A rapid finite difference algorithm, utilizing successive over-relaxation to solve the Poisson-Boltzmann equation

1991 ◽  
Vol 12 (4) ◽  
pp. 435-445 ◽  
Author(s):  
Anthony Nicholls ◽  
Barry Honig
Keyword(s):  
Boltzmann Equation ◽  
Finite Difference ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Successive Over Relaxation

Solving the finite-difference non-linear Poisson-Boltzmann equation

1992 ◽  
Vol 13 (9) ◽  
pp. 1114-1118 ◽  
Author(s):  
Brock A. Luty ◽  
Malcolm E. Davis ◽  
J. Andrew McCammon
Keyword(s):  
Boltzmann Equation ◽  
Finite Difference ◽  
Non Linear ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations

2013 ◽  
Vol 13 (1) ◽  
pp. 150-173 ◽  
Author(s):  
Mohammad Mirzadeh ◽  
Maxime Theillard ◽  
Asdís Helgadöttir ◽  
David Boy ◽  
Frédéric Gibou
Keyword(s):  
Boltzmann Equation ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Level Set ◽  
Level Set Function ◽  
Novel Approach ◽  
Uniform Grids ◽  
Poisson Boltzmann ◽  
Finite Volume Approach ◽  
Poisson Boltzmann Equation

AbstractWe present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation. The solver uses a level set framework to represent sharp, complex interfaces in a simple and robust manner. It also uses non-graded, adaptive octree grids which, in comparison to uniform grids, drastically decrease memory usage and runtime without sacrificing accuracy. The basic solver was introduced in earlier works [16,27], and here is extended to address biomolecular systems. First, a novel approach of calculating the solvent excluded and the solvent accessible surfaces is explained; this allows to accurately represent the location of the molecule’s surface. Next, a hybrid finite difference/finite volume approach is presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcing the jump boundary conditions at the interface. Since the interface is implicitly represented by a level set function, imposing the jump boundary conditions is straightforward and efficient.

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