Related papers: Immediate Calculation of some Poisson Type Integra…
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…
Self-consistent multi-particle simulation plays an important role in studying beam-beam effects and space charge effects in high-intensity beams. The Poisson equation has to be solved at each time-step based on the particle density…
We present a novel approach to Gaussian Berezin correlation functions. A formula well known in the literature expresses these quantities in terms of submatrices of the inverse matrix appearing in the Gaussian action. By using a recently…
The aim of this article is to present two different primal-dual methods for solving structured monotone inclusions involving parallel sums of compositions of maximally monotone operators with linear bounded operators. By employing some…
We recall the question of geometric integrators in the context of Poisson geometry, and explain their construction. These Poisson integrators are tested in some mechanical examples. Their properties are illustrated numerically and they are…
In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
Pulling back sets of functions in involution by Poisson mappings and adding Casimir functions during the process allows to construct completely integrable systems. Some examples are investigated in detail.
In this paper we propose two different primal-dual splitting algorithms for solving inclusions involving mixtures of composite and parallel-sum type monotone operators which rely on an inexact Douglas-Rachford splitting method, however…
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…
In this paper, we present two feasible and efficient methods to numerically solve the quark's Dyson-Schwinger (qDSE), the qDSE is mathematical systems of nonlinear integral equations of the second kind with high degrees of freedom. It is…
Inspired by the Galerkin and particular method, a new approximation approach is recalled in the Cartesian case. In this paper, we are interested specially by constructing this method, when the domain of consideration is a two dimensional…
We demonstrate how path integrals often used in problems of theoretical physics can be adapted to provide a machinery for performing Bayesian inference in function spaces. Such inference comes about naturally in the study of inverse…
In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation has a stronger non-local feature and is not the dual of any PDE. We obtain the existence of…
The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, the Christoffel-Darboux-type bilinear generating function and their asymptotic expressions, we obtain quadrature formulas for integral transforms…
For the finite element solution of Poisson's equation, a local a posteriori error estimation based on the Hypercircle method is proposed. Even for the solution of Poisson's equation without the $H^2$ regularity, this method can provide…
A short pedagogical introduction to a differential method used to calculate multi-loop scalar integrals is presented. As an example it is shown how to obtain, using the method, large mass expansion of the two loop sunrise master integrals.
The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form.