CRPC-TR94447

Title:    A Robust and Efficient Numerical Method
          for Nonlinear Protein Modeling Equations

Authors:  Michael Holst

Date:     May 1994

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Keywords (list up to 8):

   Poisson-Boltzmann, Inexact-Newton, Multigrid, 
   Rapid Nonlinearities, Discontinuities.

Abstract:

      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 a previous paper.  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 SOR.  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 this method is substantially more efficient, and 
   the superiority of this method grows with the problem size.  The method is 
   very easy to implement once a linear multilevel solver is available, and 
   can also easily be used in conjuction with linear methods other than 
   multigrid.

Publication History:

   Submitted to:  Journal of Computational Chemistry

   Published in: