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Numerical solution of the nonlinear Poisson–Boltzmann equation: Developing more robust and efficient methods
Author(s) -
Holst Michael J.,
Saied Faisal
Publication year - 1995
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540160308
Subject(s) - multigrid method , nonlinear system , conjugate gradient method , discretization , relaxation (psychology) , mathematics , solver , numerical analysis , poisson's equation , computer science , partial differential equation , mathematical optimization , mathematical analysis , physics , psychology , social psychology , quantum mechanics
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. © 1995 by John Wiley & Sons, Inc.