Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: Application to harbor agitation

• Novel parameterized solutions for a scattering problem with the proper generalized decomposition (PGD).
• Development and viability of PGD for non-Hermitian operator in an unbounded and heterogeneous domain.
• Adapt the perfectly matched layer approach for artificial boundaries to be used within a PGD scheme.
• Formalization of the higher-order PGD-projection to obtain an optimal separable representation.
• Comparison of the higher-order PGD-projection with High Order Singular Value Decomposition (HOSVD).

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 contributions of the paper include the PGD implementation into a perfectly matched layer framework to model the unbounded domain, and the separability of the operator which is addressed here using an efficient higher-order projection scheme.Then, the performance of the PGD in this framework is discussed and improved using the higher-order projection and a Petrov–Galerkin approach to construct the separated basis. Moreover, the efficiency of the higher-order projection scheme is demonstrated and compared with the higher-order singular value decomposition.