In this article we describe recent progress on the design, analysis and implementation of
hybrid numerical-asymptotic boundary integral methods for boundary value problems for the …

Isogeometric analysis is a topic of considerable interest in the field of numerical analysis.
The boundary element method (BEM) requires only the bounding surface of geometries to …

In this paper we obtain new results on Filon-type methods for computing oscillatory integrals
of the form∫− 1 1 f (s) exp (iks) ds. We use a Filon approach based on interpolating f at the …

In this paper we consider the problem of time-harmonic acoustic scattering in two
dimensions by convex polygons. Standard boundary or finite element methods for acoustic …

We consider two-dimensional scattering problems, formulated as an integral equation
defined on the boundary of the scattering obstacle. The oscillatory nature of high-frequency …

In this paper we consider the problem of scattering of time-harmonic acoustic waves by a
bounded, sound soft obstacle in two and three dimensions, studying dependence on the …

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in
the sense that the bilinear forms cannot be bounded below by a positive multiple of the …

We consider the classical coupled, combined‐field integral equation formulations for time‐
harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have …

We consider three problems for the Helmholtz equation in interior and exterior domains in
R^d (d=2,3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for …

In this paper we propose and analyze composite Filon--Clenshaw--Curtis quadrature rules
for integrals of the form I_k^a,b(f,g):=\int_a^bf(x)\exp(ikg(x))dx, where k≧0, f may have …