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 …

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 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 …

The time-harmonic Maxwell equations at high wavenumber k in domains with an analytic
boundary and impedance boundary conditions are considered. A wavenumber-explicit …

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 …

In the analysis of the $ h $-version of the finite-element method (FEM), with fixed polynomial
degree $ p $, applied to the Helmholtz equation with wavenumber $ k\gg 1$, the $\textit …

We consider the scalar Helmholtz equation with variable, discontinuous coefficients,
modeling transmission of acoustic waves through an anisotropic penetrable obstacle. We …

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

We present a wavenumber-explicit convergence analysis of the $ hp $ Finite Element
Method applied to a class of heterogeneous Helmholtz problems with piecewise analytic …