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@INPROCEEDINGS{Babamehdi:1019407,
      author       = {Babamehdi, Mehdi},
      title        = {{U}sing nonlinear domain decomposition as smoother in
                      nonlinear multigrid},
      reportid     = {FZJ-2023-05367},
      year         = {2023},
      abstract     = {Nonlinear partial differential equations frequently arise
                      in different fields ofscience. Discretization of the
                      nonlinear problems usually leads to large non-linear
                      systems. Solution of such big discretized nonlinear problems
                      needsfast, highly scalable, and parallelize
                      solvers.Nonlinear multigrid is a well-known method for
                      efficiently solving nonlin-ear boundary value problems. The
                      full approximation scheme (FAS) solvesnonlinear problems on
                      fine and coarse grids. To smooth the nonlinear prob-lem a
                      suitable nonlinear solver is needed and since a matrix-free
                      implemen-tation is desirable, this form of implementation of
                      the smoother should beplausible. For this purpose, the
                      nonlinear additive Schwarz method (NASM)seems to be an
                      appropriate choice. NASM converges with the same rateas
                      linear iterations applied to the linearised equation. In
                      addition, it is inher-ently parallel and proper to be
                      implemented in matrix-free form.We combine FAS and NASM to
                      obtain hybrid NASM/FAS. The FAS solvesthe nonlinear problem
                      and the NASM is the smoother of the nonlinearboundary value
                      problem in local subdomains on each level of the
                      multigridmethod. Within the NASM, Jacobian-Free Newton
                      Krylov method is usedas a solver on each subdomain. We
                      consider different nonlinear equationsin 3D space as test
                      problems. We investigated several parameters of themethods
                      to have a better understanding of influence of the
                      parameters onthe efficiency of the method and its
                      convergence rate.},
      month         = {Feb},
      date          = {2023-02-26},
      organization  = {SIAM-CSE, Amsterdam (Netherlands), 26
                       Feb 2023 - 3 Mar 2023},
      subtyp        = {After Call},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5112},
      typ          = {PUB:(DE-HGF)24},
      url          = {https://juser.fz-juelich.de/record/1019407},
}