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Multigrid methods for H (div) in three dimensions with nonoverlapping domain decomposition smoothers
Author(s) -
Brenner Susanne C.,
Oh DukSoon
Publication year - 2018
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2191
Subject(s) - multigrid method , domain decomposition methods , mathematics , hexahedron , discretization , schwarz alternating method , domain (mathematical analysis) , bounded function , convergence (economics) , finite element method , additive schwarz method , preconditioner , mathematical optimization , mathematical analysis , partial differential equation , iterative method , physics , economics , thermodynamics , economic growth
Summary 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.