Sciweavers

MOC
2010

H(div) preconditioning for a mixed finite element formulation of the diffusion problem with random data

12 years 10 months ago
H(div) preconditioning for a mixed finite element formulation of the diffusion problem with random data
We study H(div) preconditioning for the saddle-point systems that arise in a stochastic Galerkin mixed formulation of the steady-state diffusion problem with random data. The key ingredient is a multigrid V-cycle for an H(div) operator with random weight function acting on a certain tensor product space of random fields with finite variance. We build on the ArnoldFalk-Winther multigrid algorithm presented in 1997 by varying the spatial discretization from grid to grid whilst keeping the stochastic discretization fixed. We extend the deterministic analysis to accommodate the modified H(div) operator and establish spectral equivalence bounds with a new multigrid V-cycle operator that are independent of the spatial and stochastic discretization parameters. We implement multigrid within a block-diagonal preconditioner for the full saddle-point problem, derive eigenvalue bounds for the preconditioned system matrices and investigate the impact of all the discretization parameters on the conv...
Howard C. Elman, Darran G. Furnival, Catherine E.
Added 20 May 2011
Updated 20 May 2011
Type Journal
Year 2010
Where MOC
Authors Howard C. Elman, Darran G. Furnival, Catherine E. Powell
Comments (0)