TY - JOUR
T1 - Nodal auxiliary space preconditioning in H(curl) and H(div) spaces
AU - Hiptmair, Ralf
AU - Xu, Jinchao
N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15
PY - 2007/12/1
Y1 - 2007/12/1
N2 - In this paper, we develop and analyze a general approach to preconditioning linear systems of equations arising from conforming finite element discretizations of H(curl, Ω)- and H(div, Ω)-elliptic variational problems. The preconditioners exclusively rely on solvers for discrete Poisson problems. We prove mesh-independent effectivity of the preconditioners by using the abstract theory of auxiliary space preconditioning. The main tools are discrete analogues of so-called regular decomposition results in the function spaces H(curl, Ω) and H(div, Ω). Our preconditioner for H(curl, Ω) is similar to an algorithm proposed in [R. Beck, Algebraic Multigrid by Component Splitting for Edge Elements on Simplicial Triangulations, Tech. rep. SC 99-40, ZIB, Berlin, Germany, 1999]. © 2007 Society for Industrial and Applied Mathematics.
AB - In this paper, we develop and analyze a general approach to preconditioning linear systems of equations arising from conforming finite element discretizations of H(curl, Ω)- and H(div, Ω)-elliptic variational problems. The preconditioners exclusively rely on solvers for discrete Poisson problems. We prove mesh-independent effectivity of the preconditioners by using the abstract theory of auxiliary space preconditioning. The main tools are discrete analogues of so-called regular decomposition results in the function spaces H(curl, Ω) and H(div, Ω). Our preconditioner for H(curl, Ω) is similar to an algorithm proposed in [R. Beck, Algebraic Multigrid by Component Splitting for Edge Elements on Simplicial Triangulations, Tech. rep. SC 99-40, ZIB, Berlin, Germany, 1999]. © 2007 Society for Industrial and Applied Mathematics.
UR - http://epubs.siam.org/doi/10.1137/060660588
UR - http://www.scopus.com/inward/record.url?scp=44049108809&partnerID=8YFLogxK
U2 - 10.1137/060660588
DO - 10.1137/060660588
M3 - Article
SN - 0036-1429
VL - 45
SP - 2483
EP - 2509
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 6
ER -