Volume 13, Issue 1
Numerical Optimization of a Walk-on-Spheres Solver for the Linear Poisson-Boltzmann Equation

Travis Mackoy, Robert C. Harris, Jesse Johnson, Michael Mascagni & Marcia O. Fenley

Commun. Comput. Phys., 13 (2013), pp. 195-206.

Published online: 2013-01

Preview Full PDF 383 1054
Export citation
  • Abstract

Stochastic walk-on-spheres (WOS) algorithms for solving the linearized Poisson-Boltzmann equation (LPBE) provide several attractive features not available in traditional deterministic solvers: Gaussian error bars can be computed easily, the algorithm is readily parallelized and requires minimal memory and multiple solvent environments can be accounted for by reweighting trajectories. However, previouslyreported computational times of these Monte Carlo methods were not competitive with existing deterministic numerical methods. The present paper demonstrates a series of numerical optimizations that collectively make the computational time of these Monte Carlo LPBE solvers competitive with deterministic methods. The optimization techniques used are to ensure that each atom’s contribution to the variance of the electrostatic solvation free energy is the same, to optimize the bias-generating parameters in the algorithm and to use an epsilon-approximate rather than exact nearest-neighbor search when determining the size of the next step in the Brownian motion when outside the molecule. 

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-13-195, author = {Travis Mackoy, Robert C. Harris, Jesse Johnson, Michael Mascagni and Marcia O. Fenley}, title = {Numerical Optimization of a Walk-on-Spheres Solver for the Linear Poisson-Boltzmann Equation}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {1}, pages = {195--206}, abstract = {

Stochastic walk-on-spheres (WOS) algorithms for solving the linearized Poisson-Boltzmann equation (LPBE) provide several attractive features not available in traditional deterministic solvers: Gaussian error bars can be computed easily, the algorithm is readily parallelized and requires minimal memory and multiple solvent environments can be accounted for by reweighting trajectories. However, previouslyreported computational times of these Monte Carlo methods were not competitive with existing deterministic numerical methods. The present paper demonstrates a series of numerical optimizations that collectively make the computational time of these Monte Carlo LPBE solvers competitive with deterministic methods. The optimization techniques used are to ensure that each atom’s contribution to the variance of the electrostatic solvation free energy is the same, to optimize the bias-generating parameters in the algorithm and to use an epsilon-approximate rather than exact nearest-neighbor search when determining the size of the next step in the Brownian motion when outside the molecule. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.220711.041011s}, url = {http://global-sci.org/intro/article_detail/cicp/7218.html} }
TY - JOUR T1 - Numerical Optimization of a Walk-on-Spheres Solver for the Linear Poisson-Boltzmann Equation AU - Travis Mackoy, Robert C. Harris, Jesse Johnson, Michael Mascagni & Marcia O. Fenley JO - Communications in Computational Physics VL - 1 SP - 195 EP - 206 PY - 2013 DA - 2013/01 SN - 13 DO - http://dor.org/10.4208/cicp.220711.041011s UR - https://global-sci.org/intro/cicp/7218.html KW - AB -

Stochastic walk-on-spheres (WOS) algorithms for solving the linearized Poisson-Boltzmann equation (LPBE) provide several attractive features not available in traditional deterministic solvers: Gaussian error bars can be computed easily, the algorithm is readily parallelized and requires minimal memory and multiple solvent environments can be accounted for by reweighting trajectories. However, previouslyreported computational times of these Monte Carlo methods were not competitive with existing deterministic numerical methods. The present paper demonstrates a series of numerical optimizations that collectively make the computational time of these Monte Carlo LPBE solvers competitive with deterministic methods. The optimization techniques used are to ensure that each atom’s contribution to the variance of the electrostatic solvation free energy is the same, to optimize the bias-generating parameters in the algorithm and to use an epsilon-approximate rather than exact nearest-neighbor search when determining the size of the next step in the Brownian motion when outside the molecule. 

Travis Mackoy, Robert C. Harris, Jesse Johnson, Michael Mascagni & Marcia O. Fenley. (1970). Numerical Optimization of a Walk-on-Spheres Solver for the Linear Poisson-Boltzmann Equation. Communications in Computational Physics. 13 (1). 195-206. doi:10.4208/cicp.220711.041011s
Copy to clipboard
The citation has been copied to your clipboard