Multilevel Schwarz preconditioners for singularly perturbed symmetric reaction-diffusion systems

[摘要] 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.

[学科分类] 数学（综合）

[关键词] multilevel;Schwarz;preconditioner;multigrid;reaction;diffusion;discontinuous;Galerkin