Perturbation of Eigenvalues of Preconditioned Navier-Stokes Operators
Perturbation of Eigenvalues of Preconditioned Navier-Stokes Operators
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Date
1998-10-15
Authors
Elman, Howard C.
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Abstract
We study the sensitivity of algebraic eigenvalue problems
associated with matrices arising from linearization and discretization of
the steady-state Navier-Stokes equations. In particular, for several
choices of Reconditioners applied to the system of discrete equations, we
derive upper bounds on perturbations of eigenvalues as functions of the
viscosity and discretization mesh size. The bounds suggest that the
sensitivity of the eigenvalues is at worst linear in the inverse of the
viscosity and quadratic in the inverse of the mesh size, and that scaling
can be used to decrease the sensitivity in some cases. Experimental
results supplement these results and confirm the relatively mild
dependence on viscosity. They also indicate a dependence on the mesh size
of magnitude smaller than the analysis suggests.
(Also cross-referenced as UMIACS-TR-95-110)