Application of Sobolev gradient method to Poisson–Boltzmann system

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.