Research On EXCMG Method For Solving Nonliner Poisson-Boltzmann Equation

The nonlinear Poisson-Boltzmann equation(PB)is widely used in physics,chemistry and biology.The nonlinear Poisson-Boltzmann electrostatic model is an important tool for plasma research in physics.Therefore,solving the nonlinear Poisson-Boltzmann equation is also very important.This paper studies extrapolation cascadic multigrid method(Extrapolated cascadic multigrid method,EXCMG)for solving nonlinear Poisson-Boltzmann equation.First two grid for solving finite element discretization were the most coarse,then this two grid finite element solution according to the new extrap-olation operator and two interpolation provides a layer of iterative initial value the encryption of the grid,the linearization of the original problem,accord-ing to the multilevel linearization method,equations by extrapolation cascadic multigrid method for solving a series of linearized equations.In this paper,we prove the optimal convergence of the extrapolation cas-cadic multigrid method in the sense of energy norm,and analyze the compu-tational effort of the algorithm when the parameter of the nonlinear Poisson-Boltzmann equation is ? = 1.The numerical test termination conditions in two different iterations re-spectively,namely accuracy control and iterative step control,the nonlinear Poisson-Boltzmann equation is discussed.The cases of ?= 1,0.25,0.1,0.01 are calculated and analyzed.The numerical results show that the 2 order convergence can be reached in the sense of discrete L2 norm,and is 1 order convergence under the energy norm.Both of them can guarantee the best convergence,The numerical results confirm the theoretical analysis.