Hybridizable discontinuous Galerkin p‐adaptivity for wave propagation problems

By Giorgio Giorgiani, S. Fernández‐Méndez, Antonio Huerta. 2013

63 citations recorded by the source corpus.

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.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/91db6fcf2a9ad70885b2abf389d86ac01a756046

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Tutorial on Hybridizable Discontinuous Galerkin (HDG) for second-order elliptic problems (2016, methodology): “The extra accuracy of the postprocessed solution has been recently exploited by Giorgiani et al. (2013, 2014) to define a simple and inexpensive error estimator than can be used to develop highly efficient p-adaptive procedures.”
Efficiency of high‐order elements for continuous and discontinuous Galerkin methods (2013, methodology): “Nevertheless, even in this case, high order elements are more competitive than low order ones as shown numerically in [9, 10] and also in [20] where a hybrid discontinuous enrichment method [21] is compared with an ultra-weak variational formulation [22] and a partition of unity method [23], the thr”
Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations ✩ (2014, unknown): “The elemental tolerance ǫ i usually corresponds to the tolerance ε in (9), but can also be set diﬀerently element-by-element, for instance, to intensify the reﬁnement in the region of interest Ω int , see [27].”