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Several methods for handling sloping fluid-solid interfaces with the elastic parabolic equation are tested. A single-scattering approach that is modified for the fluid-solid case is accurate for some problems but breaks down when the…
This work presents spectral, mesh-free, Green's theorem-based numerical quadrature schemes for integrating functions over planar regions bounded by rational parametric curves. Our algorithm proceeds in two steps: (1) We first find…
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Based on the regularity property introduced in Part I, the…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
An efficient hybrid numerical method for multiple scattering calculations is proposed. We use the well established doubling--adding method to find the reflection function of the lowermost homogeneous slab comprising the atmosphere of our…
In this paper, we establish new results for the uniform far-field asymptotics of the two-layered Green function (together with its derivatives) in 2D in the frequency domain. To the best of our knowledge, our results are the sharpest yet…
Traditional boundary integral methods suffer from the singularity of Green's kernels. The paper develops, for a model problem of 2D scattering as an illustrative example, singularity-free boundary difference equations. Instead of converting…
We consider the wave scattering and inverse scattering in an inhomogeneous medium embedded a homogeneous droplet with a small size, which is modeled by a constant mass density and a small bulk modulus. Based on the Lippmann-Schwinger…
The single particle Green's function provides valuable information on the momentum and energy-resolved spectral properties for a strongly correlated system. In large-scale numerical calculations using quantum Monte Carlo (QMC), dynamical…
This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…
The functional integral method can be used in quantum mechanics to find the scattering amplitude for particles in the external field. We will obtain the potential scattering amplitude form the complete Green function in the corresponding…
We establish a new type of local asymptotic formula for the Green's function ${\mathcal G}_t(x,y)$ of a uniformly parabolic linear operator $\partial_t - L$ with non-constant coefficients using dilations and Taylor expansions at a point…
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…
We investigate the use of a functional analytical version of the Backus-Gilbert Method as a reconstruction strategy to get specific information about the solution of linear and slightly non-linear systems with Frech\'et derivable operators.…
The forward-backward splitting technique is a popular method for solving monotone inclusions that has applications in optimization. In this paper we explore the behaviour of the algorithm when the inclusion problem has no solution. We…
We revisit the volume Green's function integral equation for modelling light scattering with discretization strategies as well as numerical integration recipes borrowed from finite element method. The merits of introducing finite element…
This paper discusses a fast direct solver using boundary integral equations for Helmholtz transmission problems involving multiple inclusions in two dimensions. Efficiently addressing scattering problems in the presence of numerous…
In this paper, a new model is proposed for the inverse random source scattering problem of the Helmholtz equation with attenuation. The source is assumed to be driven by a fractional Gaussian field whose covariance is represented by a…
In this work, we are devoted to the reconstruction of an unknown initial value from the terminal data. The asymptotic and root-distribution properties of Mittag-Leffler functions are used to establish stability of the backward problem.…
A blurring algorithm with linear time complexity can reduce the small-scale content of data observed at scattered locations in a spatially extended domain of arbitrary dimension. The method works by forming a Gaussian interpolant of the…