Benedusi, Pietro Minion, Michael L. Krause, Rolf 2021-10-01 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. application/pdf https://susi.usi.ch/global/documents/319392 https://n2t.net/ark:/12658/srd1319392 https://susi.usi.ch/documents/319392/files/Benedusi_camwa_2021.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.camwa.2021.07.008 info:eu-repo/semantics/altIdentifier/ark/12658/srd1319392 info:eu-repo/semantics/openAccess CC BY-NC-ND 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 info:eu-repo/classification/udc/004 An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem http://purl.org/coar/resource_type/c_6501