Title :
Auxiliary Space Preconditioning for Edge Elements
Author :
Hiptmair, Ralf ; Xu, Jinchao
Author_Institution :
Seminar for Appl. Math., ETH Zurich, Zurich
fDate :
6/1/2008 12:00:00 AM
Abstract :
We present a general approach to preconditioning large sparse linear systems of equations arising from conforming finite-element discretizations of -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 -equations.
Keywords :
boundary-elements methods; electromagnetism; elliptic equations; mesh generation; sparse matrices; arbitrarily fine meshes; auxiliary space preconditioning; discrete second-order elliptic problems; edge elements; elliptic variational problems; finite-element discretizations; geometric multigrid; practical magneto-quasi-static finite-element computations; sparse linear systems; standard algebraic multigrid codes; $H({bf curl})$-elliptic boundary value problems; Algebraic multigrid; auxiliary space preconditioning; edge finite elements;
Journal_Title :
Magnetics, IEEE Transactions on
DOI :
10.1109/TMAG.2007.916508