scholarly journals Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation

2015 ◽  
Vol 48 ◽  
pp. 420-446 ◽  
Author(s):  
Mireille Bossy ◽  
Nicolas Champagnat ◽  
Hélène Leman ◽  
Sylvain Maire ◽  
Laurent Violeau ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Monte Carlo Methods ◽  
Non Linear ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

Geometry entrapment in Walk-on-Subdomains

2019 ◽  
Vol 25 (4) ◽  
pp. 329-340 ◽  
Author(s):  
Preston Hamlin ◽  
W. John Thrasher ◽  
Walid Keyrouz ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Monte Carlo Method ◽  
Electrostatic Energy ◽  
Potential Solution ◽  
Long Time ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Monte Carlo Implementation

Abstract One method of computing the electrostatic energy of a biomolecule in a solution uses a continuum representation of the solution via the Poisson–Boltzmann equation. This can be solved in many ways, and we consider a Monte Carlo method of our design that combines the Walk-on-Spheres and Walk-on-Subdomains algorithms. In the course of examining the Monte Carlo implementation of this method, an issue was discovered in the Walk-on-Subdomains portion of the algorithm which caused the algorithm to sometimes take an abnormally long time to complete. As the problem occurs when a walker repeatedly oscillates between two subdomains, it is something that could cause a large increase in runtime for any method that used a similar algorithm. This issue is described in detail and a potential solution is examined.

scholarly journals Using Correlated Monte Carlo Sampling for Efficiently Solving the Linearized Poisson−Boltzmann Equation Over a Broad Range of Salt Concentration

2009 ◽  
Vol 6 (1) ◽  
pp. 300-314 ◽  
Author(s):  
Marcia O. Fenley ◽  
Michael Mascagni ◽  
James McClain ◽  
Alexander R. J. Silalahi ◽  
Nikolai A. Simonov
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Salt Concentration ◽  
Monte Carlo Sampling ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

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
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