  The Poisson-Fermi model is an extension of the classical Poisson-Boltzmann
model to include the steric and correlation effects of ions and water treated
as nonuniform spheres in aqueous solutions. Poisson-Boltzmann electrostatic
calculations are essential but computationally very demanding for molecular
dynamics or continuum simulations of complex systems in molecular biophysics
and electrochemistry. The graphic processing unit (GPU) with enormous
arithmetic capability and streaming memory bandwidth is now a powerful engine
for scientific as well as industrial computing. We propose two parallel GPU
algorithms, one for linear solver and the other for nonlinear solver, for
solving the Poisson-Fermi equation approximated by the standard finite
difference method in 3D to study biological ion channels with crystallized
structures from the Protein Data Bank, for example. Numerical methods for both
linear and nonlinear solvers in the parallel algorithms are given in detail to
illustrate the salient features of the CUDA (compute unified device
architecture) software platform of GPU in implementation. It is shown that the
parallel algorithms on GPU over the sequential algorithms on CPU (central
processing unit) can achieve 22.8x and 16.9x speedups for the linear solver
time and total runtime, respectively.
