An efficient finite element iterative method for solving a nonuniform size modified Poisson-Boltzmann ion channel model

In this paper, a nonuniform size modified Poisson-Boltzmann ion channel (nuSMPBIC) model is presented as nonlinear system of an electrostatic potential and multiple ionic concentrations. It mixes algebraic equations with Poisson boundary value problem involving Dirichlet-Neumann mixed conditions membrane surface charge density to reflect the effects sizes charges on electrostatics To overcome difficulties strong singularities exponential nonlinearities, it split into three submodels solution Model 1 collecting all singular points Models 2 3 much easier solve numerically than original nuSMPBIC model. A damped two-block iterative method then 3, along novel Newton scheme for solving each related system. end, effective finite element solver derived implemented program package that works protein three-dimensional molecular structure mixture species. Numerical results voltage-dependent anion (VDAC) in four species demonstrate fast convergence rate method, high performance software package, importance considering sizes. Moreover, validated by selectivity property VDAC.