  Context. The potential field source surface model is frequently used as a
basis for further scientific investigations where a comprehensive coronal
magnetic field is of importance. Its parameters, especially the position and
shape of the source surface, are crucial for the interpretation of the state of
the interplanetary medium. Improvements have been suggested that introduce one
or more additional free parameters to the model, for example, the current sheet
source surface (CSSS) model.
  Aims. Relaxing the spherical constraint of the source surface and allowing it
to be elliptical gives modelers the option of deforming it to more accurately
match the physical environment of the specific period or location to be
analyzed.
  Methods. A numerical solver is presented that solves Laplace's equation on a
three-dimensional grid using finite differences. The solver is capable of
working on structured spherical grids that can be deformed to create elliptical
source surfaces.
  Results. The configurations of the coronal magnetic field are presented using
this new solver. Three-dimensional renderings are complemented by
Carrington-like synoptic maps of the magnetic configuration at different
heights in the solar corona. Differences in the magnetic configuration computed
by the spherical and elliptical models are illustrated.
