34 citations · 193 across the 55 of their papers we have counts for
8 papers · 1 filter
Lower bounds for Steklov eigenfunctions
Jeffrey Galkowski, John A. Toth
Let be a compact, analytic Riemannian manifold with analytic boundary We give -lower bounds for Steklov eigenfunctions and their restrictions to inter…
Semiclassical resolvent bounds for compactly supported radial potentials
Kiril Datchev, Jeffrey Galkowski, Jacob Shapiro
We employ separation of variables to prove weighted resolvent estimates for the semiclassical Schrödinger operator in dimension , where ,…
High-frequency estimates on boundary integral operators for the Helmholtz exterior Neumann problem
Jeffrey Galkowski, Pierre Marchand, Euan A. Spence
We study a commonly-used second-kind boundary-integral equation for solving the Helmholtz exterior Neumann problem at high frequency, where, writing for the boundary of the obs…
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…
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…
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…