Hybridizable discontinuous Galerkin p‐adaptivity for wave propagation problems. (20th February 2013)

• Record Type: Journal Article
• Authors: Giorgiani, Giorgio; Fernández‐Méndez, Sonia; Huerta, Antonio
• Is Part Of: International journal for numerical methods in fluids. Volume 72:Number 12(2013:Aug.)
• Page Start: 1244
• Page End: 1262
• Publication Date: 2013-02-20
• Subjects: scattering -- Helmholtz equation -- discontinuous Galerkin method -- p‐adaptivity -- error estimation -- high‐order approximations -- hybridization; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.3784
• Languages: English
• ISSNs: 0271-2091

Abstract

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. Abstract : A p ‐adaptive hybridizable discontinuous Galerkin method based on error estimation is proposed for the solution of scattering problems (Helmholtz for nonconstant coefficients in unbounded domains). This approach outperforms high‐order continuous Galerkin. The figure shows the final distribution of the approximation order p for the desired accuracy in a challenging engineering problem: wave propagation in Barcelona's harbor.