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,



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.