11 papers · 1 filter
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…
Theory of two-level Schwarz preconditioners with piecewise-polynomial coarse spaces for the high-frequency Helmholtz equation
Ivan G. Graham, Euan A. Spence
We analyse the classic two-level additive Schwarz domain-decomposition GMRES preconditioner for finite-element discretisations of the Helmholtz equation with large wavenumber ,…
Convergence of parallel overlapping domain decomposition methods with impedance boundary conditions for time-harmonic Maxwell equations in heterogeneous media
Luyu Cen, Shihua Gong, Euan A. Spence +1
This paper analyzes the convergence of parallel overlapping domain-decomposition methods with impedance boundary conditions for the time-harmonic Maxwell equations in heterogeneous…
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…