  This paper presents an efficient finite element iterative method for solving
a nonuniform size-modified Poisson-Nernst-Planck ion channel (SMPNPIC) model,
along with a SMPNPIC program package that works for an ion channel protein with
a three-dimensional crystallographic structure and an ionic solvent with
multiple ionic species. In particular, the SMPNPIC model is constructed and
then reformulated by novel mathematical techniques so that each iteration of
the method only involves linear boundary value problems and nonlinear algebraic
systems, circumventing the numerical difficulties caused by the strong
nonlinearities, strong asymmetries, and strong differential equation coupling
of the SMPNPIC model. To further improve the method's efficiency, an efficient
modified Newton iterative method is adapted to the numerical solution of each
related nonlinear algebraic system. Numerical results for a voltage-dependent
anion channel (VDAC) and a mixture solution of four ionic species demonstrate
the method's convergence, the package's high performance, and the importance of
considering nonuniform ion size effects. They also partially validate the
SMPNPIC model by the anion selectivity property of VDAC.
