Poisson's equation

Also found in: Wikipedia.

Poisson's equation

[pwä′sōnz i‚kwā·zhən]

(mathematics)

The partial differential equation which states that the Laplacian of an unknown function is equal to a given function.

Mentioned in ?

References in periodicals archive ?

Poisson's equation is a fundamental equation describing the spatial relationship between a certain electron density distribution and the corresponding electric field.

Variation Effect of Silicon Film Thickness on Electrical Properties of NANOMOSFET

Kang, "A boundary condition capturing method for Poisson's equation on irregular domains," Journal of Computational Physics, vol.

On Solving the Poisson Equation with Discontinuities on Irregular Interfaces: GFM and VIM

Given the matter density [rho](x, t), the dynamics of the gravitational field is being determined through Poisson's equation [[nabla].sup.2][phi] = ([kappa]/2)[rho].

Field Equations for Lovelock Gravity: An Alternative Route

To make the used plasma system equations ((1a), (1b), and (1c)) self-consistent, Poisson's equation is proceeded as

Plasma Parameters Effects on Dust Acoustic Solitary Waves in Dusty Plasmas of Four Components

Thus, the problem of solving (15) is reduced to the problem of solving the following Poisson's equation:

On Surface Completion and Image Inpainting by Biharmonic Functions: Numerical Aspects

We can write the divergence of Equation 4 as a form of Poisson's equation, giving

Realistic visual simulation of water effects in response to human motion using a depth camera

Poisson's equation is changed into Laplace's equation [[nabla.sup.2][phi] = 0.

Modeling of the Stepped Leader Initiation Process in an Altitude Triggered Lightning

In particular, applying normalized systems and Almansi expansions, Karachik studied solutions of some partial equations and some boundary value problems for Poisson's Equation (see [17,18]).

Dunkl-Poisson Equation and Related Equations in Superspace

This calculation leads to solving the Poisson's equation, which needs models of the source (brain activities) and the head.

FEM Method for the EEG Forward Problem and Improvement Based on Modification of the Saint Venant's Method

Finite difference approximation of Poisson's equation in polar irregular mesh is defined as

Numerical analysis of electric field in three-electrode corona system containing ionized and non-ionized areas

Sweet, "The Fourier and cyclic reduction methods for solving Poisson's equation," in Handbook of Fluid Dynamics and Fluid Machinery, J.

Simulation of fluid-structure and fluid-mediated structure-structure interactions in stokes regime using immersed boundary method

This equation is shown to lead to Poisson's equation for a newtonian gravitational potential in the next section.