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math.AP2024
Helmholtz quasi-resonances are unstable under most single-signed perturbations of the wave speed
Euan A. Spence, Jared Wunsch, Yuzhou Zou
We consider Helmholtz problems with a perturbed wave speed, where the single-signed perturbation is linear in a parameter . Both the wave speed and the perturbation are allowed…
math.AP2021
Scattering by finely-layered obstacles: frequency-explicit bounds and homogenization
Théophile Chaumont-Frelet, Euan A. Spence
We consider the scalar Helmholtz equation with variable, discontinuous coefficients, modelling transmission of acoustic waves through an anisotropic penetrable obstacle. We first p…
math.AP2021
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…