Recent content by kolmog

I have a known charge distribution defined on a grid (it is an electrostatics problem). The integral of the right hand side is zero because the system is neutrally charged.

Hello, With respect to the first question, this is a condition that has to be fulfilled. The equation is for sure discretized with a given approximation for the laplacian, the right hand side taking into account periodic boundary conditions. What I was asking, is that, a priori, multigrid...

Hello, When trying to solve Poisson equation with multigrid considering periodic boundary conditions (PBC) in all directions: \begin{equation}\nabla^2\phi=f\end{equation} where\begin{equation}f=-4\pi\rho\end{equation} I know that the integral over the volume should be equal to zero. That is...

Boundary conditions are periodic. They are easy to implement. With respect to 'Chestermiller' comment. I have also implemented the 2nd order discretization with similar results.

With respect to 'Strum' comment. I just use the values at x, x±hx, x±2hx, x±3hx (and the same for y and z) because I use the formula given in the article by Bernt Fornberg, that just uses the values at these positions for the derivatives of a function. If you wanted, you could have used another...

Yes I do. However, my question was related to the discretization of the equation.

I am going to solve it numerically. In fact, I think I have solved it but I am not sure if the discretization was properly done.

Hello, I am trying to solve the following differential equation in a tri-dimensional grid with grid spacing of hx , hy , and hz along the x, y, and z coordinates. \begin{equation}\nabla\cdot(\epsilon\nabla\phi)=-4\pi\rho\end{equation} Here, ε is a scalar quantity that is a function of x, y...

Hi, As I see that maybe not many people use this scheme to discretize differential equations, I would reword this post. I have discretized a differential equation (generalized Poisson equation) in a real space grid. If you take a look to the attached file, this is the first equation. The left...

Hi everybody, I need to discretize a differential equation. The grid that I am considering has a different grid spacing along the three space directions. That is, hx different than hy and hz. For that purpose, I would like to discretize the differential equation through the Mehrstellenverfahren...