A proof of high-order convergence of three deterministic particle methods for the convectiondiffusion equation in two dimensions is presented. The methods are based on discretizations of an integro-differential equation in which an integral operator approximates the diffusion operator. The methods differ in the discretization of this operator. The conditions for convergence imposed on the kerne...

This paper is concerned with the source-type of integral equation to compute the electromagnetic scattering by an inhomogeneous 3D object in a planar layered medium in the frequency domain. By decomposing the scattered field into a particular and a general constituent, the structure of the integral operator of the integral equation is constructed. The particular constituent represents the scatt...

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Any compact C∞ manifold with boundary admits a Riemann metric on its interior taking the form x−4dx2 + x−2h′ near the boundary, where x is a boundary defining function and h′ is a smooth symmetric 2-cotensor restricting to be positive-definite, and hence a metric, h, on the boundary. The scattering theory associated to the Laplacian for such a ‘scattering metric’ was discussed by the first auth...

Abstract. We develop an algorithm for the canonical computation of general Fourier integral operators whose canonical relations are graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation of the action of such operators on data in the presence of caustics. The procedure consists in the construction of a universal operat...

We use Fourier multipliers of the Dirac operator and Cauchy transform to obtain composition theorems and integral representations. In particular we calculate the multiplier of the Π-operator. This operator is the hypercomplex version of the Beurling Ahlfors transform in the plane. The hypercomplex Beuling Ahlfors transform is a direct generalization of the Beurling Ahlfors transform and reduces...

Let X and Y be two closed connected Riemannian manifolds of the same dimension and φ : S∗X 7→ S∗Y a contact diffeomorphism. We show that the index of an elliptic Fourier operator Φ associated with φ is given by ∫ B(X) e 0Â(T ∗X) −

In this paper we prove new ` → ` bounds for a discrete fractional integral operator by applying techniques motivated by the circle method of Hardy and Littlewood to the Fourier multiplier of the operator. From a different perspective, we describe explicit interactions between the Fourier multiplier and mean values of Weyl sums. These mean values express the average behaviour of the number rs,k(...

We establish sharp L2-Sobolev estimates for classes of pseudodifferential operators with singular symbols [27, 20] whose non-pseudodifferential (Fourier integral operator) parts exhibit two-sided fold singularities. The operators considered include both singular integral operators along curves in R2 with simple inflection points and normal operators arising in linearized seismic imaging in the ...

planar d-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as electrical impedance tomography (eit). recently two different methodologies are considered for the numerical solution of d-bar integrals equation, namely product integrals and multigrid. the first one involves high computational ...