49 citations · 144 across the 45 of their papers we have counts for
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math.AP2022★ 2 cited
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…
math.AP2022
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…
math.AP2022★ 1 cited
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…