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04/28/2023
Helmholtz FEM solutions are locally quasi-optimal modulo low frequencies
For h-FEM discretisations of the Helmholtz equation with wavenumber k, w...
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01/09/2023
Sharp preasymptotic error bounds for the Helmholtz h-FEM
In the analysis of the h-version of the finite-element method (FEM), wit...
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11/09/2022
Lower bounds for piecewise polynomial approximations of oscillatory functions
We prove sharp lower bounds on the error incurred when approximating any...
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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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01/24/2022
The Helmholtz boundary element method does not suffer from the pollution effect
In d dimensions, approximating an arbitrary function oscillating with fr...
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09/13/2021
High-frequency estimates on boundary integral operators for the Helmholtz exterior Neumann problem
We study a commonly-used second-kind boundary-integral equation for solv...
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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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02/10/2021
Applying GMRES to the Helmholtz equation with strong trapping: how does the number of iterations depend on the frequency?
We consider GMRES applied to discretisations of the high-frequency Helmh...
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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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01/06/2021