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Title: Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

Abstract

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numerical results.

Authors:
 [1];  [2];  [3];  [4];  [5];  [1];  [6]
  1. Duke Univ., Durham, NC (United States). Dept. of Computer Science
  2. Chinese Academy of Sciences (CAS), Beijing (China). Inst. of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Molecular Biophysics
  4. Univ. of North Carolina, Chapel Hill, NC (United States). Dept. of Mathematics
  5. Duke Univ., Durham, NC (United States). Dept. of Computer Science; Aristotle Univ., Thessaloniki (Greece). Dept. of Electrical and Computer Engineering
  6. Howard Hughes Medical Inst., Chevy Chase, MD (United States). Dept. of Pharmacology; Univ. of California, San Diego, CA (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF); National Institutes of Health (NIH); Chinese Academy of Sciences
OSTI Identifier:
1376302
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Communications in Computational Physics
Additional Journal Information:
Journal Volume: 13; Journal Issue: 01; Journal ID: ISSN 1815-2406
Publisher:
Global Science Press
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Biomolecular System; Electrostatics; Poisson-Boltzmann Equation; Fast Multipole Methods; Mesh Generation; Directed Acyclic Graph; Dynamic Prioritization; Parallelization

Citation Formats

Zhang, Bo, Lu, Benzhuo, Cheng, Xiaolin, Huang, Jingfang, Pitsianis, Nikos P., Sun, Xiaobai, and McCammon, J. Andrew. Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver. United States: N. p., 2013. Web. doi:10.4208/cicp.210711.111111s.
Zhang, Bo, Lu, Benzhuo, Cheng, Xiaolin, Huang, Jingfang, Pitsianis, Nikos P., Sun, Xiaobai, & McCammon, J. Andrew. Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver. United States. doi:10.4208/cicp.210711.111111s.
Zhang, Bo, Lu, Benzhuo, Cheng, Xiaolin, Huang, Jingfang, Pitsianis, Nikos P., Sun, Xiaobai, and McCammon, J. Andrew. Tue . "Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver". United States. doi:10.4208/cicp.210711.111111s. https://www.osti.gov/servlets/purl/1376302.
@article{osti_1376302,
title = {Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver},
author = {Zhang, Bo and Lu, Benzhuo and Cheng, Xiaolin and Huang, Jingfang and Pitsianis, Nikos P. and Sun, Xiaobai and McCammon, J. Andrew},
abstractNote = {This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numerical results.},
doi = {10.4208/cicp.210711.111111s},
journal = {Communications in Computational Physics},
number = 01,
volume = 13,
place = {United States},
year = {2013},
month = {1}
}

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