34 citations · 193 across the 55 of their papers we have counts for
15 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…
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…
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…
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…
Sharp error bounds for edge-element discretisations of the high-frequency Maxwell equations
Théophile Chaumont-Frelet, Jeffrey Galkowski, Euan A. Spence
We prove sharp wavenumber-explicit error bounds for first- or second-family-Nédélec-element (a.k.a. edge-element) conforming discretisations, of arbitrary (fixed) order, of the var…
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…
Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies
Martin Averseng, Euan A. Spence, Jeffrey Galkowski
For -FEM discretisations of the Helmholtz equation with wavenumber , we obtain -explicit analogues of the classic local FEM error bounds of [Nitsche, Schatz 1974], [Wahlbi…
Sharp preasymptotic error bounds for the Helmholtz -FEM
Jeffrey Galkowski, Euan A. Spence
In the analysis of the -version of the finite-element method (FEM), with fixed polynomial degree , applied to the Helmholtz equation with wavenumber , the $\textit{as…
Lower bounds for piecewise polynomial approximations of oscillatory functions
Jeffrey Galkowski
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and h…
Does the Helmholtz boundary element method suffer from the pollution effect?
Jeffrey Galkowski, Euan A. Spence
In dimensions, accurately approximating an arbitrary function oscillating with frequency requires degrees of freedom. A numerical method for solving the…
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?
Pierre Marchand, Jeffrey Galkowski, Alastair Spence +1
We consider GMRES applied to discretisations of the high-frequency Helmholtz equation with strong trapping; recall that in this situation the problem is exponentially ill-condition…
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 analysis for the Helmholtz -BEM: error estimates and iteration counts for the Dirichlet problem
Jeffrey Galkowski, Eike H. Müller, Euan A. Spence
We consider solving the exterior Dirichlet problem for the Helmholtz equation with the -version of the boundary element method (BEM) using the standard second-kind combined-fiel…