Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1153.78006
Hiptmair, Ralf; Xu, Jinchao
Nodal auxiliary space preconditioning in H(curl) and H(div) spaces.
(English)
[J] SIAM J. Numer. Anal. 45, No. 6, 2483-2509 (2007). ISSN 0036-1429; ISSN 1095-7170/e

Summary: We develop and analyze a general approach to preconditioning linear systems of equations arising from conforming finite element discretizations of $\bold H(\bold{curl}, \Omega)$- and $\bold H(\bold{div}, \Omega)$-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 $\bold H(\bold{curl}, \Omega)$ and $\bold H(\bold{div}, \Omega)$. Our preconditioner for $\bold H(\bold{curl}, \Omega)$ is similar to an algorithm proposed in [{\it R. Beck}, Algebraic multigrid by component splitting for edge elements on simplicial triangulations, Tech. rep. SC 99-40, ZIB, Berlin, Germany (1999)].
MSC 2000:
*78M10 Finite element methods (optics)
65N30 Finite numerical methods (BVP of PDE)
65N55 Multigrid methods; domain decomposition (BVP of PDE)
65N22 Solution of discretized equations (BVP of PDE)
65F10 Iterative methods for linear systems

Keywords: auxiliary space preconditioning; fictitious space preconditioning; $\bold H(\bold{curl})$ and $\bold H(\bold{div})$, edge and face finite elements; algebraic multigrid

Highlights
Master Server