Details
Original language | English |
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Article number | 112863 |
Journal | Journal of computational physics |
Volume | 504 |
Early online date | 19 Feb 2024 |
Publication status | Published - 1 May 2024 |
Abstract
In this work, the dual-weighted residual (DWR) method is applied to obtain an error-controlled incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) is being introduced. It marries tensor-product space-time reduced-order modeling with time slabbing and an incremental POD basis generation with goal-oriented error control based on dual-weighted residual estimates. The error in the goal functional is being estimated during the simulation and the POD basis is being updated if the estimate exceeds a given threshold. This allows an adaptive enrichment of the POD basis in case of unforeseen changes in the solution behavior. Consequently, the offline phase can be skipped, the reduced-order model is being solved directly with the POD basis extracted from the solution on the first time slab and –if necessary– the POD basis is being enriched on-the-fly during the simulation with high-fidelity finite element solutions. Therefore, the full-order model solves can be reduced to a minimum, which is demonstrated on numerical tests for the heat equation and elastodynamics using time-averaged quantities of interest.
Keywords
- Dual-weighted residual method, Goal-oriented error control, Incremental proper orthogonal decomposition, Tensor-product space-time reduced-order modeling
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of computational physics, Vol. 504, 112863, 01.05.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - MORe DWR: Space-time goal-oriented error control for incremental POD-based ROM for time-averaged goal functionals
AU - Fischer, Hendrik
AU - Roth, Julian
AU - Wick, Thomas
AU - Chamoin, Ludovic
AU - Fau, Amelie
N1 - Funding Information: The authors acknowledge the funding of the German Research Foundation (DFG) within the framework of the International Research Training Group on Computational Mechanics Techniques in High Dimensions GRK 2657 under Grant Number 433082294 . In addition, we thank Hendrik Geisler (Leibniz University Hannover, GRK 2657) for fruitful discussions and comments. The support of the French-German University through the French-German Doctoral college “Sophisticated Numerical and Testing Approaches” ( CDFA-DFDK 19-04 ) is also acknowledged. We thank the anonymous reviewers for their extensive questions that helped to improve the manuscript.
PY - 2024/5/1
Y1 - 2024/5/1
N2 - In this work, the dual-weighted residual (DWR) method is applied to obtain an error-controlled incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) is being introduced. It marries tensor-product space-time reduced-order modeling with time slabbing and an incremental POD basis generation with goal-oriented error control based on dual-weighted residual estimates. The error in the goal functional is being estimated during the simulation and the POD basis is being updated if the estimate exceeds a given threshold. This allows an adaptive enrichment of the POD basis in case of unforeseen changes in the solution behavior. Consequently, the offline phase can be skipped, the reduced-order model is being solved directly with the POD basis extracted from the solution on the first time slab and –if necessary– the POD basis is being enriched on-the-fly during the simulation with high-fidelity finite element solutions. Therefore, the full-order model solves can be reduced to a minimum, which is demonstrated on numerical tests for the heat equation and elastodynamics using time-averaged quantities of interest.
AB - In this work, the dual-weighted residual (DWR) method is applied to obtain an error-controlled incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) is being introduced. It marries tensor-product space-time reduced-order modeling with time slabbing and an incremental POD basis generation with goal-oriented error control based on dual-weighted residual estimates. The error in the goal functional is being estimated during the simulation and the POD basis is being updated if the estimate exceeds a given threshold. This allows an adaptive enrichment of the POD basis in case of unforeseen changes in the solution behavior. Consequently, the offline phase can be skipped, the reduced-order model is being solved directly with the POD basis extracted from the solution on the first time slab and –if necessary– the POD basis is being enriched on-the-fly during the simulation with high-fidelity finite element solutions. Therefore, the full-order model solves can be reduced to a minimum, which is demonstrated on numerical tests for the heat equation and elastodynamics using time-averaged quantities of interest.
KW - Dual-weighted residual method
KW - Goal-oriented error control
KW - Incremental proper orthogonal decomposition
KW - Tensor-product space-time reduced-order modeling
UR - http://www.scopus.com/inward/record.url?scp=85185832719&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2024.112863
DO - 10.1016/j.jcp.2024.112863
M3 - Article
AN - SCOPUS:85185832719
VL - 504
JO - Journal of computational physics
JF - Journal of computational physics
SN - 0021-9991
M1 - 112863
ER -