A new MOX report entitled “A reduced order model for domain decompositions with non-conforming interfaces” by Zappon E.; Manzoni A.; Gervasio P.; Quarteroni A. has appeared in the MOX Report Collection.
The report can be donwloaded at the following link:
https://www.mate.polimi.it/biblioteca/add/qmox/43/2022.pdf
Abstract: In this paper we propose a reduced order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two sub-problems with Dirichlet and Neumann interface conditions, respectively. After discretization by (e.g.) the finite element method, the full-order model (FOM) is solved by Dirichlet- Neumann iterations between the two sub-problems until interface convergence is reached. We, then, apply the reduced basis (RB) method to obtain a low-dimensional representation of the solution of each sub-problem. Furthermore, we use the discrete empirical interpolation method (DEIM) applied at the interface level to achieve a fully reduced-order representation of the DD techniques implemented. To deal with interface data when non-conforming FE interface discretizations are considered, we employ the INTERNODES method combined with the interface DEIM reduction. The reduced-order model (ROM) is then solved by sub-iterating between the two reduced-order sub-problems until convergence of the approximated high-fidelity interface solutions. The ROM scheme is numerically verified on both steady and unsteady coupled problems, in the case of non-conforming FE interfaces.
