Domain Decomposition Preconditioners for Discontinuous Galerkin Discretizations of Compressible Fluid Flows
Year: 2014
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 2 : pp. 123–148
Abstract
In this article we consider the application of Schwarz-type domain decomposition preconditioners to the discontinuous Galerkin finite element approximation of the compressible Navier-Stokes equations. To discretize this system of conservation laws, we exploit the (adjoint consistent) symmetric version of the interior penalty discontinuous Galerkin finite element method. To define the necessary coarse-level solver required for the definition of the proposed preconditioner, we exploit ideas from composite finite element methods, which allow for the definition of finite element schemes on general meshes consisting of polygonal (agglomerated) elements. The practical performance of the proposed preconditioner is demonstrated for a series of viscous test cases in both two- and three-dimensions.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2014.1311nm
Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), Iss. 2 : pp. 123–148
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Composite finite element methods discontinuous Galerkin methods domain decomposition Schwarz preconditioners compressible fluid flows.
-
hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
Introduction
Cangiani, Andrea | Dong, Zhaonan | Georgoulis, Emmanuil H. | Houston, Paul2017
https://doi.org/10.1007/978-3-319-67673-9_1 [Citations: 0] -
Advances in Discretization Methods
Adaptive Discontinuous Galerkin Methods on Polytopic Meshes
Collis, Joe | Houston, Paul2016
https://doi.org/10.1007/978-3-319-41246-7_9 [Citations: 5] -
Encyclopedia of Computational Mechanics Second Edition
Discontinuous Galerkin Methods for Computational Fluid Dynamics
Cockburn, Bernardo
2017
https://doi.org/10.1002/9781119176817.ecm2053 [Citations: 6] -
Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations
Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains
Antonietti, Paola F. | Cangiani, Andrea | Collis, Joe | Dong, Zhaonan | Georgoulis, Emmanuil H. | Giani, Stefano | Houston, Paul2016
https://doi.org/10.1007/978-3-319-41640-3_9 [Citations: 28] -
V-cycle Multigrid Algorithms for Discontinuous Galerkin Methods on Non-nested Polytopic Meshes
Antonietti, P. F. | Pennesi, G.Journal of Scientific Computing, Vol. 78 (2019), Iss. 1 P.625
https://doi.org/10.1007/s10915-018-0783-x [Citations: 20] -
CONVERGENCE ANALYSIS OF NEW ADDITIVE SCHWARZ METHOD FOR SOLVING NONSELFADJOINT ELLIPTIC PROBLEMS
Qi, Fenfen | Li, Shishun | Shao, XinpingJournal of Applied Analysis & Computation, Vol. 11 (2021), Iss. 1 P.192
https://doi.org/10.11948/20190256 [Citations: 0] -
Parallel multiplicative Schwarz preconditioner for solving nonselfadjoint elliptic problems
Zhang, Ruyi | Li, ShishunInternational Journal of Computer Mathematics, Vol. 98 (2021), Iss. 7 P.1438
https://doi.org/10.1080/00207160.2020.1822995 [Citations: 0] -
Fast Numerical Integration on Polytopic Meshes with Applications to Discontinuous Galerkin Finite Element Methods
Antonietti, Paola F. | Houston, Paul | Pennesi, GiorgioJournal of Scientific Computing, Vol. 77 (2018), Iss. 3 P.1339
https://doi.org/10.1007/s10915-018-0802-y [Citations: 28]