Integral equation methods for the solution of partial differential equations, when coupled with
suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well …

This paper presents an accelerated quadrature scheme for the evaluation of layer potentials
in three dimensions. Our scheme combines a generic, high order quadrature method for …

We establish shape holomorphy results for general weakly-and hyper-singular boundary
integral operators arising from second-order partial differential equations in unbounded two …

This paper presents novel methodologies for the numerical simulation of scattering of elastic
waves by both closed and open surfaces in three-dimensional space. The proposed …

For the scattering problem for time-harmonic waves from an impedance crack in two
dimensions, we give a uniqueness and existence analysis via a combined single-and …

We consider the elastic scattering problem by multiple disjoint arcs or\emph {cracks} in two
spatial dimensions. A key aspect of our approach lies in the parametric description of each …

Quadrature by Expansion (QBX) is a quadrature method for approximating the value of the
singular integrals encountered in the evaluation of layer potentials. It exploits the …

In this work we consider the inverse elastic scattering problem by an inclusion in two
dimensions. The elastic inclusion is placed in an isotropic homogeneous elastic medium …

This paper is concerned with the boundary integral equation method for solving the exterior
Neumann boundary value problem of dynamic poroelasticity in two dimensions. The main …

Helmholtz decompositions of elastic fields is a common approach for the solution of Navier
scattering problems. Used in the context of Boundary Integral Equations (BIE), this approach …