Localized model reduction for nonlinear elliptic partial differential equations: localized training, partition of unity, and adaptive enrichment - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Scientific Computing Année : 2023

Localized model reduction for nonlinear elliptic partial differential equations: localized training, partition of unity, and adaptive enrichment

Résumé

We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized nonlinear elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order solves are not affordable in a reasonable time frame or parameters' variations induce topology changes that prevent the application of monolithic pMOR techniques. We rely on the partition-of-unity method (PUM) to devise global approximation spaces from local reduced spaces, and on Galerkin projection to compute the global state estimate. We propose a randomized data compression algorithm based on oversampling for the construction of the components' reduced spaces: the approach exploits random boundary conditions of controlled smoothness on the oversampling boundary. We further propose an adaptive residual-based enrichment algorithm that exploits global reduced-order solves on representative systems to update the local reduced spaces. We prove exponential convergence of the enrichment procedure for linear coercive problems; we further present numerical results for a two-dimensional nonlinear diffusion problem to illustrate the many features of our proposal and demonstrate its effectiveness.
Fichier principal
Vignette du fichier
KSTT_arxiv.pdf (1.74 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03910541 , version 1 (22-12-2022)

Identifiants

Citer

Kathrin Smetana, Tommaso Taddei. Localized model reduction for nonlinear elliptic partial differential equations: localized training, partition of unity, and adaptive enrichment. SIAM Journal on Scientific Computing, 2023, 45 (3), pp.A1300-A1331. ⟨10.1137/22M148402X⟩. ⟨hal-03910541⟩
57 Consultations
21 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More