Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2016

Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method

Résumé

The discontinuous Galerkin time-stepping method has many advantageous properties for solving parabolic equations. However, it requires the solution of a large nonsymmetric system at each time-step. This work develops a fully robust and efficient preconditioning strategy for solving these systems. Drawing on parabolic inf-sup theory, we first construct a left preconditioner that transforms the linear system to a symmetric positive definite problem to be solved by the preconditioned conjugate gradient algorithm. We then prove that the transformed system can be further preconditioned by an ideal block diagonal preconditioner, leading to a condition number bounded by 4 for any time-step size, any approximation order and any positive-definite self-adjoint spatial operators. Numerical experiments demonstrate the low condition numbers and fast convergence of the algorithm for both ideal and approximate preconditioners, and show the feasibility of the high-order solution of large problems.
Fichier principal
Vignette du fichier
hal_precondition_dg_timestepping.pdf (321.92 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01357497 , version 1 (29-08-2016)

Identifiants

Citer

Iain Smears. Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method. IMA Journal of Numerical Analysis, 2016, ⟨10.1093/imanum/drw050⟩. ⟨hal-01357497⟩
208 Consultations
183 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More