Domain Decomposition Preconditioners for Discontinuous Galerkin Discretizations of Compressible Fluid Flows. Issue 2 (May 2014)

• Record Type: Journal Article
• Authors: Giani, Stefano; Houston, Paul
• Is Part Of: Numerical mathematics. Volume 7:Issue 2(2014)
• Page Start: 123
• Page End: 148
• Publication Date: 2014-05
• Subjects: 65F08, -- 65N12, -- 65N15, -- 65N30; Composite finite element methods, -- discontinuous Galerkin methods, -- domain decomposition, -- Schwarz preconditioners, -- compressible fluid flows; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.1017/S100489790000091X
• Languages: English
• ISSNs: 1004-8979

Abstract

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.