12 papers
The -FEM does not suffer from the pollution effect for piecewise-smooth Helmholtz problems with Gevrey regularity at boundaries
Jeffrey Galkowski, Mostafa Meliani, Euan A. Spence
We consider the -FEM applied to the Helmholtz scattering problem with wavenumber , truncated with a perfectly-matched layer. The scatterer consists of a combination of Diric…
Localised Davies generators for (pseudo)differential operators
Jeffrey Galkowski, Maciej Zworski
A classical Davies generator provides a Lindbladian for which the Gibbs state is stationary. Its construction involves precise knowledge of the Bohr spectrum or equivalently state…
Logarithmic improvements in the Weyl law and exponential bounds on the number of closed geodesics are predominant
Yaiza Canzani, Jeffrey Galkowski
Let be a smooth compact manifold of dimension without boundary. We introduce the concept of predominance for Riemannian metrics on , a notion analogous to full Lebesgue…
Non-uniform finite-element meshes defined by ray dynamics for Helmholtz problems
Martin Averseng, Jeffrey Galkowski, Euan A. Spence
The -version of the finite-element method (-FEM) applied to the high-frequency Helmholtz equation has been a classic topic in numerical analysis since the 1990s. It is now ri…
Numerical analysis of the high-frequency Helmholtz equation using semiclassical analysis
Jeffrey Galkowski, Euan A. Spence
We consider the numerical solution of high-frequency scattering problems modeled by the Helmholtz equation with a bounded obstacle. Although the analysis of this problem dates back…
Helmholtz boundary integral methods and the pollution effect
Jeffrey Galkowski, Manas Rachh, Euan A. Spence
This paper is concerned with solving the Helmholtz exterior Dirichlet and Neumann problems with large wavenumber and smooth obstacles using the standard second-kind boundary in…