In this work the use of a p-multigrid preconditioned flexible GMRES solver to deal with the solution of stiff linear systems arising from high order time discretization is explored in the context of two high-order spatial discretizations. The first one is a standard modal discontinuous Galerkin method, while the second one is an hybridizable discontinuous Galerkin method, which for high order has fewer globally-coupled degrees of freedom compared to DG. The efficiency of the proposed solution strategy is assessed on low-Mach, two-dimensional, compressible flow problems. The numerical results highlight that a considerable reduction in the number of GMRES iterations can be achieved for both space discretizations, but that only with DG is this gain reflected in the CPU time. Moreover, a comparison of the performance shed light on the convenience of using the former or the latter space discretization.
P-multigrid preconditioners applied to high-order DG and HDG discretizations / Franciolini, M.; Fidkowski, K. J.; Crivellini, A.. - (2020), pp. 3622-3633. (Intervento presentato al convegno 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 tenutosi a Scottish Events Campus, gbr nel 2018).
P-multigrid preconditioners applied to high-order DG and HDG discretizations
Crivellini A.
2020-01-01
Abstract
In this work the use of a p-multigrid preconditioned flexible GMRES solver to deal with the solution of stiff linear systems arising from high order time discretization is explored in the context of two high-order spatial discretizations. The first one is a standard modal discontinuous Galerkin method, while the second one is an hybridizable discontinuous Galerkin method, which for high order has fewer globally-coupled degrees of freedom compared to DG. The efficiency of the proposed solution strategy is assessed on low-Mach, two-dimensional, compressible flow problems. The numerical results highlight that a considerable reduction in the number of GMRES iterations can be achieved for both space discretizations, but that only with DG is this gain reflected in the CPU time. Moreover, a comparison of the performance shed light on the convenience of using the former or the latter space discretization.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
