Scattering for NLS with a potential on the line. - David Lafontaine (Asymptot. Anal., 2016)

Wavenumber-explicit convergence of the hp-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients. - David Lafontaine; Euan A. Spence; Jared Wunsch (CoRR, 2020)

Local absorbing boundary conditions on fixed domains give order-one errors for high-frequency waves. - Jeffrey Galkowski; David Lafontaine; Euan A. Spence (CoRR, 2021)

Decompositions of high-frequency Helmholtz solutions via functional calculus, and application to the finite element method. - David Lafontaine; Euan A. Spence; Jared Wunsch (CoRR, 2021)

Wavenumber-explicit convergence of the hp-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients. - David Lafontaine; Euan A. Spence; Jared Wunsch (Comput. Math. Appl., 2022)

The hp-FEM applied to the Helmholtz equation with PML truncation does not suffer from the pollution effect. - Jeffrey Galkowski; David Lafontaine; Euan A. Spence; Jared Wunsch (CoRR, 2022)

Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition. - David Lafontaine; Euan A. Spence (CoRR, 2022)

Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation. - Shihua Gong; Martin J. Gander; Ivan G. Graham; David Lafontaine; Euan A. Spence (Numerische Mathematik, 2022)

A sharp relative-error bound for the Helmholtz h-FEM at high frequency. - David Lafontaine; Euan A. Spence; Jared Wunsch (Numerische Mathematik, 2022)

Perfectly-Matched-Layer Truncation is Exponentially Accurate at High Frequency. - Jeffrey Galkowski; David Lafontaine; Euan A. Spence (SIAM J. Math. Anal., 2023)

Decompositions of High-Frequency Helmholtz Solutions via Functional Calculus, and Application to the Finite Element Method. - Jeffrey Galkowski; David Lafontaine; Euan A. Spence; Jared Wunsch (SIAM J. Math. Anal., 2023)

Convergence of overlapping domain decomposition methods with PML transmission conditions applied to nontrapping Helmholtz problems. - Jeffrey Galkowski; Shihua Gong; Ivan G. Graham; David Lafontaine; Euan A. Spence (CoRR, 2024)

Schwarz methods with PMLs for Helmholtz problems: fast convergence at high frequency. - Jeffrey Galkowski; Shihua Gong; Ivan G. Graham; David Lafontaine; Euan A. Spence (CoRR, 2024)