A Reduced Order Model for Domain Decompositions with Non-conforming Interfaces

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 apply the discrete empirical interpolation method (DEIM) at the interface level to achieve a fully reduced-order representation of the DD techniques implemented. To deal with non-conforming FE interface discretizations, 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 the 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.