Solving the Helmholtz equation for a large number of input data in an heterogeneous
media and unbounded domain still represents a challenge. This is due to
the particular nature of the Helmholtz operator and the sensibility of the solution to
small variations of the data. Here a reduced order model is used to determine the
scattered solution everywhere in the domain for any incoming wave direction and
frequency. Moreover, this is applied to a real engineering problem: water agitation
inside real harbors for low to mid-high frequencies.

The Proper Generalized Decomposition (PGD) model reduction approach is used
to obtain a separable representation of the solution at any point and for any incoming
wave direction and frequency. Here, its applicability to such a problem is discussed
and demonstrated. More precisely, the separability of the operator is addressed
taking into account both the non-constant coefficients in the domain and the use of
the Perfectly Matched Layers in order to model the unbounded domain.

Then, the performance of the PGD in this framework is discussed and improved
using a higher-order projection and a Petrov-Galerkin approach to construct the
separated basis. Moreover, the PGD is also discussed as an efficient higher-order
projection scheme and compared with the higher-order singular value decomposition.