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I was wondering if anybody can recommend an easy-to-use library/program to solve the 3D Poisson equation $\Delta V(r,\theta,\phi) = \rho(r,\theta,\phi)$ 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 is 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.

Best wishes,

Emil

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