49 citations · 144 across the 45 of their papers we have counts for
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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…
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…
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 theory for two-level hybrid Schwarz preconditioners for high-frequency Helmholtz problems
Jeffrey Galkowski, Euan A. Spence
We give a novel convergence theory for two-level hybrid Schwarz domain-decomposition (DD) methods for finite-element discretisations of the high-frequency Helmholtz equation. This…