相关论文: Lattice Green function for extended defect calcula…

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…

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…

Flexible boundary condition methods couple an isolated defect to a harmonically responding medium through the bulk lattice Green's function; in the case of an interface, interfacial lattice Green's functions. We present a method to compute…

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…

In this Brief Report, we present an algorithm for calculating the elastic Lattice Greens Function of a regular lattice, in which defects are created by removing lattice points. The method is computationally efficient, since the required…

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 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…

Localised defect modes generated by a finite line defect composed of several masses, embedded an infinite square cell lattice, are analysed using the linear superposition of Green's function for a single mass defect. Several representations…

We present a novel efficient implementation of the flexible boundary condition (FBC) method, initially proposed by Sinclair et al., for large single-periodic problems. Efficiency is primarily achieved by constructing a hierarchical matrix…

Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…

Many material properties can be traced back to properties of their grain boundaries. Grain boundary energy (GBE), as a result, is a key quantity of interest in the analysis and modeling of microstructure. A standard method for calculating…

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…

A first order differential equation of Green's Function, at the origin G(0), for the one- dimensional lattice is derived by simple recurrence relation. Green's Function at site (m)is then calculated in terms of G(0). A simple recurrence…

The Fast Multipole Method (FMM) obeys periodic boundary conditions "natively" if it uses a periodic Green function for computing the multipole expansion in the interaction zone of each FMM oct-tree node. One can define the "optimal" Green…

We use DFT to compute core structures of $a_0[100](010)$ edge, $a_0[100](011)$ edge, $a_0/2[\bar{1}\bar{1}1](1\bar{1}0)$ edge, and $a_0/2[111](1\bar{1}0)$ $71^{\circ}$ mixed dislocations in bcc Fe. The calculations use flexible boundary…

We study the lattice Green's function (LGF) of the screened Poisson equation on a two-dimensional rectangular lattice. This LGF arises in numerical analysis, random walks, solid-state physics, and other fields. Its defining characteristic…

We present an unfitted boundary algebraic equation (BAE) method for solving elliptic partial differential equations in complex geometries. The method employs lattice Green's functions on infinite regular grids combined with discrete…

We investigate boundary estimates for elliptic operators with stationary random coefficients exhibiting integrable correlations, arising from stochastic homogenization theory. As practical applications, we establish decay estimates for…

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,…