  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.
