Hybridizable Discontinuous Galerkin p-adaptivity for wave propagation problems

Author (s): Giorgiani, G.; Fernández-Méndez, S.; and Huerta, A.
Journal: International Journal for Numerical Methods in Fluids

Volume: 72, Num: 12
Pages: 1244 – 1262
Date: 2013

Abstract:
A r-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, while the particular choice of the numerical fluxes opens the path to a super-convergent post-processed solution. This super-convergent post-processed 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 non-homogeneous scattering problem in an unbounded domain. This is a challenging problem because, on one hand, for high frequencies numerical difficulties are an important issue due to 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 non-constant 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 to a high-order continuous Galerkin method using static condensation of the interior nodes.

Journal paper (from the publisher)  
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Bibtex:

@article {GG-GFH:13,
	Author   = {Giorgio Giorgiani and Sonia Fern\'andez-M\'endez and Antonio Huerta},
	Title    = {Hybridizable {D}iscontinuous {G}alerkin p-adaptivity for wave propagation problems},
	Fjournal = {International Journal for Numerical Methods in Fluids},
	Journal  = {Int. J. Numer. Methods Fluids},
	Volume   = {72},
	Number   = {12},
	Pages    = {1244--1262},
	Year     = {2013},
	Doi      = {10.1002/fld.3784}
	}