49 citations · 144 across the 45 of their papers we have counts for
17 papers · 1 filter
Cartesian PML truncation for the Helmholtz equation is exponentially accurate at high frequency
Martin Averseng, Jeffrey Galkowski, Euan A. Spence
For a wide class of Helmholtz scattering problems (namely, those fitting in the black-box framework of Sjöstrand--Zworski) we prove that the error incurred by approximating the rad…
Explicit bounds for the high-frequency time-harmonic Maxwell equations in heterogeneous media
Théophile Chaumont-Frelet, Andrea Moiola, Euan A. Spence
We consider the time-harmonic Maxwell equations posed in . We prove a priori bounds on the solution for coefficients and satisfying certain monoton…
Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition
David Lafontaine, Euan A. Spence
We prove sharp bounds on certain impedance-to-impedance maps (and their compositions) for the Helmholtz equation with large wavenumber (i.e., at high-frequency) using semiclassical…
The -FEM applied to the Helmholtz equation with PML truncation does not suffer from the pollution effect
Jeffrey Galkowski, David Lafontaine, Euan A. Spence +1
We consider approximation of the variable-coefficient Helmholtz equation in the exterior of a Dirichlet obstacle using perfectly-matched-layer (PML) truncation; it is well known th…
Wavenumber-explicit parametric holomorphy of Helmholtz solutions in the context of uncertainty quantification
Euan A. Spence, Jared Wunsch
A crucial role in the theory of uncertainty quantification (UQ) of PDEs is played by the regularity of the solution with respect to the stochastic parameters; indeed, a key propert…
Spurious Quasi-Resonances in Boundary Integral Equations for the Helmholtz Transmission Problem
Ralf Hiptmair, Andrea Moiola, Euan A. Spence
We consider the Helmholtz transmission problem with piecewise-constant material coefficients, and the standard associated direct boundary integral equations. For certain coefficien…
Perfectly-matched-layer truncation is exponentially accurate at high frequency
Jeffrey Galkowski, David Lafontaine, Euan A. Spence
We consider a wide variety of scattering problems including scattering by Dirichlet, Neumann, and penetrable obstacles. We consider a radial perfectly-matched layer (PML) and show…
Decompositions of high-frequency Helmholtz solutions via functional calculus, and application to the finite element method
Jeffrey Galkowski, David Lafontaine, Euan A. Spence +1
Over the last ten years, results from [Melenk-Sauter, 2010], [Melenk-Sauter, 2011], [Esterhazy-Melenk, 2012], and [Melenk-Parsania-Sauter, 2013] decomposing high-frequency Helmholt…
Eigenvalues of the truncated Helmholtz solution operator under strong trapping
Jeffrey Galkowski, Pierre Marchand, Euan A. Spence
For the Helmholtz equation posed in the exterior of a Dirichlet obstacle, we prove that if there exists a family of quasimodes (as is the case when the exterior of the obstacle has…
For most frequencies, strong trapping has a weak effect in frequency-domain scattering
David Lafontaine, Euan A. Spence, Jared Wunsch
It is well known that when the geometry and/or coefficients allow stable trapped rays, the outgoing solution operator of the Helmholtz equation (a.k.a. the resolvent of the Laplaci…
Optimal constants in nontrapping resolvent estimates and applications in numerical analysis
Jeffrey Galkowski, Euan A. Spence, Jared Wunsch
We study the resolvent for nontrapping obstacles on manifolds with Euclidean ends. It is well known that for such manifolds, the outgoing resolvent satisfies $\|χR(k) χ\|_{L^2\to L…
Wavenumber-explicit regularity estimates on the acoustic single- and double-layer operators
Jeffrey Galkowski, Euan A. Spence
We prove new, sharp, wavenumber-explicit bounds on the norms of the Helmholtz single- and double-layer boundary-integral operators as mappings from $L^2(\partial Ω)\rightarrow H^1(…
The Helmholtz equation in random media: well-posedness and a priori bounds
O. R. Pembery, E. A. Spence
We prove well-posedness results and a priori bounds on the solution of the Helmholtz equation , posed either in or in the exte…
The Helmholtz equation in heterogeneous media: a priori bounds, well-posedness, and resonances
Ivan G. Graham, Owen R. Pembery, Euan A. Spence
We consider the exterior Dirichlet problem for the heterogeneous Helmholtz equation, i.e. the equation where both and are functions…
High-frequency bounds for the Helmholtz equation under parabolic trapping and applications in numerical analysis
Simon N. Chandler-Wilde, Euan A. Spence, Andrew Gibbs +1
This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the…
Acoustic transmission problems: wavenumber-explicit bounds and resonance-free regions
Andrea Moiola, Euan A. Spence
We consider the Helmholtz transmission problem with one penetrable star-shaped Lipschitz obstacle. Under a natural assumption about the ratio of the wavenumbers, we prove bounds on…
Sharp high-frequency estimates for the Helmholtz equation and applications to boundary integral equations
Dean Baskin, Euan Spence, Jared Wunsch
We consider three problems for the Helmholtz equation in interior and exterior domains in R^d (d=2,3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgo…