Multilevel Schwarz preconditioners for singularly perturbed symmetric reaction-diffusion systems

@article{Lorca2018MultilevelSP,
  title={Multilevel Schwarz preconditioners for singularly perturbed symmetric reaction-diffusion systems},
  author={Jos{\'e} Pablo Lucero Lorca and G. Kanschat},
  journal={ArXiv},
  year={2018},
  volume={abs/1811.03839}
}
  • José Pablo Lucero Lorca, G. Kanschat
  • Published 2018
  • Mathematics, Computer Science
  • ArXiv
  • We present robust and highly parallel multilevel non-overlapping Schwarz preconditioners, to solve an interior penalty discontinuous Galerkin finite element discretization of a system of steady state, singularly perturbed reaction-diffusion equations with a singular reaction operator, using a GMRES solver. We provide proofs of convergence for the two-level setting and the multigrid V-cycle as well as numerical results for a wide range of regimes. 
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