Volume 54, pp. 89-107, 2021.

Multilevel Schwarz preconditioners for singularly perturbed symmetric reaction-diffusion systems

José Pablo Lucero Lorca and Guido Kanschat


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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Key words

multilevel, Schwarz, preconditioner, multigrid, reaction, diffusion, discontinuous, Galerkin

AMS subject classifications

65N55, 65N30, 65J10, 65F08

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