Why it is so difficult to solve Helmholtz problems with iterative methods

Monday, November 29, 2010 - 3:00pm - 3:45pm
Keller 3-180
Martin Gander (Universite de Geneve)

In contrast to the positive definite Helmholtz equation, the

deceivingly similar looking indefinite Helmholtz equation is difficult

to solve using classical iterative methods. Applying directly a Krylov

method to the discretized equations without preconditioning leads in

general to stagnation and very large iteration counts. Using classical

incomplete LU preconditioners can even make the situation worse.

Classical domain decomposition and multigrid methods also fail to

converge when applied to such systems.

The purpose of this presentation is to investigate in each case where

the problems lie, and to explain why classical iterative methods have

such difficulties to solve indefinite Helmholtz problems. I will also

present remedies that have been proposed over the last decade, for

incomplete LU type preconditioners, domain decomposition and also

multigrid methods.

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