MORe DWR: Space-time goal-oriented error control for incremental POD-based ROM for time-averaged goal functionals

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Hendrik Fischer
  • Julian Roth
  • Thomas Wick
  • Ludovic Chamoin
  • Amelie Fau

Research Organisations

External Research Organisations

  • Université Paris-Saclay
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Details

Original languageEnglish
Article number112863
JournalJournal of computational physics
Volume504
Early online date19 Feb 2024
Publication statusPublished - 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

Cite this

MORe DWR: Space-time goal-oriented error control for incremental POD-based ROM for time-averaged goal functionals. / Fischer, Hendrik; Roth, Julian; Wick, Thomas et al.
In: Journal of computational physics, Vol. 504, 112863, 01.05.2024.

Research output: Contribution to journalArticleResearchpeer review

Fischer H, Roth J, Wick T, Chamoin L, Fau A. MORe DWR: Space-time goal-oriented error control for incremental POD-based ROM for time-averaged goal functionals. Journal of computational physics. 2024 May 1;504:112863. Epub 2024 Feb 19. doi: 10.1016/j.jcp.2024.112863
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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.",
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note = "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. ",
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