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Volume 7, Issue 2
Domain Decomposition Preconditioners for Discontinuous Galerkin Discretizations of Compressible Fluid Flows

Stefano Giani & Paul Houston

DOI: 10.4208/nmtma.2014.1311nm

Numer. Math. Theor. Meth. Appl., 7 (2014), pp. 123-148.

Published online: 2014-07

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  • 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.

  • Keywords

Composite finite element methods, discontinuous Galerkin methods, domain decomposition, Schwarz preconditioners, compressible fluid flows.

  • AMS Subject Headings

65F08, 65N12, 65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-7-123, author = {Stefano Giani and Paul Houston}, title = {Domain Decomposition Preconditioners for Discontinuous Galerkin Discretizations of Compressible Fluid Flows}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2014}, volume = {7}, number = {2}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.1311nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5868.html} }
TY - JOUR T1 - Domain Decomposition Preconditioners for Discontinuous Galerkin Discretizations of Compressible Fluid Flows AU - Stefano Giani & Paul Houston JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 123 EP - 148 PY - 2014 DA - 2014/07 SN - 7 DO - http://doi.org/10.4208/nmtma.2014.1311nm UR - https://global-sci.org/intro/article_detail/nmtma/5868.html KW - Composite finite element methods, discontinuous Galerkin methods, domain decomposition, Schwarz preconditioners, compressible fluid flows. AB -

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.

Stefano Giani and Paul Houston. (2014). Domain Decomposition Preconditioners for Discontinuous Galerkin Discretizations of Compressible Fluid Flows. Numerical Mathematics: Theory, Methods and Applications. 7 (2). 123-148. doi:10.4208/nmtma.2014.1311nm
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