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Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: application to harbor agitation. (English) Zbl 1423.76261
Summary: 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.

76M10 Finite element methods applied to problems in fluid mechanics
86-08 Computational methods for problems pertaining to geophysics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
86A05 Hydrology, hydrography, oceanography
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