NUMERICAL-SOLUTION OF THE NONLINEAR POISSON-BOLTZMANN EQUATION - DEVELOPING MORE ROBUST AND EFFICIENT METHODS
NUMERICAL-SOLUTION OF THE NONLINEAR POISSON-BOLTZMANN EQUATION - DEVELOPING MORE ROBUST AND EFFICIENT METHODS
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DOI：
10.1002/jcc.540160308
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发表时间：
1995-03-01
影响因子：
3
通讯作者：
SAIED, F
中科院分区：
文献类型：
--
作者：
HOLST, MJ;SAIED, F
本文给出了分子生物物理学中非线性泊松-玻尔兹曼方程的一种鲁棒、高效的数值求解方法。该方程用盒法离散化，离散方程的解用全局非精确牛顿法，结合我们在本杂志先前发表的一篇文章中描述的线性多层技术来完成。对所得方法进行了详细的分析，并与文献中提出的其他方法进行了比较，包括经典的非线性多网格法、非线性共轭梯度法和非线性松弛法，如连续过松弛法。理论和数值证据都表明，这种方法在分子的情况下是收敛的，而许多现有的方法都不能。此外，对于其他方法能够解决的问题，数值实验表明，新方法的效率大大提高，并且该方法的优越性随着问题规模的增加而增强。一旦有了线性多层求解器，该方法就很容易实现，并且可以很容易地与除多重网格之外的线性方法结合使用。(C) 1995年，John Wiley & Sons, Inc。
We present a robust and efficient numerical method for solution of the nonlinear Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the box method, and solution of the discrete equations is accomplished with a global inexact-Newton method, combined with linear multilevel techniques we have described in an article appearing previously in this journal. A detailed analysis of the resulting method is presented, with comparisons to other methods that have been proposed in the literature, including the classical nonlinear multigrid method, the nonlinear conjugate gradient method, and nonlinear relaxation methods such as successive overrelaxation. Both theoretical and numerical evidence suggests that this method will converge in the case of molecules for which many of the existing methods will not. In addition, for problems which the other methods are able to solve, numerical experiments show that the new method is substantially more efficient, and the superiority of this method grows with the problem size. The method is easy to implement once a linear multilevel solver is available and can also easily be used in conjunction with linear methods other than multigrid. (C) 1995 by John Wiley & Sons, Inc.