Proper Generalized Decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: application to harbor agitation

Author (s): Modesto, D., Zlotnik, S. and Huerta, A.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 295
Pages: 127 – 149
Date: 2015

Abstract:
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.

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Bibtex:

@article{DM-MZH:15,
        Author = {David Modesto and Sergio Zlotnik and Antonio Huerta},
        Title = {{P}roper {G}eneralized {D}ecomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: application to harbor agitation},
        Fjournal = {Computer Methods in Applied Mechanics and Engineering},
        Journal = {Comput. Methods Appl. Mech. Eng.},
        Volume = {295},
        Pages = {127-149},
        Year = {2015},
        Doi = {10.1016/j.cma.2015.03.026}
        }