An experimental comparison of a spacetime multigrid method with PFASST for a reactiondiffusion problem

Benedusi, Pietro
Euler Institute, Università della Svizzera italiana, Switzerland

Minion, Michael L.
Lawrence Berkeley National Laboratory, Berkeley, CA, USA

Krause, Rolf
Euler Institute, Università della Svizzera italiana, Switzerland
Published in:
 Computers and mathematics with applications.  Elsevier.  2021, vol. 99, p. 162170
English
We consider two parallelintime approaches applied to a (reaction) diffusion problem, possibly nonlinear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and spacetime 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 spacetime 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 nonlinear 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 nonlinear problem, PFASST is more flexible in terms of solution strategy, while spacetime multigrid requires a full nonlinear solve.

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