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We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

The boundary element method is an efficient algorithm for simulating acoustic propagation through homogeneous objects embedded in free space. The conditioning of the system matrix strongly depends on physical parameters such as density,…

We introduce and analyze various Regularized Combined Field Integral Equations (CFIER) formulations of time-harmonic Navier equations in media with piece-wise constant material properties. These formulations can be derived systematically…

We present a novel hybrid numerical-asymptotic boundary element method for high frequency acoustic and electromagnetic scattering by penetrable (dielectric) convex polygons. Our method is based on a standard reformulation of the associated…

Many inverse problems have to deal with complex, evolving and often not exactly known geometries, e.g. as domains of forward problems modeled by partial differential equations. This makes it desirable to use methods which are robust with…

Several important problems in partial differential equations can be formulated as integral equations. Often the integral operator defines the solution of an elliptic problem with specified jump conditions at an interface. In principle the…

We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the…

The dynamics of ionization fronts that generate a conducting body, are in simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a…

This paper devotes to developing novel boundary integral equation (BIE) solvers for the problem of thermoelastic scattering by open-arcs with four different boundary conditions in two dimensions. The proposed methodology is inspired by the…

We present Nystr\"om discretizations of multitrace formulations and non-overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz transmission problems for bounded composite scatterers with piecewise constant material…

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

A symmetric boundary integral formulation for the transient scattering of acoustic waves off homogeneous and isotropic elastic obstacles is analyzed. Both the acoustic scattered field and the elastodynamic excited field are represented…

Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…

We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray…

Caetano et al. (Proc. R. Soc. A. 481:20230650, 2025) have proposed a formulation for sound-soft acoustic scattering by a compact scatterer O $\subset$ Rn, in which the scattered field is represented as an acoustic Newtonian potential whose…

This paper introduces a new approach for generating globally consistent normals for point clouds sampled from manifold surfaces. Given that the generalized winding number (GWN) field generated by a point cloud with globally consistent…

In this paper, the integral initial value problems for Boussinesq type equations are studied. The equation include the general differential operators. The existence, uniqueness and regularity properties of solution of these problems are…

In this paper we revisit the classical Cauchy problem for Laplace's equation as well as two further related problems in the light of regularisation of this highly ill-conditioned problem by replacing integer derivatives with fractional…

Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…

The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric…