| A FINITE DIFFERENCE SCHEME FOR SOLVING THE NONLINEAR POISSON-BOLTZMANN EQUATION MODELING CHARGED SPHERES |
| |
| 作者姓名： | Zhong-hua Qiao Zhi-lin Li Tao Tang |
| |
| 作者单位： | [1]Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China [2]Center for Research in Scientific Computation and Department of Mathematics North Carolina State University, Raleigh, NC 27695, USA |
| |
| 基金项目： | The research of the first author is supported by the Hong Kong Baptist University. The research of the second author is partially supported by a USA-AR0 grant 43751-MA and USA- NFS grants DMS0201094 and DMS-0412654. The third author is partially supported by CERG Grants of Hong Kong Research Grant Council, FRG grants of Hong Kong Baptist University, and an NSAF Grant （#10476032） of National Science Foundation of Chian. |
| |
| 摘 要： | In this work, we propose an efficient numerical method for computing the electrostaticinteraction between two like-charged spherical particles which is governed by the nonlinearPoisson-Boltzmann equation. The nonlinear problem is solved by a monotone iterativemethod which leads to a sequence of linearized equations. A modified central finite differ-ence scheme is developed to solve the linearized equations on an exterior irregular domainusing a uniform Cartesian grid. With uniform grids, the method is simple, and as aconsequence, multigrid solvers can be employed to speed up the convergence. Numericalexperiments on cases with two isolated spheres and two spheres confined in a chargedcylindrical pore are carried out using the proposed method. Our numerical schemes arefound efficient and the numerical results are found in good agreement with the previouspublished results.
|
| 关 键 词： | 非线性Poisson-Boltzmann方程 静电相互作用 单调迭代法 非线性问题 |
| 收稿时间： | 2006-03-01 |
| 修稿时间： | 2006-03-01 |
A FINITE DIFFERENCE SCHEME FOR SOLVING THE NONLINEAR POISSON-BOLTZMANN EQUATION MODELING CHARGED SPHERES |
| |
| Zhong-hua Qiao Zhi-lin Li Tao Tang.A FINITE DIFFERENCE SCHEME FOR SOLVING THE NONLINEAR POISSON-BOLTZMANN EQUATION MODELING CHARGED SPHERES[J].Journal of Computational Mathematics,2006,24(3):252-264. |
| |
| Authors: | Zhong-hua;Qiao;Zhi-lin;Li;Tao;Tang |
| |
| Abstract: | In this work, we propose an efficient numerical method for computing the electrostatic interaction between two like-charged spherical particles which is governed by the nonlinear Poisson-Boltzmann equation. The nonlinear problem is solved by a monotone iterative method which leads to a sequence of linearized equations. A modified central finite difference scheme is developed to solve the linearized equations on an exterior irregular domain using a uniform Cartesian grid. With uniform grids, the method is simple, and as a consequence, multigrid solvers can be employed to speed up the convergence. Numerical experiments on cases with two isolated spheres and two spheres confined in a charged cylindrical pore are carried out using the proposed method. Our numerical schemes are found efficient and the numerical results are found in good agreement with the previous published results. |
| |
| Keywords: | Nonlinear Poisson-Boltzmann equation Electrostatic interaction Irregulardomain Monotone iterative method Multigrid solver |
| 本文献已被 CNKI 维普 等数据库收录！ |
