63 citations · 243 across the 31 of their papers we have counts for
35 papers
A note on the convergence analysis of Laguerre approximations for analytic functions
Thomas Caussade, David P. Hewett
In a recent paper (H. Wang, Math. Comp. 93, 2861-2884, 2024), Wang has presented a number of results concerning the convergence of approximations based on generalised Laguerre poly…
Integral Equation Methods for Scattering by Multifractal Obstacles
Simon N. Chandler-Wilde, Gabriel Claret, David P. Hewett +2
Caetano et al. (Proc. R. Soc. A. 481:20230650, 2025) have proposed a formulation for sound-soft acoustic scattering by a compact scatterer O Rn, in which the scattered fi…
A discontinuous Galerkin method with fractal elements
Sergio Gómez, David Hewett, Andrea Moiola
We formulate, analyse, and implement a discontinuous Galerkin finite element method (DG-FEM) for the approximation of the solution of an elliptic boundary value problem in a domain…
Acoustic scattering by fractal inhomogeneities via geometry-conforming Galerkin methods for the Lippmann-Schwinger equation
Joshua Bannister, David P. Hewett, Andrew Gibbs
We propose and analyse a numerical method for time-harmonic acoustic scattering in , , by a class of inhomogeneities (penetrable scatterers) with fractal bound…
Discontinuous piecewise polynomial approximation on non-Lipschitz domains
David P Hewett
We prove best approximation error estimates for discontinuous piecewise polynomial approximation in fractional Sobolev spaces on non-Lipschitz meshes of non-Lipschitz domains. In p…
Properties of IFS attractors with non-empty interiors, related rough domains, and associated function spaces and scattering problems
António Caetano, Simon N. Chandler-Wilde, David P. Hewett
We study fractal sets with non-empty interior , that are attractors of iterated function systems (IFSs) of contracting similarities satisfying the open s…
Kernels of trace operators via fine continuity
Michael Hinz, Simon N. Chandler-Wilde, David P. Hewett
Given a closed subset of that is the support of a measure , we study the kernels of trace operators from fractional Sobolev spaces into…
A caustic terminating at an inflection point
J. R. Ockendon, H. Ockendon, R. H. Tew +2
We present an asymptotic and numerical study of the evolution of an incoming wavefield which has a caustic close to a curve with an inflection point. Our results reveal the emergen…
Integral equation methods for acoustic scattering by fractals
A. M. Caetano, S. N. Chandler-Wilde, X. Claeys +3
We study sound-soft time-harmonic acoustic scattering by general scatterers, including fractal scatterers, in 2D and 3D space. For an arbitrary compact scatterer we reformulate…
Numerical evaluation of oscillatory integrals via automated steepest descent contour deformation
A. Gibbs, D. P. Hewett, D. Huybrechs
Steepest descent methods combining complex contour deformation with numerical quadrature provide an efficient and accurate approach for the evaluation of highly oscillatory integra…
Numerical evaluation of singular integrals on non-disjoint self-similar fractal sets
Andrew Gibbs, David P. Hewett, Botond Major
We consider the numerical evaluation of a class of double integrals with respect to a pair of self-similar measures over a self-similar fractal set (the attractor of an iterated fu…
A Hausdorff-measure boundary element method for acoustic scattering by fractal screens
António M. Caetano, Simon N. Chandler-Wilde, Andrew Gibbs +2
Sound-soft fractal screens can scatter acoustic waves even when they have zero surface measure. To solve such scattering problems we make what appears to be the first application o…
Numerical Quadrature for Singular Integrals on Fractals
A. Gibbs, D. P. Hewett, A. Moiola
We present and analyse numerical quadrature rules for evaluating regular and singular integrals on self-similar fractal sets. The integration domain is assumed to be…
Acoustic scattering by impedance screens/cracks with fractal boundary: well-posedness analysis and boundary element approximation
J. Bannister, A. Gibbs, D. P. Hewett
We study time-harmonic scattering in () by a planar screen (a "crack" in the context of linear elasticity), assumed to be a non-empty bounded relatively open…
Accelerated Calderón preconditioning for Maxwell transmission problems
Antigoni Kleanthous, Timo Betcke, David P. Hewett +3
We investigate a range of techniques for the acceleration of Calderón (operator) preconditioning in the context of boundary integral equation methods for electromagnetic transmissi…
Fast hybrid numerical-asymptotic boundary element methods for high frequency screen and aperture problems based on least-squares collocation
Andrew Gibbs, David Hewett, Daan Huybrechs +1
We present a hybrid numerical-asymptotic (HNA) boundary element method (BEM) for high frequency scattering by two-dimensional screens and apertures, whose computational cost to ach…
Boundary element methods for acoustic scattering by fractal screens
Simon N. Chandler-Wilde, David P. Hewett, Andrea Moiola +1
We study boundary element methods for time-harmonic scattering in () by a fractal planar screen, assumed to be a non-empty bounded subset of the hyperplan…
Density results for Sobolev, Besov and Triebel--Lizorkin spaces on rough sets
António Caetano, David P. Hewett, Andrea Moiola
We investigate two density questions for Sobolev, Besov and Triebel--Lizorkin spaces on rough sets. Our main results, stated in the simplest Sobolev space setting, are that: (i) fo…
Calderón preconditioning of PMCHWT boundary integral equations for scattering by multiple absorbing dielectric particles
Antigoni Kleanthous, Timo Betcke, David P. Hewett +2
We consider the simulation of electromagnetic scattering by single and multiple isotropic homogeneous dielectric particles using boundary integral equations. Galerkin discretizatio…
Electromagnetic shielding by thin periodic structures and the Faraday cage effect
Bérangère Delourme, David P. Hewett
In this note we consider the scattering of electromagnetic waves (governed by the time-harmonic Maxwell equations) by a thin periodic layer of perfectly conducting obstacles. The s…
Contour integral solutions of the parabolic wave equation
David P. Hewett, John R. Ockendon, Valery P. Smyshlyaev
We present a simple systematic construction and analysis of solutions of the two-dimensional parabolic wave equation that exhibit far-field localisation near a given algebraic plan…
A hybrid numerical-asymptotic boundary element method for high frequency scattering by penetrable convex polygons
Samuel P. Groth, David P. Hewett, Stephen Langdon
We present a novel hybrid numerical-asymptotic boundary element method for high frequency acoustic and electromagnetic scattering by penetrable (dielectric) convex polygons. Our me…
Well-posed PDE and integral equation formulations for scattering by fractal screens
Simon N. Chandler-Wilde, David P. Hewett
We consider time-harmonic acoustic scattering by planar sound-soft (Dirichlet) and sound-hard (Neumann) screens embedded in for or . In contrast to previo…
A note on properties of the restriction operator on Sobolev spaces
David P. Hewett, Andrea Moiola
In our companion paper (S.N. Chandler Wilde, D.P. Hewett, A. Moiola, Sobolev spaces on non-Lipschitz subsets of with application to boundary integral equations on fr…