Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems

Engwer, Christian; Ohlberger, Mario; Renelt, Lukas

Research article (journal) | Peer reviewed

Abstract

This contribution introduces a model order reduction approach for an advection-reaction problem with a parametrized reaction function. The underlying discretization uses an ultraweak formulation with an L2-like trial space and an 'optimal' test space as introduced by Demkowicz et al. This ensures the stability of the discretization and in addition allows for a symmetric reformulation of the problem in terms of a dual solution which can also be interpreted as the normal equations of an adjoint least-squares problem. Classic model order reduction techniques can then be applied to the space of dual solutions which also immediately gives a reduced primal space. We show that the necessary computations do not require the reconstruction of any primal solutions and can instead be performed entirely on the space of dual solutions. We prove exponential convergence of the Kolmogorov N-width and show that a greedy algorithm produces quasi-optimal approximation spaces for both the primal and the dual solution space. Numerical experiments based on the benchmark problem of a catalytic filter confirm the applicability of the proposed method.

Details about the publication

JournalSIAM Journal on Scientific Computing (SIAM J. Sci. Comput.)
Volume46
Issue5
Page rangeA3205-A3229
StatusPublished
Release year2024 (08/10/2024)
Language in which the publication is writtenEnglish
DOI10.1137/23M1613402
Link to the full texthttps://epubs.siam.org/doi/full/10.1137/23M1613402
Keywordsreactive transport; model order reduction; optimal stability; ultraweak formulations

Authors from the University of Münster

Engwer, Christian
Professorship for Applications of Partial Differential Equations
Ohlberger, Mario
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
Renelt, Lukas
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)

Projects the publication originates from

Duration: 01/01/2019 - 31/12/2025 | 1st Funding period
Funded by: DFG - Cluster of Excellence
Type of project: Main DFG-project hosted at University of Münster
Duration: 01/01/2019 - 31/12/2025 | 1st Funding period
Funded by: DFG - Cluster of Excellence
Type of project: Subproject in DFG-joint project hosted at University of Münster

Promotionen, aus denen die Publikation resultiert

Numerical methods for Friedrichs’ systems: Approximation theory, localized training and inherently stable model order reduction
Candidate: Renelt, Lukas | Supervisors: Ohlberger, Mario; Engwer, Christian | Reviewers: Ohlberger, Mario; Engwer, Christian; Vohralík; Martin
Period of time: 01/02/2021 - 10/01/2025
Doctoral examination procedure finished at: Doctoral examination procedure at University of Münster