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Context. The potential field source surface model is frequently used as abasis for further scientific investigations where a comprehensive coronalmagnetic field is of importance. Its parameters, especially the position andshape of the source surface, are crucial for the interpretation of the state ofthe interplanetary medium. Improvements have been suggested that introduce oneor more additional free parameters to the model, for example, the current sheetsource surface (CSSS) model.  Aims. Relaxing the spherical constraint of the source surface and allowing itto be elliptical gives modelers the option of deforming it to more accuratelymatch the physical environment of the specific period or location to beanalyzed.  Methods. A numerical solver is presented that solves Laplace's equation on athree-dimensional grid using finite differences. The solver is capable ofworking on structured spherical grids that can be deformed to create ellipticalsource surfaces.  Results. The configurations of the coronal magnetic field are presented usingthis new solver. Three-dimensional renderings are complemented byCarrington-like synoptic maps of the magnetic configuration at differentheights in the solar corona. Differences in the magnetic configuration computedby the spherical and elliptical models are illustrated.

An elliptic expansion of the potential field source surface model