An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem
Informazioni aggiuntive
Autori
Benedusi P.,
Minion M. L.,
Krause R.
Tipo
Articolo pubblicato in rivista scientifica
Lingua
Inglese
Sommario
We consider two parallel-in-time approaches applied to a (reaction) diffusion problem, possibly non-linear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and space-time multigrid strategies. For both approaches, we start from an integral formulation of the continuous time dependent problem. Then, a collocation form for PFASST and a discontinuous Galerkin discretization in time for the space-time multigrid are employed, resulting in the same discrete solution at the time nodes. Strong and weak scaling of both multilevel strategies are compared for varying orders of the temporal discretization. Moreover, we investigate the respective convergence behavior for non-linear problems and highlight quantitative differences in execution times. For the linear problem, we observe that the two methods show similar scaling behavior with PFASST being more favorable for high order methods or when few parallel resources are available. For the non-linear problem, PFASST is more flexible in terms of solution strategy, while space-time multigrid requires a full non-linear solve.
Parole chiave
Space-time multigrid, PFASST, Parallel-in-time, DG discretization, Strong and weak scalability, Reaction-diffusion equation
Periodico
Computers and mathematics with applications
Volume
99
Pagine (o numero dell’articolo)
162-170
Diffusione
Licenza
CC BY-NC-ND
Visibilità
Pubblico
Status open access
Hybrid
