There has been much recent research on preconditioning discretisations of the Helmholtz
operator Δ+ k^ 2 Δ+ k 2 (subject to suitable boundary conditions) using a discrete version of …

In this paper, we propose a fast block α-circulant preconditioner for solving the
nonsymmetric linear system arising from an all-at-once implicit discretization scheme in time …

We discuss the stability theory and numerical analysis of the Helmholtz equation with
variable and possibly nonsmooth or oscillatory coefficients. Using the unique continuation …

This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations
with absorption, where the PDE is discretised using curl-conforming finite-element methods …

A non-overlapping domain decomposition method (DDM) is proposed for the parallel finite-
element solution of large-scale time-harmonic wave problems. It is well-known that the …

We consider one-level additive Schwarz preconditioners for a family of Helmholtz problems
with increasing wavenumber k. These problems are discretized using the Galerkin method …

The shifted Helmholtz operator has received a lot of attention over the past decade as a
preconditioner for the iterative solution of the Helmholtz equation. The idea is that if one …

Solving time-harmonic wave propagation problems in the frequency domain and within
heterogeneous media brings many mathematical and computational challenges, especially …

It is well-known that the convergence rate of non-overlapping domain decomposition
methods (DDMs) applied to the parallel finite-element solution of large-scale time-harmonic …

We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a
nontrapping obstacle, with boundary data coming from plane-wave incidence, by the …