Edited by: F. Magoulès

Keywords: Helmholtz equation, Krylov methods, preconditioning, absorbing boundary conditions.

We consider the numerical solution of the Helmholtz equation in unbounded regions. Given an interior discretisation this requires the construction of an artificial surface to bound the domain of interest and the specification of a boundary condition that limits the reflections of waves back into the interior region. We discuss various options for this absorbing boundary condition. The resultant complex valued system of non-Hermitian equations needs to be solved. For high frequencies a direct solver is no longer feasible. The iterative method is usually a Krylov space technique. To speed the convergence a preconditioner is introduced. Various types of preconditioners are described.

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