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 …

Functions of one or more variables are usually approximated with a basis: a complete,
linearly independent system of functions that spans a suitable function space. The topic of …

This paper deals with the design and validation of accurate local absorbing boundary
conditions set on convex polygonal and polyhedral computational domains for the finite …

We analyze the singular behaviour of the Helmholtz equation set in a non-convex polygon.
Classically, the solution of the problem is split into a regular part and one singular function …

This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation
posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the …

We propose and analyse a hybrid numerical–asymptotic boundary element method (BEM)
for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of …

We consider solving the exterior Dirichlet problem for the Helmholtz equation with the h-
version of the boundary element method (BEM) using the standard second-kind combined …

For the h-finite-element method (h-FEM) applied to the Helmholtz equation, the question of
how quickly the meshwidth h must decrease with the frequency k to maintain accuracy as k …

We consider solving the sound-soft scattering problem for the Helmholtz equation with the h
h-version of the boundary element method using the standard second-kind combined-field …

In this paper we propose and analyze a hybrid hp boundary element method for the solution
of problems of high frequency acoustic scattering by sound-soft convex polygons, in which …