This paper is concerned with the direct and inverse acoustic or electromagnetic scattering problems by a locally perturbed, perfectly reflecting, infinite plane (which is called a locally rough surface in this paper). We propose a novel integral equation formulation for the direct scattering problem which is defined on a bounded curve (consisting of a bounded part of the infinite plane containi...

We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to complex, non-manifold boundaries. This approach is motivated by the observation that while several methods exist for adaptive tetrahedral meshing, they typically have difficulty at geometric boundaries. The proposed strategy avoid...

We present an adaptive refinement strategy for the h-version of the boundary element method with weakly singular operators on surfaces. The model problem deals with the exterior Stokes problem, and thus considers vector functions. Our error indicators are computed by local projections onto 1D subspaces defined by mesh refinement. These indicators measure the error separately for the vector comp...

We consider finite element methods for a model second-order el-liptic equation on a general bounded convex polygonal or polyhedral domain. Our first main goal is to extend the best approximation property of the error in the í µí±Š 1 ∞ norm, which is known to hold on quasi-uniform meshes, to more general graded meshes. We accomplish it by a novel proof technique. This result holds under a condit...

Boundary integral methods for the solution of boundary value PDEs are an alternative to ‘interior’ methods, such as finite difference and finite element methods. They are attractive on domains with corners, particularly when the solution has singularities at these corners. In these cases, interior methods can become excessively expensive, as they require a finely discretised 2D mesh in the vici...

Lenses are used for multiple applications, including communications, surveillance and security, medical instruments. In homogeneous lenses, the contour is to control electromagnetic propagation. Differently, graded-index lenses make use of inhomogeneous materials, which an extra degree freedom. This freedom enables design devices with a high performance. For instance, rotationally symmetric wit...

We take a fairly comprehensive approach to the problem of solving elliptic partial differential equations numerically using integral equation methods on domains where the boundary has a large number of corners and branching points. Use of non-standard integral equations, graded meshes, interpolatory quadrature, and compressed inverse preconditioning are techniques that are explored, developed, ...

For optical waveguides with high index-contrast and sharp corners, existing full-vectorial mode solvers including those based on boundary integral equations typically have only second or third order of accuracy. In this paper, a new full-vectorial waveguide mode solver is developed based on a new formulation of boundary integral equations and the so-called Neumann-to-Dirichlet operators for sub...

We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound ...

We consider the numerical solution of the problem of time-harmonic acoustic scattering in two dimensions by a sound soft convex polygon. Standard boundary or finite element methods with piecewise polynomial approximation spaces have a computational cost that grows at least linearly with respect to the frequency of the incident wave. By including in the approximation space the products of plane ...