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Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: application to harbor agitation Modesto Galende, David Zlotnik, Sergio Huerta, Antonio Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics Numerical methods and algorithms Reduced order models Proper generalized decomposition Helmholtz Parameterized solutions Wave propagation Harbor Anàlisi numèrica Classificació AMS::65 Numerical analysis::65E05 Numerical methods in complex analysis (potential theory, etc.) 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 higherorder projection scheme is demonstrated and compared with the higher-order singular value decomposition. Peer Reviewed Postprint (author’s final draft) 2015-10-01 Article Modesto, D., Zlotnik, S., Huerta, A. Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: application to harbor agitation. "Computer methods in applied mechanics and engineering", 01 Octubre 2015, p. 127-149. 0045-7825 https://hdl.handle.net/2117/76946 10.1016/j.cma.2015.03.026 eng http://www.sciencedirect.com/science/article/pii/S004578251500136X http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access 23 p. application/pdf