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