A greedy MOR method for the tracking of eigensolutions to parametric elliptic PDEs
In this paper we introduce a Model Order Reduction (MOR) algorithm based on a sparse grid adaptive refinement, for the approximation of the eigensolutions to parametric problems arising from elliptic partial differential equations. In particular, we are interested in detecting the crossing of the hypersurfaces describing the eigenvalues as a function of the parameters. The a priori matching is followed by an a posteriori verification, driven by a suitably defined error indicator. At a given refinement level, a sparse grid approach is adopted for the construction of the grid of the next level, by using the marking given by the a posteriori indicator. Various numerical tests confirm the good performance of the scheme.
Authors
- Daniele Boffi (ORCID: https://orcid.org/0000-0003-0717-2940)
- Moataz Alghamdi (ORCID: https://orcid.org/0000-0001-9640-8438)
- Francesca Bonizzoni (ORCID: https://orcid.org/0000-0002-6222-3352)
Institutions
- University of Pavia (IT)
- King Abdullah University of Science and Technology (SA)
- Politecnico di Milano (IT)
Publication Details
- Journal
- Journal of Computational and Applied Mathematics
- Published
- 2024-09-17
- DOI
- https://doi.org/10.1016/j.cam.2024.116270
- Citations
- 2
- Primary Topic
- Advanced Numerical Methods in Computational Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 0.75
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- European Commission
- Ministero dell’Istruzione, dell’Università e della Ricerca
- King Abdullah University of Science and Technology
- Gruppo Nazionale per il Calcolo Scientifico
- Global Collaborative Research, King Abdullah University of Science and Technology
- HORIZON EUROPE European Research Council