Multigrid methods for H(div) in three dimensions with nonoverlapping domain decomposition smoothers
We design and analyze V-cycle multigrid methods for an H(div) problem discretized by the lowest-order Raviart–Thomas hexahedral element. The smoothers in the multigrid methods involve nonoverlapping domain decomposition preconditioners that are based on substructuring. We prove uniform convergence of the V-cycle methods on bounded convex hexahedral domains (rectangular boxes). Numerical experiments that support the theory are also presented.
Publication Source (Journal or Book title)
Numerical Linear Algebra with Applications
Brenner, S., & Oh, D. (2018). Multigrid methods for H(div) in three dimensions with nonoverlapping domain decomposition smoothers. Numerical Linear Algebra with Applications, 25 (5) https://doi.org/10.1002/nla.2191