TY - JOUR
T1 - Finite element approximation to a finite-size modified poisson-boltzmann equation
AU - Chaudhry, Jehanzeb Hameed
AU - Bond, Stephen D.
AU - Olson, Luke N.
N1 - Funding Information:
Research of J.H. Chaudhry was supported by the University of Illinois Computational Science and Engineering Fellowship Program. Research of S.D. Bond was supported in part by NSF-CCF 08-30578. Research of L.N. Olson was supported in part by NSF-DMS 07-46676.
PY - 2011/6
Y1 - 2011/6
N2 - The inclusion of steric effects is important when determining the electrostatic potential near a solute surface. We consider a modified form of the Poisson-Boltzmann equation, often called the Poisson-Bikerman equation, in order to model these effects. The modifications lead to bounded ionic concentration profiles and are consistent with the Poisson- Boltzmann equation in the limit of zero-size ions. Moreover, the modified equation fits well into existing finite element frameworks for the Poisson-Boltzmann equation. In this paper, we advocate a wider use of the modified equation and establish well-posedness of the weak problem along with convergence of an associated finite element formulation.We also examine several practical considerations such as conditioning of the linearized form of the nonlinear modified Poisson-Boltzmann equation, implications in numerical evaluation of the modified form, and utility of the modified equation in the context of the classical Poisson- Boltzmann equation.
AB - The inclusion of steric effects is important when determining the electrostatic potential near a solute surface. We consider a modified form of the Poisson-Boltzmann equation, often called the Poisson-Bikerman equation, in order to model these effects. The modifications lead to bounded ionic concentration profiles and are consistent with the Poisson- Boltzmann equation in the limit of zero-size ions. Moreover, the modified equation fits well into existing finite element frameworks for the Poisson-Boltzmann equation. In this paper, we advocate a wider use of the modified equation and establish well-posedness of the weak problem along with convergence of an associated finite element formulation.We also examine several practical considerations such as conditioning of the linearized form of the nonlinear modified Poisson-Boltzmann equation, implications in numerical evaluation of the modified form, and utility of the modified equation in the context of the classical Poisson- Boltzmann equation.
KW - Finite elements
KW - Poisson-Bikerman
KW - Poisson-Boltzmann
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U2 - 10.1007/s10915-010-9441-7
DO - 10.1007/s10915-010-9441-7
M3 - Article
AN - SCOPUS:79959545610
VL - 47
SP - 347
EP - 364
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
SN - 0885-7474
IS - 3
ER -