Subcell finite volume multigrid preconditioning for high-order discontinuous Galerkin methods. Issue 9 (21st October 2019)

• Record Type: Journal Article
• Authors: Birken, Philipp; Gassner, Gregor J.; Versbach, Lea M.
• Is Part Of: International journal of computational fluid dynamics. Volume 33:Issue 9(2019)
• Page Start: 353
• Page End: 361
• Publication Date: 2019-10-21
• Subjects: Discontinuous Galerkin -- multigrid preconditioner -- W smoother -- Euler equations; Fluid dynamics -- Data processing -- Periodicals; 532.05
• DOI: 10.1080/10618562.2019.1667983
• Languages: English
• ISSNs: 1061-8562

Abstract

ABSTRACT: We suggest a new multigrid preconditioning strategy for use in Jacobian-free Newton–Krylov (JFNK) methods for the solution of algebraic equation systems arising from implicit Discontinuous Galerkin (DG) discretisations. To define the new preconditioner, use is made of an auxiliary first-order finite volume discretisation that refines the original DG mesh, but can still be implemented algebraically. As smoother, we consider the pseudo-time iteration W3 with a symmetric Gauss–Seidel-type approximation of the Jacobian. As a proof of concept numerical tests are presented for the one-dimensional Euler equations, demonstrating the potential of the new approach.