Related papers: Fourier-based schemes with modified Green operator…
We consider the Green's functions associated to a scalar field propagating on a curved, ultra-static background, in the presence of modified dispersion relations. The usual proper-time deWitt-Schwinger procedure to obtain a series…
Photon echo schemes are excellent candidates for high efficiency coherent optical memory. They are capable of high-bandwidth multi-pulse storage, pulse resequencing and have been shown theoretically to be compatible with quantum information…
This paper provides a new analytical method to obtain Green's functions of linear dispersive partial differential equations. The Euler-Bernoulli beam equation and the one-dimensional heat conduction equation (dissipation equation) under…
Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for…
In this article we use linear algebra to improve the computational time for the obtaining of Green's functions of linear differential equations with reflection (DER). This is achieved by decomposing both the `reduced' equation (the ODE…
We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green's representation formula in…
We have developed a Green's function formalism to compute the local field distribution near an interface separating two media of different dielectric constants. The Maxwell's equations are converted into a surface integral equation; thus it…
We present an efficient implementation of coupled-cluster Green's function (CCGF) method for simulating photoemission spectra of periodic systems. We formulate the periodic CCGF approach with Brillouin zone sampling in Gaussian basis at the…
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of…
We present a super-high-efficiency approximate computing scheme for series sum and discrete Fourier transform. The summation of a series sum or a discrete Fourier transform is approximated by summing over part of the terms multiplied by…
The imaginary-time Green's function is a building block of various numerical methods for correlated electron systems. Recently, it was shown that a model-independent compact orthogonal representation of the Green's function can be…
In this letter, an approach to accelerate the matrix filling in method of moment (MOM) is presented. Based on the fact that the Green function is dependent on the Euclidean distance between the source and the observation points, we…
Calculating dynamical diffraction patterns for X-ray topography and similar x-ray scattering-imaging techniques require the numerical integration of the Takagi-Taupin equations. This is usually performed with a simple second order finite…
This paper introduces a fast algorithm, applicable throughout the electromagnetic spectrum, for the numerical solution of problems of scattering by periodic surfaces in two-dimensional space. The proposed algorithm remains highly accurate…
The Fourier analysis of the \emph{p}-multigrid acceleration technique is considered for a dual-time scheme applied to the advection-diffusion equation with various cycle configurations. It is found that improved convergence can be achieved…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…
We improve on Fourier transforms (FT) between imaginary time $\tau$ and imaginary frequency $\omega_n$ used in certain quantum cluster approaches using the Hirsch-Fye method. The asymptotic behavior of the electron Green's function can be…
The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate…
In this study, we address the challenge of obtaining a Green's function operator for linear partial differential equations (PDEs). The Green's function is well-sought after due to its ability to directly map inputs to solutions, bypassing…