Steepest descent methods combining complex contour deformation with numerical
quadrature provide an efficient and accurate approach for the evaluation of highly oscillatory …

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 …

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 …

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 …

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 …

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 …

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 …

In recent work (Maierhofer and Huybrechs, 2022, Adv. Comput. Math.), the authors showed
that least-squares oversampling can improve the convergence properties of collocation …

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 …

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 …