Relaxation algorithms, Poisson-Boltzmann equation

Nicholls, A., Honig, B. A rapid finite difference algorithm, utilizing successive over-relaxation to solve the Poisson-Boltzmann equation. J. Comp. Chem. 12 (1991) 435-445. 

Algorithm, Utilizing Successive Over-Relaxation to Solve the Poisson-Boltzmann Equation. 

M. E. Davis and J. A. McCammon, J. Comput. Chem., 10, 386 (1989). Solving the Finite Difference Linearized Poisson-Boltzmann Equation A Comparison of Relaxation and Conjugate Gradient Algorithms. 

A. Nicholls and B. Honig, /. Comput. Chem., 12, 435 (1991). A Rapid Finite Difference Algorithm, Utilizing Successive Over-Relaxation to Solve the Poisson-Boltzmann Equation. 

Following earlier work by Wood et al., Luo and Tucker have relaxed the constant density restriction, and developed a continuum model in which the dielectric constant may be position-dependent. This dielectric function, s(7), is defined, at each point r in the fluid, in terms of the local density of the fluid at , pi(f), which is itself determined by the local values of the electric field and the compressibility. However, the local value of the electric field at 7 must be found from electrostatic equations (see Poisson-Boltzmann Type Equations Numerical Methods) which depend upon the dielectric function s(r) everywhere. Hence, all of the relevant equations must be solved self-consistently, and this is done using a numerical grid algorithm (see Poisson-Boltzmann Type Equations Numerical Methods). The result of such calculations are the density profile of the fluid around the solute and the position-dependent electric field, from which the free energy of solvation may be evaluated. The effects of solvent compression on solvation energetics can be quite substantial. Compression-induced enhancements to the solvation free energy of nearly 15 kcal mol" have been calculated for molecular ions in SC water at Tt = 1.01 and pr = 0.8. ... 

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