A convergence theory for the hp-FEM applied to a variety of constant-coefficient Helmholtz
problems was pioneered in the papers [35],[36],[15],[34]. This theory shows that, if the …

It is well‐known that when the geometry and/or coefficients allow stable trapped rays, the
outgoing solution operator of the Helmholtz equation grows exponentially through a …

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

In the analysis of the-version of the finite-element method (FEM), with fixed polynomial
degree, applied to the Helmholtz equation with wavenumber, the asymptotic regime is when …

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 …

We consider one-level additive Schwarz domain decomposition preconditioners for the
Helmholtz equation with variable coefficients (modelling wave propagation in …

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 consider approximation of the variable-coefficient Helmholtz equation in the exterior of a
Dirichlet obstacle using perfectly-matched-layer (PML) truncation; it is well known that this …