Related papers: Green's function of the screened Poisson's equatio…
In present paper we suggest exact solution of the Poisson problem which appears in frequently addressed applications regarding calculation of the gravitational potential of spiral galaxies. We suggest an analytical solution for the problem…
A new method is presented to obtain a closed form of the generalized Green function to the Poisson and the Helmholtz equations on the $n$-dimensional unit sphere.
We study the steady state motion of incompressible and viscous fluid flow in a rotating reference frame where vortices may take place. An approximated analytic solution of the Stokes flow problem is proposed for situations where the…
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…
This paper presents a novel framework for enclosing solutions of Poisson's equation based on generalized sub- and super-solutions constructed using fundamental solutions. The conventional definition of sub- and super-solutions based on…
Quantifying the contribution of vortex structures to pressure stress is useful for designing flow control strategies to mitigate low or drag. The traditional force-element method focuses on the contribution of vortex structures to the…
Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green's function is difficult to compute. The troubles arise in the following…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
Potential flow has many applications, including the modelling of unsteady flows in aerodynamics. For these models to work efficiently, it is best to avoid Biot-Savart interactions. This work presents a grid-based treatment of potential…
This paper is a revised version of the original paper of same title--published in Applied Mathematics Letters 89--containing some corrections and clarifications to the original text. We derive non-singular Green's functions for the…
An efficient algorithm for solving Poisson's equation in two and three spatial dimensions is discussed. The algorithm, which is described in detail, is based on the integral form of Poisson's equation and utilizes spherical coordinates and…
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…
In this work we present a three step procedure for generating a closed form expression of the Green's function on both closed and open finite quantum graphs with general self-adjoint matching conditions. We first generalize and simplify the…
A Green's function based solver for the modified Bessel equation has been developed with the primary motivation of solving the Poisson equation in cylindrical geometries. The method is implemented using a Discrete Hankel Transform and a…
We present a method of solving partial differential equations on the $n$-dimensional unit sphere using methods based on the continuous wavelet transform derived from approximate identities. We give an explicit analytical solution to the…
In the present work we discuss how to address the solution of electrostatic problems, in professional cycle, using Green's functions and the Poisson's equation. By using this procedure, it was possible to verify its relation with the method…
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…
Spectral methods are well suited for solving hydrodynamic problems in which the self-gravity of the flow needs to be considered. Because Poisson's equation is linear, the numerical solution for the gravitational potential for each…
Unique transformation properties under the hyperspherical inversion of a partial differential equation describing a stationary scalar wave in an $N$-dimensional ($N\geqslant2$) Maxwell fish-eye medium are exploited to construct a closed…
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…