Loading [MathJax]/jax/output/HTML-CSS/config.js
full
search.png

Search

close.png

Cancel

arrow
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

Preview Full PDF 3194 35729

Cited by

google scholar semantic scholar
Export citation
  • 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

  • Email address
  • BibTex
  • RIS
  • TXT
@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
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard