Hybridizable discontinuous Galerkin p-adaptivity for wave propagation problems

Authors

  • Giorgio Giorgiani,

    1. Laboratori de Calcul Numeric (LaCaN). Departament de Matematica Aplicada III E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politecnica de Catalunya – BarcelonaTech, 08034 Barcelona, Spain
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  • Sonia Fernández-Méndez,

    1. Laboratori de Calcul Numeric (LaCaN). Departament de Matematica Aplicada III E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politecnica de Catalunya – BarcelonaTech, 08034 Barcelona, Spain
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  • Antonio Huerta

    Corresponding author
    • Laboratori de Calcul Numeric (LaCaN). Departament de Matematica Aplicada III E.T.S. de Ingenieros de Caminos, Canales y Puertos, Universitat Politecnica de Catalunya – BarcelonaTech, 08034 Barcelona, Spain
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Correspondence to: Antonio Huerta, Laboratori de Càlcul Numèric (LaCàN), E.T.S. Ingenieros de Caminos, Universitat Politècnica de Catalunya, Jordi Girona 1, E-08034 Barcelona, Spain.

E-mail: antonio.huerta@upc.edu

SUMMARY

A p-adaptive hybridizable discontinuous Galerkin method for the solution of wave problems is presented in a challenging engineering problem. Moreover, its performance is compared with a high-order continuous Galerkin. The hybridization technique allows to reduce the coupled degrees of freedom to only those on the mesh element boundaries, whereas the particular choice of the numerical fluxes opens the path to a superconvergent postprocessed solution. This superconvergent postprocessed solution is used to construct a simple and inexpensive error estimator. The error estimator is employed to obtain solutions with the prescribed accuracy in the area (or areas) of interest and also drives a proposed iterative mesh adaptation procedure. The proposed method is applied to a nonhomogeneous scattering problem in an unbounded domain. This is a challenging problem because, on the one hand, for high frequencies, numerical difficulties are an important issue because of the loss of the ellipticity and the oscillatory behavior of the solution. And on the other hand, it is applied to real harbor agitation problems. That is, the mild slope equation in frequency domain (Helmholtz equation with nonconstant coefficients) is solved on real geometries with the corresponding perfectly matched layer to damp the diffracted waves. The performance of the method is studied on two practical examples. The adaptive hybridizable discontinuous Galerkin method exhibits better efficiency compared with a high-order continuous Galerkin method using static condensation of the interior nodes. Copyright © 2013 John Wiley & Sons, Ltd.

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