An efficient linear solver for the hybridized discontinuous Galerkin method. Issue 1 (October 2016)

• Record Type: Journal Article
• Authors: Jaust, Alexander; Schütz, Jochen; Aizinger, Vadym
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 16:Issue 1(2016)
• Page Start: 845
• Page End: 846
• Publication Date: 2016-10
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201610411
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Discretizing partial differential equations by an implicit solving technique ultimately leads to a linear system of equations that has to be solved. The number of globally coupled unknowns is especially large for discontinuous Galerkin (DG) methods. It can be reduced by using hybridized discontinuous Galerkin (HDG) methods, but still efficient linear solvers are needed. It has been shown that, if hierarchical basis functions are used, a hierarchical scale separation (HSS) ansatz can be an efficient solver. In this work, we couple the HDG method with an HSS solver to solve a scalar nonlinear problem. It is validated by comparing the results with results obtained by GMRES with ILU(3) preconditioning as linear solver. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)