A Hausdorff-measure boundary element method for acoustic scattering by fractal screens

DOI10.1007/S00211-024-01399-7MaRDI QIDQ6493744

A. Gibbs, Simon N. Chandler-Wilde, Andrea Moiola, António M. Caetano, D. P. Hewett

Publication date: 29 April 2024

Published in: Numerische Mathematik (Search for Journal in Brave)

Numerical methods for integral equations (65R20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fractals (28A80) Boundary element methods for boundary value problems involving PDEs (65N38) Linear integral equations (45A05)

Cites Work

Sobolev spaces on non-Lipschitz subsets of \(\mathbb {R}^n\) with application to boundary integral equations on fractal screens
Boundary integral equations for screen problems in \({\mathbb{R}}^ 3\)
Duality estimates for the numerical solution of integral equations
Wavelets on fractals and Besov spaces
Boundary layer methods for Lipschitz domains in Riemannian manifolds
A fast direct algorithm for the solution of the Laplace equation on regions with fractal boundaries
The Hausdorff measure of a class of Sierpiński carpets
Boundary element methods for acoustic scattering by fractal screens
Density results for Sobolev, Besov and Triebel-Lizorkin spaces on rough sets
New preconditioners for the Laplace and Helmholtz integral equations on open curves: analytical framework and numerical results
Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens
Exact Hausdorff and packing measure of certain Cantor sets, not necessarily self-similar or homogeneous
On the Hausdorff dimension of continuous functions belonging to Hölder and Besov spaces on fractal \(d\)-sets
Quotient-space boundary element methods for scattering at complex screens
Numerical quadrature for singular integrals on fractals
On the type of convergence in atomic representations
Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering
An augmented galerkin procedure for the boundary integral method applied to two-dimensional screen and crack problems
The Galerkin Method for Integral Equations of the First Kind with Logarithmic Kernel: Theory
Reduction of order for pseudodifferential operators on lipschitz domains
The FEM and BEM for fractal boundaries and interfaces. Applications to unilateral problems
Well-Posed PDE and Integral Equation Formulations for Scattering by Fractal Screens
Inverse inequalities on non-quasi-uniform meshes and application to the mortar element method
Interpolation of compact operators by the methods of Calderón and Gustavsson–Peetre
Spectral Galerkin method for solving Helmholtz boundary integral equations on smooth screens
Acoustic scattering by impedance screens/cracks with fractal boundary: Well-posedness analysis and boundary element approximation
INTERPOLATION OF HILBERT AND SOBOLEV SPACES: QUANTITATIVE ESTIMATES AND COUNTEREXAMPLES
On the maximal Sobolev regularity of distributions supported by subsets of Euclidean space
An improved boundary element method for the charge density of a thin electrified plate in ℝ³

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