Related papers: A Windowed Green Function method for elastic scatt…
A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate,…
Green's functions characterize the fundamental solutions of partial differential equations; they are essential for tasks ranging from shape analysis to physical simulation, yet they remain computationally prohibitive to evaluate on…
The fractional diffraction optics theory has been elaborated using the Green function technique. The optics-fractional equation describing the diffraction X-ray scattering by imperfect crystals has been derived as the fractional matrix…
The Wigner function formalism has been applied to the analysis of elastic scattering processes. The new element of known formalism is the choice of the phase space on which the Wigner function is defined. This phase space is 4-dimensional…
The pointwise space-time behaviors of the Green's function and the global solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system in spatial three dimension are studied in this paper. It is shown that the Green's function consists of the…
Fast and high-order accurate algorithms for three dimensional elastic scattering are of great importance when modeling physical phenomena in mechanics, seismic imaging, and many other fields of applied science. In this paper, we develop a…
During the past three years, Wapenaar, Snieder, Broggini and others have developed an algorithm to compute the Green's function for any point inside a medium to points on the surface from measurements on that surface only. Their algorithm…
The nonequilibrium Green's function (NEGF) method is often used to predict transport in atomistically resolved nanodevices and yields an immense numerical load when inelastic scattering on phonons is included. To ease this load, this work…
This manuscript presents an efficient boundary integral equation technique for solving two-dimensional Helmholtz problems defined in the half-plane bounded by an infinite, periodic curve with Neumann boundary conditions and an aperiodic…
This paper presents an arbitrary order locking-free numerical scheme for linear elasticity on general polygonal/polyhedral partitions by using weak Galerkin (WG) finite element methods. Like other WG methods, the key idea for the linear…
We present a novel methodology for the numerical solution of problems of diffraction by infinitely thin screens in three dimensional space. Our approach relies on new integral formulations as well as associated high-order quadrature rules.…
We present a numerically efficient technique to evaluate the Green's function for extended two dimensional systems without relying on periodic boundary conditions. Different regions of interest, or `patches', are connected using self energy…
In this paper, a new inversion model for 2D microwave imaging is introduced by means of a convenient rewriting of the usual Lippmann Schwinger integral scattering equation. Such model is derived by decomposing the Greens function and the…
We present a spectrally accurate fast algorithm for evaluating the solution to the scalar wave equation in free space driven by a large collection of point sources in a bounded domain. With $M$ sources temporally discretized by $N_t$ time…
We present an efficient implementation of a surface Green's-function method for atomistic modeling of surfaces within the framework of density functional theory using a pseudopotential localized basis set approach. In this method, the…
We report a linear-scaling random Green's function (rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states to stochastically express the density matrix, and rGF is…
The scattering of a wave obeying Helmholtz equation by an elliptic obstacle can be described exactly using series of Mathieu functions. This situation is relevant in optics, quantum mechanics and fluid dynamics. We focus on the case when…
Single-particle resonances are crucial for exotic nuclei near and beyond the drip lines. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold becomes very important and can lead…
This paper concerns the numerical simulation of time domain inverse acoustic scattering problems with a point-like scatterer, multiple point-like scatterers or normal size scatterers. Based on the Green's function and the application of the…
We introduce a new class of computationally tractable scattering problems in unbounded domains, which we call decomposable problems. In these decomposable problems, the computational domain can be split into a finite collection of…