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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.

MSC:

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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