Application of Sobolev gradient method to Poisson-Boltzmann system. (English) Zbl 1194.82105

Summary: The idea of a weighted Sobolev gradient, introduced and applied to singular differential equations, 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.


82D37 Statistical mechanics of semiconductors
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65F08 Preconditioners for iterative methods
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