Convergence bounds for preconditioned GMRES using element-by-element estimates of the field of values

Convergence bounds for preconditioned GMRES using element-by-element estimates of the field of values

Van Gijzen, M.B.
Erlangga, Y.A.

Electrical Engineering, Mathematics and Computer Science

2006-09-05

By combining element-by-element estimates for the field of values of a preconditioned matrix with GMRES-convergence estimates it is possible to derive an easily computable upper bound on the GMRES-residual norm. This method can be applied to general finite element systems, but the preconditioner has to be Hermitian and positive definite. The resulting upper bound for the GMRES-residual norm can be used to analyse a given preconditioner, or to optimize a parameter dependent preconditioner. In this paper we will apply this approach to derive a suitable shift for a so-called shifted Laplace preconditioner for the damped Helmholtz equation. Numerical experiments show that the shift that is derived in this way is close to optimal.

GMRES
convergence estimates
field of values
element-by-element techniques
shifted Laplace preconditioner

http://resolver.tudelft.nl/uuid:5ef44831-ef30-4114-b91a-2a63544406a7

Delft University of Technology; European Community on Computational Methods in Applied Sciences (ECCOMAS)

90-9020970-0

ECCOMAS CFD 2006: Proceedings of the European Conference on Computational Fluid Dynamics, Egmond aan Zee, The Netherlands, September 5-8, 2006

Institutional Repository

conference paper

(c) 2006 The Author(s)