期刊
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
卷 16, 期 2, 页码 491-515出版社
GLOBAL SCIENCE PRESS
DOI: 10.4208/cicp.270713.280214a
关键词
Poisson-Boltzmann equation; nonlinear; existence; uniqueness; DDG methods; numerical flux
资金
- NSFC Project [11201397]
- Hunan Education Department Project [12B127]
- Hunan Provincial Innovation Foundation for Postgraduate [CX2012B272]
- NSFC Key Project [11031006]
- PCSIRT [IRT1179]
- ISTCP of China [2010DFR00700]
- National Science Foundation [DM509-07963, DMS13-12636]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1312636] Funding Source: National Science Foundation
An iterative discontinuous Galerkin (DG) method is proposed to solve the nonlinear Poisson Boltzmann (PB) equation. We first identify a function space in which the solution of the nonlinear PB equation is iteratively approximated through a series of linear PB equations, while an appropriate initial guess and a suitable iterative parameter are selected so that the solutions of linear PB equations are monotone within the identified solution space. For the spatial discretization we apply the direct discontinuous Galerkin method to those linear PB equations. More precisely, we use one initial guess when the Debye parameter lambda = 0(1), and a special initial guess for lambda <1 to ensure convergence. The iterative parameter is carefully chosen to guarantee the existence, uniqueness, and convergence of the iteration. In particular, iteration steps can be reduced for a variable iterative parameter. Both one and two-dimensional numerical results are carried out to demonstrate both accuracy and capacity of the iterative DG method for both cases of lambda = 0(1) and lambda 1. The (m +1)th order of accuracy for L2 and mth order of accuracy for HI- for Pm elements are numerically obtained.
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