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

Published online by Cambridge University Press:  03 June 2015

Bo Zhang ,
Benzhuo Lu ,
Xiaolin Cheng ,
Jingfang Huang ,
Nikos P. Pitsianis ,
Xiaobai Sun  and
J. Andrew McCammon
Bo Zhang*
Affiliation:
Department of Computer Science, Duke University, NC 27708, USA
Benzhuo Lu*
Affiliation:
Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100910, China
Xiaolin Cheng*
Affiliation:
Center for Molecular Biophysics, Oak Ridge National Laboratory, TN 37831, USA
Jingfang Huang*
Affiliation:
Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USA
Nikos P. Pitsianis*
Affiliation:
Department of Computer Science, Duke University, NC 27708, USA Department of Electrical and Computer Engineering, Aristotle University, Thessaloniki, 54124, Greece
Xiaobai Sun*
Affiliation:
Department of Computer Science, Duke University, NC 27708, USA
J. Andrew McCammon*
Affiliation:
Department of Chemistry & Biochemistry, Center for Theoretical Biological Physics, Department of Pharmacology, Howard Hughes Medical Institute, University of California, San Diego, CA 92093, USA
*
Email:[email protected]
Email:[email protected]
Email:[email protected]
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
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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. The potential of the solver is demonstrated with preliminary numerical results.

Keywords

45B0565Y0568W1090B1092C0592C40Biomolecular systemelectrostaticsPoisson-Boltzmann equationfast multipole methodsmesh generationdirected acyclic graphdynamic prioritizationparallelization
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 1 , January 2013 , pp. 107 - 128
Copyright
Copyright © Global Science Press Limited 2013

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