We consider a wide variety of Helmholtz scattering problems including scattering by
Dirichlet, Neumann, and penetrable obstacles. We consider a radial perfectly matched layer …

We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for
time-harmonic scattering problems of Helmholtz type with high wavenumber. On a coarse …

We present a wavenumber-explicit convergence analysis of the hp finite element method
applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients …

In d dimensions, accurately approximating an arbitrary function oscillating with frequency
\lesssimk requires ∼ k^d degrees of freedom. A numerical method for solving the Helmholtz …

Over the last 10 years, results from [JM Melenk and S. Sauter, Math. Comp., 79 (2010), pp.
1871–1914],[JM Melenk and S. Sauter, SIAM J. Numer. Anal., 49 (2011), pp. 1210–1243],[S …

We analyse parallel overlapping Schwarz domain decomposition methods for the Helmholtz
equation, where the exchange of information between subdomains is achieved using first …

For the h-finite-element method (h-FEM) applied to the Helmholtz equation, the question of
how quickly the meshwidth h must decrease with the frequency k to maintain accuracy as k …

A crucial role in the theory of uncertainty quantification (UQ) of PDEs is played by the
regularity of the solution with respect to the stochastic parameters; indeed, a key property …

We consider GMRES applied to discretisations of the high-frequency Helmholtz equation
with strong trapping; recall that in this situation the problem is exponentially ill-conditioned …

For the Helmholtz equation posed in the exterior of a Dirichlet obstacle, we prove that if there
exists a family of quasimodes (as is the case when the exterior of the obstacle has stable …