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 …

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 …

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

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 …

The scattering phase, defined as where is the (unitary) scattering matrix, is the analogue of
the counting function for eigenvalues when dealing with exterior domains and is closely …

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 consider frequency-domain acoustic scattering at a homogeneous star-shaped
penetrable obstacle, whose shape is uncertain and modelled via a radial spectral …

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