Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909233128144896 |
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| author | Engwer, Christian Ohlberger, Mario Renelt, Lukas |
| author_facet | Engwer, Christian Ohlberger, Mario Renelt, Lukas |
| contents | 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 $L^2$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19674 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems Engwer, Christian Ohlberger, Mario Renelt, Lukas Numerical Analysis 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 $L^2$-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. |
| title | Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2310.19674 |