Abstract
The Poisson-Nernst-Planck (PNP) model is a basic continuum model for simulating ionic flows in an open ion channel. It is one of commonly used models in theoretical and computational. The Poisson equation is derived from Coulomb's law in electrostatics and Gauss's theorem in calculus. The Nernst-Planck equation is equivalent to the convection-diffussion model. Many computation methods have been constructed for the solution of the PNP equations. However, we want to simplify the second order solver of proposed in the literature [24] but, we must to deal with some problems. For example, singular charges, nonlinear coupling and interface. First, we apply the decomposition method [5] proposed by Chern, Liu,and Wang to cope with the singular charges. Second, the matched interface and boundary (MIB) method [24] is used for the interface problem. Third, The initial guess are given by Poisson Boltzmann (PB) equation and two iterative schemes are utilized to deal with the coupled nonlinear equations. Finally, the real data of Gramicidin A (GA) channel protein is obtained from the protein data bank (PDB).
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