Solving the 3D Poisson equation

[debilo]

TL;DR

I try to solve 3D Poisson equation with boundaries condition at infinity.

Hello !

I want to solve the 3D Poisson equation using spherical coordinates and spherical harmonics.
First I must solve this : $d^2\phi/dr^2 + 1/rd\phi/dr - l*(l+1)/r^2 = \rho (r)$ with $\phi (\infty ) = 0$ (here $\phi$ is the gravitationnal potential and $\rho$ is the mass density).
To deal with the infinite grid I tried to use the hyperbolic transformation $r = X*arctanh(R)$ with $X$ a constant and $R$ between 0 and 1.
I use a LU-decomposition method to solve this. For $\phi (0)$ I apply symmetrical conditions.
I tried to solve the problem in the case of a spherical mass distribution. I compared the calculated potential with the theoretical potential.
I find a pretty good result when I fix the value in rmax.
But for $\phi (\infty )$ I have a problem. In fact I obviously get in trouble when I let R go to 1 (or 0) ; so I take $Rmin = 0+\varepsilon$ and $Rmax = 1-\varepsilon$.

My question is : do you know a trick to really set the value of the potential to zero at infinity ?

 

[debilo]

I finally found a solution it's ok !

 

[jedishrfu]

Are you going to post it here? I'm sure others would be interested and they may see something you can to make it even better.

 

[Fleurpink]

I finally found a solution it's ok !

Hi, can you please post the solution?