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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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01/25/2023
Optimisation of seismic imaging via bilevel learning
The implementation of Full Waveform Inversion (FWI) requires the a prior...
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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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11/26/2022
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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10/05/2022
Coercive second-kind boundary integral equations for the Laplace Dirichlet problem on Lipschitz domains
We present new second-kind integral-equation formulations of the interio...
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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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03/19/2022
Wavenumber-explicit parametric holomorphy of Helmholtz solutions in the context of uncertainty quantification
A crucial role in the theory of uncertainty quantification (UQ) of PDEs ...
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02/14/2022
A simple proof that the hp-FEM does not suffer from the pollution effect for the constant-coefficient full-space Helmholtz equation
In d dimensions, approximating an arbitrary function oscillating with fr...
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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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10/27/2021
Convergence of Restricted Additive Schwarz with impedance transmission conditions for discretised Helmholtz problems
The Restricted Additive Schwarz method with impedance transmission condi...
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09/17/2021
Spurious Quasi-Resonances in Boundary Integral Equations for the Helmholtz Transmission Problem
We consider the Helmholtz transmission problem with piecewise-constant m...
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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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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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05/24/2021
Coercivity, essential norms, and the Galerkin method for second-kind integral equations on polyhedral and Lipschitz domains
It is well known that, with a particular choice of norm, the classical d...
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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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03/21/2021
A variational interpretation of Restricted Additive Schwarz with impedance transmission condition for the Helmholtz problem
In this paper we revisit the Restricted Additive Schwarz method for solv...
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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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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
Eigenvalues of the truncated Helmholtz solution operator under strong trapping
For the Helmholtz equation posed in the exterior of a Dirichlet obstacle...
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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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05/27/2020
Analysis of a Helmholtz preconditioning problem motivated by uncertainty quantification
This paper analyses the following question: let A_j, j=1,2, be the Galer...
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04/08/2020
Domain decomposition preconditioners for high-order discretisations of the heterogeneous Helmholtz equation
We consider one-level additive Schwarz domain decomposition precondition...
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11/25/2019