Advanced Search

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

Cited in: Zbl 1217.78062 Zbl 1212.65128 Zbl 1193.65209

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]