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 …

We review the stability properties of several discretizations of the Helmholtz equation at
large wavenumbers. For a model problem in a polygon, a complete k-explicit stability …

We consider the exterior Dirichlet problem for the heterogeneous Helmholtz equation, ie the
equation∇⋅(A∇ u)+ k 2 nu=− f where both A and n are functions of position. We prove new …

We consider the Helmholtz transmission problem with one penetrable star-shaped Lipschitz
obstacle. Under a natural assumption about the ratio of the wavenumbers, we prove bounds …

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in
the sense that the bilinear forms cannot be bounded below by a positive multiple of the …

This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation
posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the …

We consider the time-harmonic Maxwell equations with constant coefficients in a bounded,
uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak …

Computer simulation of the propagation and interaction of linear waves is a core task in
computational science and engineering. It is fundamentally important in a wide range of …

We consider solving the exterior Dirichlet problem for the Helmholtz equation with the h-
version of the boundary element method (BEM) using the standard second-kind combined …

We prove that the standard second‐kind integral equation formulation of the exterior
Dirichlet problem for the Helmholtz equation is coercive (ie, sign‐definite) for all smooth …