Mat-1.3656 Seminar on
numerical analysis and computational science
Monday, Sept 26, 2011, room
U322 at 14.15, Eirola & Stenberg
Antti Hannukainen, A?
Preconditioning of the Helmholtz equation
In this talk, we discuss the convergence of the preconditioned GMRES
method for the first order finite element discretizations of the
Helmholtz equation in media with losses. We consider a Laplace
preconditioner, an inexact Laplace preconditioner and a two-level
preconditioner. Our analysis is based on bounding the field of values
of the preconditioned system matrix in the complex plane. The analysis
takes the non-normal nature of the linear system naturally into account
and allows us to easily consider certain type of inexact Laplace
preconditioners via a perturbation argument. For the two-level
preconditioner, our convergence analysis takes into account a media,
which has not been considered in previous works.