I was wondering if anybody can recommend an easy-to-use library/program to solve the 3D Poisson equation $\nabla^2 V(r,\theta,\phi) = \rho(r,\theta,\phi)$ with vanishing solutions at infinity:

$$V(r,\theta,\phi) = \int d^3\mathbf{r}'\frac{\rho(\mathbf{r}')}{|\mathbf{r}-\mathbf{r}'|},$$

where $\mathbf{r} \rightarrow (r,\theta,\phi)$. Here $\rho$ is a discrete + continuous charge density. The intended application is to calculate the electrostatic potential of a model polyatomic molecule composed of static, point-like nuclear charges and an arbitrary continuous electron density.

This question is a follow up to: 3D Poisson equation solver for arbitrary charge distribution? , which remains unanswered.

I am looking for a library, which is straightforward to use and which does not invoke the multipole expansion. There are plenty of solvers available on the market. I am familiar with three:

  1. The Fenics project (finite element methods)
  2. The 'multipoles' python library (solutions in the form of the multipole expansion)
  3. COMSOL Multiphysics (not a freeware, finite elements),

but if anybody has a good experience with some other library (ideally in python or Fortran), sharing this experience here would be appreciated. The widely used J. Burkardt's libraries do not seem to contain such a solver routine.

Ideally, I wish to define the charge distribution $\rho$ (on a grid or analytically) and receive the value of the potential $V$ at any point $(r,\theta,\phi)$, without too much hustle.

  • 2
    $\begingroup$ I'm sorry this question hasn't seemed to get a lot of attention. While its certainly on-topic for this site, you may have better luck on the Computational Science SE. $\endgroup$
    – Tyberius
    Nov 10, 2021 at 19:35
  • 3
    $\begingroup$ In what functional form is the continuous part of $\rho$ given? There are dedicated solvers for the special cases where $\rho$ is given as (apart from a finite number of point charges) a linear combination of Gaussian functions or Slater functions. If you are interested in an algorithm that is applicable to $\rho$ given by an arbitrary formula, then these solvers would have to be ruled out $\endgroup$
    – wzkchem5
    Feb 7, 2022 at 12:49
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    $\begingroup$ I haven't looked thoroughly, but there's always APBS: poissonboltzmann.org $\endgroup$ Feb 8, 2022 at 20:45
  • $\begingroup$ Emil, how are you doing with this now? Were the comments by Geoff and wzkchem5 helpful? $\endgroup$ Feb 24, 2022 at 3:36
  • $\begingroup$ This question has been closed as it seems to be abandoned. It can be reopened if someone wants to add an answer or the OP addresses questions/suggestions in the comments. $\endgroup$
    – Tyberius
    Feb 24, 2022 at 14:27