through proper orthogonal decomposition. The effectiveness of the proposed algorithm is demonstrated through numerical experiments, showcasing its computational prowess.http://www.sciencedirect.com/science/article/pii/S2590037423000766Linear thermo-poroelasticityIterativeFixed-stressReduced order modelingProper orthogonal decomposition |
| spellingShingle | Francesco Ballarin Sanghyun Lee Son-Young Yi Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity Results in Applied Mathematics Linear thermo-poroelasticity Iterative Fixed-stress Reduced order modeling Proper orthogonal decomposition |
| title | Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity |
| title_full | Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity |
| title_fullStr | Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity |
| title_full_unstemmed | Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity |
| title_short | Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity |
| title_sort | projection based reduced order modeling of an iterative scheme for linear thermo poroelasticity |
| topic | Linear thermo-poroelasticity Iterative Fixed-stress Reduced order modeling Proper orthogonal decomposition |
| url | http://www.sciencedirect.com/science/article/pii/S2590037423000766 |
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