Multilevel Schwarz preconditioners for singularly perturbed symmetric reaction-diffusion systems

11/09/2018

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by   José Pablo Lucero Lorca, et al.

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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.