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11/26/2022
Sharp bounds on Helmholtz impedance-to-impedance maps and application to overlapping domain decomposition
We prove sharp bounds on certain impedance-to-impedance maps (and their ...
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07/12/2022
The hp-FEM applied to the Helmholtz equation with PML truncation does not suffer from the pollution effect
We consider approximation of the variable-coefficient Helmholtz equation...
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06/09/2021
Convergence of parallel overlapping domain decomposition methods for the Helmholtz equation
We analyse parallel overlapping Schwarz domain decomposition methods for...
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05/17/2021
Perfectly-matched-layer truncation is exponentially accurate at high frequency
We consider a wide variety of scattering problems including scattering b...
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02/25/2021
Decompositions of high-frequency Helmholtz solutions via functional calculus, and application to the finite element method
Over the last ten years, results from [Melenk-Sauter, 2010], [Melenk-Sau...
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01/06/2021
Local absorbing boundary conditions on fixed domains give order-one errors for high-frequency waves
We consider approximating the solution of the Helmholtz exterior Dirichl...
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10/01/2020
Wavenumber-explicit convergence of the hp-FEM for the full-space heterogeneous Helmholtz equation with smooth coefficients
A convergence theory for the hp-FEM applied to a variety of constant-coe...
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11/25/2019