Engwer, Christian; Ohlberger, Mario; Renelt, Lukas
Research article (journal) | Peer reviewedThis 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.
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) |
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 |
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 |