Related papers: Poisson solvers for self-consistent multi-particle…
In high-temperature plasma physics, a strong magnetic field is usually used to confine charged particles. Therefore, for studying the classical mathematical models of the physical problems it is needed to consider the effect of external…
Simulation of plasmas in electromagnetic fields requires numerical solution of a kinetic equation that describes the time evolution of the particle distribution function. In this paper we propose a finite volume scheme based on integral…
We describe and implement an adaptive particle-mesh algorithm to solve the Poisson equation for grid-based hydrodynamics codes with nested grids. The algorithm is implemented and extensively tested within the astrophysical code Enzo against…
We propose a spectral solver for the Poisson equation on a square domain, achieving optimal complexity through the ultraspherical spectral method and the alternating direction implicit (ADI) method. Compared with the state-of-the-art…
We have developed an adaptive multigrid code for solving the Poisson equation in gravitational simulations. Finer rectangular subgrids are adaptively created in locations where the density exceeds a local level-dependent threshold. We…
Bertaut's equivalent electric density idea (E. F. Bertaut, Journal de Physique {\bf 39}, 1331 (1978)) is applied to the case of two dimensional periodic continuous charge density distributions. The following derivation differs from what was…
We present an algorithm for generating Poisson-disc patterns taking O(N) time to generate $N$ points. The method is based on a grid of regions which can contain no more than one point in the final pattern, and uses an explicit model of…
In this paper, Particle-in-Cell algorithms for the Vlasov-Poisson system are presented based on its Poisson bracket structure. The Poisson equation is solved by finite element methods, in which the appropriate finite element spaces are…
In this paper, the application of quantum computing (QC) in solving gate insulator Poisson equation is studied, through QC simulator and hardware in IBM. Various gate insulator stacks with and without fixed charges are studied. It is found…
This review discusses progress in efficient solvers which have as their foundation a representation in real space, either through finite-difference or finite-element formulations. The relationship of real-space approaches to linear-scaling…
We present a simple and effective multigrid-based Poisson solver of second-order accuracy in both gravitational potential and forces in terms of the one, two and infinity norms. The method is especially suitable for numerical simulations…
This work discusses the main analogies and differences between the deterministic approach underlying most cosmological N-body simulations and the probabilistic interpretation of the problem that is often considered in mathematics and…
The self-consistent quantum-electrostatic (also known as Poisson-Schr\"odinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low temperatures, these fluctuations make the problem…
Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…
For problems in astrophysics, planetary science and beyond, numerical simulations are often limited to simulating fewer particles than in the real system. To model collisions, the simulated particles (aka superparticles) need to be inflated…
This paper proposes a novel Machine Learning-based approach to solve a Poisson problem with mixed boundary conditions. Leveraging Graph Neural Networks, we develop a model able to process unstructured grids with the advantage of enforcing…
This work delves into solving the two dimensional Poisson problem through the Finite Element Method which is relevant in various physical scenarios including heat conduction, electrostatics, gravity potential, and fluid dynamics. However,…
Partial differential equations (PDE) on manifolds arise in many areas, including mathematics and many applied fields. Among all kinds of PDEs, the Poisson-type equations including the standard Poisson equation and the related eigenproblem…
The Poisson compound decision problem is a long-standing problem in statistics, where empirical Bayes methodologies are commonly used to estimate Poisson's means in static or batch domains. In this paper, we study the Poisson compound…
The Poisson-Fermi model is an extension of the classical Poisson-Boltzmann model to include the steric and correlation effects of ions and water treated as nonuniform spheres in aqueous solutions. Poisson-Boltzmann electrostatic…