TY - JOUR
T1 - Auxiliary space preconditioning for edge elements
AU - Hiptmair, Ralf
AU - Xu, Jinchao
N1 - Funding Information:
ACKNOWLEDGMENT The work of J. Xu was supported in part by an Alexander von Humboldt Research Award for Senior U.S. Scientists, by the National Science Foundation under Grant DMS-0609727, and by the National Natural Science Foundation of China under Grant NSFC-10528102.
PY - 2008/6
Y1 - 2008/6
N2 - We present a general approach to preconditioning large sparse linear systems of equations arising from conforming finite-element discretizations of H(curl, Ω)-elliptic variational problems. Like geometric multigrid, the methods are asymptotically optimal in the sense that their performance does not deteriorate on arbitrarily fine meshes. Unlike geometric multigrid, no hierarchy of nested meshes is required; only fast solvers for discrete second-order elliptic problems have to be available, which are provided, for example, by standard algebraic multigrid codes. In a sense, the method described in this paper enables us to construct optimal algebraic preconditioners for discrete curl curl-equations.
AB - We present a general approach to preconditioning large sparse linear systems of equations arising from conforming finite-element discretizations of H(curl, Ω)-elliptic variational problems. Like geometric multigrid, the methods are asymptotically optimal in the sense that their performance does not deteriorate on arbitrarily fine meshes. Unlike geometric multigrid, no hierarchy of nested meshes is required; only fast solvers for discrete second-order elliptic problems have to be available, which are provided, for example, by standard algebraic multigrid codes. In a sense, the method described in this paper enables us to construct optimal algebraic preconditioners for discrete curl curl-equations.
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U2 - 10.1109/TMAG.2007.916508
DO - 10.1109/TMAG.2007.916508
M3 - Article
AN - SCOPUS:44049095994
SN - 0018-9464
VL - 44
SP - 938
EP - 941
JO - IEEE Transactions on Magnetics
JF - IEEE Transactions on Magnetics
IS - 6
M1 - 4526887
ER -