5 citations · 15 across the 17 of their papers we have counts for
21 papers
On scattering and profile decomposition for critical nonlinear waves outside weakly trapping obstacles
David Lafontaine, Camille Laurent
We prove scattering for the defocusing energy-critical non-linear wave equation with Dirichlet boundary conditions outside two strictly convex obstacles in dimension three. This is…
Scattering for Defocusing NLS with Inhomogeneous Nonlinear Damping and Nonlinear Trapping Potential
David Lafontaine, Boris Shakarov
We investigate an energy-subcritical defocusing nonlinear Schrödinger equation in subject to a lower order nonlinear trapping potential and a spatially dependent nonl…
Observability estimates for the Schrödinger equation on the equilateral triangle
Paul Alphonse, David Lafontaine
We prove observability estimates for the Schrödinger equation posed on the equilateral triangle in the plane, under both Neumann and Dirichlet boundary conditions. No geometric con…
Scattering for defocusing cubic NLS under locally damped strong trapping
David Lafontaine, Boris Shakarov
We are interested in the scattering problem for the cubic 3D nonlinear defocusing Schrödinger equation with variable coefficients. Previous scattering results for such problems add…
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…
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…
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…
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…
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…
Scattering for critical radial Neumann waves outside a ball
Thomas Duyckaerts, David Lafontaine
We show that the solutions of the three-dimensional critical defocusing nonlinear wave equation with Neumann boundary conditions outside a ball and radial initial data scatter. Thi…
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…
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…
Strichartz estimates without loss outside many strictly convex obstacles
David Lafontaine
We prove Strichartz estimates without loss for the Schrödinger equation and the wave equation outside finitely many strictly convex obstacles verifying Ikawa's condition, extending…
Scattering for NLS with a sum of two repulsive potentials
David Lafontaine
We prove the scattering for a defocusing nonlinear Schrödinger equation with a sum of two repulsive potentials with strictly convex level surfaces, thus providing a scattering resu…
About the wave equation outside two strictly convex obstacles
David Lafontaine
We prove global Strichartz estimates without loss for the wave equation outside two strictly convex obstacles, following the roadmap introduced in [Lafontaine, 2017] for the Schröd…
Strichartz estimates without loss outside two strictly convex obstacles
David Lafontaine
We prove global Strichartz estimates without loss outside two strictly convex obstacles, combining arguments from M.Ikawa (1982,1988) with more recent ones inspired by N.Burq, C.Gu…
Scattering for NLS with a potential on the line
David Lafontaine
We show the scattering for a one dimensional nonlinear Schrödinger equation with a non-negative, repulsive potential such that , and a mass-supercritic…