Application of Sobolev gradient method to Poisson-Boltzmann system

Authors:
Abdul Majid;Sultan Sial
Affiliations:
Mathematics Department, Lahore University of Management Sciences, Opposite Sector U, DHA, Lahore Cantt., Pakistan;Mathematics Department, Lahore University of Management Sciences, Opposite Sector U, DHA, Lahore Cantt., Pakistan
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

The idea of a weighted Sobolev gradient, introduced and applied to singular differential equations in [1], is extended to a Poisson-Boltzmann system with discontinuous coefficients. The technique is demonstrated on fully nonlinear and linear forms of the Poisson- Boltzmann equation in one, two, and three dimensions in a finite difference setting. A comparison between the weighted gradient and FAS multigrid is given for large jump size in the coefficient function.