Dr. Ruigang Shen, (ICMSEC, AMSS)

A class of finite element methods with averaging techniques for solving size-modified Poisson-Nernst-Planck equations for simulating biomolecular and ion flow through a channel

9 月 15 日（周三） 下午 16:00-17:00 数学院南楼 202 教室

 In this talk, we introduce a new class of finite element methods with averaging techniques for solving size-modified Poisson-Nernst-Planck equations (SMPNPE). Comparing with the classical Poisson-Nernst-Planck equations (PNPE), the SMPNP model adds a nonlinear term to each of the NPfluxes to model the steric repulsion which can able to treat multiple nonuniform particle sizes in simulations. Since the new term coupling the concentrations, the summing of the concentrations and its gradients, the strong coupling nonlinearity of the SMPNPE is much stronger than that of PNP equations. In our talk, we first briefly introduce the model and the singular decomposition of the permanent charges for Poisson equation. By generalized Slotboom transportation, the SM-NPE changes into a new reformulation with the normal concentration variables, then the Inverse Edge Averaging FE techniques is used to deal with the exponential coefficients of the reformulated formulations. Comparing with previous stabilization methods, our finite element discretization scheme is more concise and easier to implement numerically. Numerical experiments including a model problem with exact solutions is presented to numerically verify the accuracy and order of the new schemes (IEAFE) for SMPNPE. The study on size-effects for both the sphere model for simulating biomolecules and ion channel system are presented which show that the IEAFEM is more effective and robust than the traditional FEM. 

欢迎大家参加！