An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem
Additional information
Authors
Benedusi P.,
Minion M. L.,
Krause R.
Type
Journal Article
Language
English
Abstract
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.
Keywords
Space-time multigrid, PFASST, Parallel-in-time, DG discretization, Strong and weak scalability, Reaction-diffusion equation
Journal
Computers and mathematics with applications
Volume
99
Pages (or article number)
162-170
Diffusion
License
CC BY-NC-ND
Visibility
Public
Status open access
Hybrid
