  A non-intrusive proper generalized decomposition (PGD) strategy, coupled with
an overlapping domain decomposition (DD) method, is proposed to efficiently
construct surrogate models of parametric linear elliptic problems. A parametric
multi-domain formulation is presented, with local subproblems featuring
arbitrary Dirichlet interface conditions represented through the traces of the
finite element functions used for spatial discretization at the subdomain
level, with no need for additional auxiliary basis functions. The linearity of
the operator is exploited to devise low-dimensional problems with only few
active boundary parameters. An overlapping Schwarz method is used to glue the
local surrogate models, solving a linear system for the nodal values of the
parametric solution at the interfaces, without introducing Lagrange multipliers
to enforce the continuity in the overlapping region. The proposed DD-PGD
methodology relies on a fully algebraic formulation allowing for real-time
computation based on the efficient interpolation of the local surrogate models
in the parametric space, with no additional problems to be solved during the
execution of the Schwarz algorithm. Numerical results for parametric diffusion
and convection-diffusion problems are presented to showcase the accuracy of the
DD-PGD approach, its robustness in different regimes and its superior
performance with respect to standard high-fidelity DD methods.
