[HTML][HTML] Numerical evaluation of oscillatory integrals via automated steepest descent contour deformation
Steepest descent methods combining complex contour deformation with numerical
quadrature provide an efficient and accurate approach for the evaluation of highly oscillatory …
quadrature provide an efficient and accurate approach for the evaluation of highly oscillatory …
A Filon-Clenshaw-Curtis-Smolyak rule for multi-dimensional oscillatory integrals with application to a UQ problem for the Helmholtz equation
In this paper, we combine the Smolyak technique for multi-dimensional interpolation with the
Filon-Clenshaw-Curtis (FCC) rule for one-dimensional oscillatory integration, to obtain a …
Filon-Clenshaw-Curtis (FCC) rule for one-dimensional oscillatory integration, to obtain a …
An efficient frequency-independent numerical method for computing the far-field pattern induced by polygonal obstacles
For problems of time-harmonic scattering by rational polygonal obstacles, embedding
formulae express the far-field pattern induced by any incident plane wave in terms of the far …
formulae express the far-field pattern induced by any incident plane wave in terms of the far …
The numerical unified transform method for initial-boundary value problems on the half-line
B Deconinck, T Trogdon, X Yang - IMA Journal of Numerical …, 2022 - academic.oup.com
We implement the unified transform method of Fokas as a numerical method to solve linear
evolution partial differential equations on the half-line. The method computes the solution at …
evolution partial differential equations on the half-line. The method computes the solution at …
A high-frequency boundary element method for scattering by a class of multiple obstacles
A Gibbs, SN Chandler-Wilde… - IMA Journal of …, 2021 - academic.oup.com
We propose a boundary element method for problems of time-harmonic acoustic scattering
by multiple obstacles in two dimensions, at least one of which is a convex polygon. By …
by multiple obstacles in two dimensions, at least one of which is a convex polygon. By …
Analytical and numerical techniques for wave scattering
G Maierhofer - 2022 - repository.cam.ac.uk
In this thesis, we study the mathematical solution of wave scattering problems which
describe the behaviour of waves incident on obstacles and are highly relevant to a raft of …
describe the behaviour of waves incident on obstacles and are highly relevant to a raft of …
Convergence analysis of oversampled collocation boundary element methods in 2D
G Maierhofer, D Huybrechs - Advances in Computational Mathematics, 2022 - Springer
Collocation boundary element methods for integral equations are easier to implement than
Galerkin methods because the elements of the discretisation matrix are given by lower …
Galerkin methods because the elements of the discretisation matrix are given by lower …
An analysis of least-squares oversampled collocation methods for compactly perturbed boundary integral equations in two dimensions
G Maierhofer, D Huybrechs - Journal of Computational and Applied …, 2022 - Elsevier
In recent work (Maierhofer and Huybrechs, 2022, Adv. Comput. Math.), the authors showed
that least-squares oversampling can improve the convergence properties of collocation …
that least-squares oversampling can improve the convergence properties of collocation …
Oversampling collocation method for the Volterra integral equation with contaminated data
D Zhao, L Pu, Y Yu - Calcolo, 2022 - Springer
In this paper, an oversampling collocation method based on shifted generalized Jacobi
functions as a set of basis is proposed to find the numerical solutions of Volterra integral …
functions as a set of basis is proposed to find the numerical solutions of Volterra integral …
Recursive moment computation in Filon methods and application to high-frequency wave scattering in two dimensions
We study the efficient approximation of highly oscillatory integrals using Filon methods. A
crucial step in the implementation of these methods is the accurate and fast computation of …
crucial step in the implementation of these methods is the accurate and fast computation of …