  One of the major challenges of coupled problems is to manage nonconforming
meshes at the interface between two models and/or domains, due to different
numerical schemes or domains discretizations employed. Moreover, very often
complex submodels depend on (e.g., physical or geometrical) parameters.
Understanding how outputs of interest are affected by parameter variations thus
plays a key role to gain useful insights on the problem's physics; however,
expensive repeated solutions of the problem using high-fidelity, full-order
models are often unaffordable. In this paper, we propose a parametric reduced
order modeling (ROM) technique for parametrized one-way coupled problems made
by a first independent model, the master model, and a second model, the slave
model, that depends on the master model through Dirichlet interface conditions.
We combine a reduced basis (RB) method, applied to each subproblems, with the
discretized empirical interpolation method (DEIM) to efficiently interpolate or
project Dirichlet data across conforming and non-conforming meshes at the
domains interface, building a low-dimensional representation of the overall
coupled problem. The proposed technique is then numerically verified by
considering a series of test cases involving both steady and unsteady problems,
and deriving a-posteriori error estimates on the solution of the coupled
problem in both cases. This work arises from the need to solve staggered
cardiac electrophysiological models and represents the first step towards the
setting of ROM techniques for the more general two-way Dirichlet-Neumann
coupled problems solved with domain decomposition sub-structuring methods, when
interface non-conformity is involved.
