5 citations · 15 across the 17 of their papers we have counts for
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Schwarz methods with PMLs for Helmholtz problems: fast convergence at high frequency
Jeffrey Galkowski, Shihua Gong, Ivan G. Graham +2
We discuss parallel (additive) and sequential (multiplicative) variants of overlapping Schwarz methods for the Helmholtz equation in , with large real wavenumber and…
Convergence of overlapping domain decomposition methods with PML transmission conditions applied to nontrapping Helmholtz problems
Jeffrey Galkowski, Shihua Gong, Ivan G. Graham +2
We study overlapping Schwarz methods for the Helmholtz equation posed in any dimension with large, real wavenumber and smooth variable wave speed. The radiation condition is approx…
Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation
Shihua Gong, Martin J. Gander, Ivan G. Graham +2
We analyse parallel overlapping Schwarz domain decomposition methods for the Helmholtz equation, where the subdomain problems satisfy first-order absorbing (impedance) transmission…
Local absorbing boundary conditions on fixed domains give order-one errors for high-frequency waves
Jeffrey Galkowski, David Lafontaine, Euan A. Spence
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 solution…
Wavenumber-explicit convergence of the -FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients
David Lafontaine, Euan A. Spence, Jared Wunsch
A convergence theory for the -FEM applied to a variety of constant-coefficient Helmholtz problems was pioneered in the papers [Melenk-Sauter, 2010], [Melenk-Sauter, 2011], [Est…
A sharp relative-error bound for the Helmholtz -FEM at high frequency
David Lafontaine, Euan A. Spence, Jared Wunsch
For the -finite-element method (-FEM) applied to the Helmholtz equation, the question of how quickly the meshwidth must decrease with the frequency to maintain accura…