相关论文: Fast and robust method for screened Poisson lattic…

Lattice Green's Functions (LGFs) are fundamental solutions to discretized linear operators, and as such they are a useful tool for solving discretized elliptic PDEs on domains that are unbounded in one or more directions. The majority of…

We solve the incompressible Navier-Stokes equations using a lattice Green's function (LGF) approach, including immersed boundaries (IB) and adaptive mesh refinement (AMR), for external flows with one homogeneous direction (e.g. infinite…

A new method is presented for solving Poisson's equation inside an open-ended rectangular pipe. The method uses Fast Fourier Transforms (FFTs) to perform mixed convolutions and correlations of the charge density with the Green function.…

We propose a mesh refinement technique for solving elliptic difference equations on unbounded domains based on the fast lattice Green's function (FLGF) method. The FLGF method exploits the regularity of the Cartesian mesh and uses the fast…

The first passage statistics of a continuous time random walker with Poisson distributed jumps on one and two dimensional infinite lattices is investigated. An exact expression for the probability of first return to the origin in one…

In geophysical fluid dynamics, the screened Poisson equation appears in the shallow-water, quasi geostrophic equations. Recently, many attempts have been made to solve those equations on the sphere using different numerical methods. These…

Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Green's function. The inversion of the force-constant matrix for the lattice Green's function requires Fourier techniques to project out the…

We derive formulas for the matrix elements of the lattice Green function for the discrete Poisson equation on an infinite square lattice. The partial difference equation for the matrix elements is solved by reducing it to a series of first…

Computing the atomic geometry of lattice defects--point defects, dislocations, crack tips, surfaces, or boundaries--requires an accurate coupling of the local strain field to the long-range elastic field. Periodic boundary conditions used…

We present a spectrally accurate, efficient FFT-based method for the three-dimensional free-space Poisson equation with smooth, compactly supported sources. The method adopts a super-potential formulation: we first compute the convolution…

We consider loop-erased random walk (LERW) running between two boundary points of a square grid approximation of a planar simply connected domain. The LERW Green's function is the probability that the LERW passes through a given edge in the…

We study the face-centered cubic lattice (fcc) in up to six dimensions. In particular, we are concerned with lattice Green's functions (LGF) and return probabilities. Computer algebra techniques, such as the method of creative telescoping,…

We build upon a recent theoretical breakthrough by employing novel algorithms to accurately compute the fractions $F_p$ of all closed walks on the infinite square lattice whose the last erased loop corresponds is any one of the $762, 207,…

The Fast Multipole Method (FMM) for the Poisson equation is extended to the case of non-axisymmetric problems in an axisymmetric domain, described by cylindrical coordinates. The method is based on a Fourier decomposition of the source into…

This paper develops a finite-difference analogue of the boundary integral/element method for the numerical solution of two-dimensional exterior scattering from scatterers of arbitrary shapes. The discrete fundamental solution, known as the…

Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic…

The lattice Green function, i.e., the resolvent of the discrete Laplace operator, is fundamental in probability theory and mathematical physics. We derive its long-distance behaviour via a detailed analysis of an integral representation…

The Green-function technique, termed the irreducible Green functions (IGF) method, that is a certain reformulation of the equation-of motion method for double-time temperature dependent Green functions is presented. This method was…

An efficient calculation method is proposed for the face centered cubic (FCC) lattice Green function. The method is based on binomial expansion theorems, which is provide us establish analytical formulae through simple basic integrals. The…

This is the second of two papers on the end-to-end distance of a weakly self-repelling walk on a four dimensional hierarchical lattice. It completes the proof that the expected value grows as a constant times \sqrt{T} log^{1/8}T (1+O((log…