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Journal article

An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion 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
    01.10.2021
Published in:
  • Computers and mathematics with applications. - Elsevier. - 2021, vol. 99, p. 162-170
Space-time multigrid
PFASST
Parallel-in-time
DG discretization
Strong and weak scalability
Reaction-diffusion equation
English 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.
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https://n2t.net/ark:/12658/srd1319392
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