Poisson equation Definition and 63 Threads

Homework Statement Hi, I am looking for a hint, how to solve the following Dirichlet problem. All the standard textbooks have only examples for Dirichlet problems in rectangular or polar coordinate systems, but this problem is defined for a parabolic region. Homework Equations uxx+uyy=2...

Hello I am trying to build a 3D Poisson solver using method of moments. I need to find out the Green's function for the system. My system is a rectangular box and boundary conditions are as follows: On all surfaces BC is neumann. Only on the upper and lower surface, the middle 1/3 region...

Hi I am working with MOSFETs and in this context I am trying to solve poissons equation inside a MOSFET. Only in the direction from the gate through the oxide and into the silicon. I know the analytic solution but now I want solve Poissons equation with the use of finite difference...

Am just playing around, and following examples of Fourier transform solutions of the heat equation, tried the same thing for the electrostatics Poisson equation \nabla^2 \phi &= -\rho/\epsilon_0 \\ With Fourier transform pairs \begin{align*} \hat{f}(\mathbf{k}) &= \frac{1}{(\sqrt{2\pi})^3}...

Hello everybody I've been searching this today but I am a bit lost now. I've encountered two forms of Gauss law in its differential form, Poisson equation : del2V(r) = -p(r)/e del2V(r) = -4*pi*p(r)/e where V:e.potential, p:charge density, e:permivity Now, what's the difference...

Hi Homework Statement Verify, that u(\vec{x}) := - \frac{1}{2 \pi} \int \limits_{\mathbb{R}^2} \log ||\vec{x} - \vec{y} || f(\vec{y}) d \vec{y} is the general solution of the 2 dimensional Poisson equation: \Delta u = - f where f \in C^2_c(\mathbb{R}^2) is...

In many book I read, problems for electrostatic potential always lead to solving Poisson equation. I saw a problem about a spherical shell carrying some amount of charges uniformly on the surface with density \rho, and then someone put a small patch on the sphere. The patch is then made a...

Hi everyone, I have been trying to solve both laplace and poisson equation using method of separation of variable but is giving me a hard time. Pls can anyone refer me to any textbook that solve this problem in great detail? Thanks

Suppose \phi is a scalar function: R^n\to R, and it satisfies the Poisson equation: \nabla^2 \phi=-\dfrac{\rho}{\varepsilon_0} Now I want to calculate the following integral: \int \phi \nabla^2 \phi \,dV So using Greens first identity I get: \int \phi \nabla^2 \phi \,dV = \oint_S \phi...

For a magnetostatics problem I seek the solution to the following equation \frac{1}{x}\frac{d}{dx} \left( x \frac{dy(x)}{dx} \right) = -C^2 y(x) (C a real constant) or equivalently x \frac{d^2 y(x)}{dx^2} + \frac{dy(x)}{dx} + C^2 x y(x)=0 It seems so simple, but finding a...

Homework Statement numerical solution of poisson equation with application to the pumping of water from drains 1. time 2. Amount of water has been pumped Homework Equations The poisson equation The Attempt at a Solution 1. I know i have to use iteration 2. I am still...

Homework Statement Consider a 1D sample, such that for x < xb the semiconductor has a dielectric constant \varepsilon_{1}, and for x > xb has a dielectric constant \varepsilon_{2}. At the interface between the two semiconductor matierials (x = xb) there are no interface charges. Starting...

1. Of what type is Poisson’s equation uxx + uyy = f(x,y) ? I used that if you have auxx+buxy+cuyy+dux+euy +fu+g=0 where a, b, c, d, e, f, g is constants, and if b^2-4ac<0 then you get an elliptic type because b=0, a=1, c=1 gives 0^2-4*1*1=-4<0 => elliptic Is this right? And why...