Skip to main content
SpringerLink
Log in

Parallel Computing of the Adaptive N-Body Treecode Algorithm for Solving Boundary Integral Poisson-Boltzmann Equation

  • Conference paper
  • First Online:
High Performance Computing and Applications (HPCA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9576))

  • 798 Accesses

Abstract

In this paper, we study the parallelization of a Cartesian grid based treecode algorithm in evaluating electrostatic potentials in a charged particle system. The treecode algorithm uses a far-field Taylor expansion to compute \(\mathcal {O}(N \log {N})\) particle-cluster interactions to replace the \(\mathcal {O}(N^2)\) particle-particle interactions. The treecode algorithm is implemented with MPI based parallelization. We design schemes to optimize the implementation adaptive to the particle location. The numerical results show high parallel efficiency. These optimized schemes are further extended to accelerate GMRES iteration in solving boundary integral Poisson–Boltzmann equation in which the discretized linear algebraic system resembles the interactions of the charged system.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phy. 73(2), 325–348 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barnes, J., Hut, P.: A hierarchical o(n log n) force-calculation algorithm. Nature 324(6096), 446–449 (1986)

    Article  Google Scholar 

  3. Li, P., Johnston, H., Krasny, R.: A Cartesian treecode for screened Coulomb interactions. J. Comput. Phys. 228(10), 3858–3868 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Geng, W., Krasny, R.: A treecode-accelerated boundary integral Poisson-Boltzmann solver for electrostatics of solvated biomolecules. J. Comput. Phy. 247, 62–78 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, J., Krasny, R., Reynolds, D., Geng, W.: Cyclically paralleled treecode for fast computing electrostatic interactions on molecular surfaces. in preparation, 2015

    Google Scholar 

  6. Connolly, M.L.: Depth buffer algorithms for molecular modeling. J. Mol. Graphics 3, 19–24 (1985)

    Article  Google Scholar 

  7. Lee, B., Richards, F.M.: The interpretation of protein structures: estimation of static accessibility. J. Mol. Biol. 55(3), 379–400 (1971)

    Article  Google Scholar 

  8. Sanner, M.F., Olson, A.J., Spehner, J.C.: Reduced surface: an efficient way to compute molecular surfaces. Biopolymers 38, 305–320 (1996)

    Article  Google Scholar 

  9. Baker, N.A.: Improving implicit solvent simulations: a Poisson-centric view. Curr. Opin. Struct. Biol. 15(2), 137–143 (2005)

    Article  Google Scholar 

  10. Fogolari, F., Brigo, A., Molinari, H.: The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology. J. Mol. Recognit. 15(6), 377–392 (2002)

    Article  Google Scholar 

  11. Lu, B.Z., Zhou, Y.C., Holst, M.J., McCammon, J.A.: Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications. Commun. Comput. Phy. 3(5), 973–1009 (2008)

    MATH  Google Scholar 

  12. Juffer, A., Botta, E., van Keulen, B., van der Ploeg, A., Berendsen, H.: The electric potential of a macromolecule in a solvent: a fundamental approach. J. Comput. Phys. 97, 144–171 (1991)

    Article  MATH  Google Scholar 

  13. Saad, Y., Schultz, M.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7(3), 856–869 (1986)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Southern Methodist University, Dallas, Texas, 75275, USA

    Jiahui Chen & Weihua Geng

Authors
  1. Jiahui Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weihua Geng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weihua Geng .

Editor information

Editors and Affiliations

  1. School of Computer Engineering, Shanghai University, Shanghai, China

    Jiang Xie

  2. Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta, Canada

    Zhangxin Chen

  3. Mathematics Department, University of Wyoming, Laramie, Wyoming, USA

    Craig C. Douglas

  4. School of Computer Engineering, Shanghai University, Shanghai, China

    Wu Zhang

  5. Mathematics and Informatics, South China Agricultural University, Guangzhou, China

    Yan Chen

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Chen, J., Geng, W. (2016). Parallel Computing of the Adaptive N-Body Treecode Algorithm for Solving Boundary Integral Poisson-Boltzmann Equation. In: Xie, J., Chen, Z., Douglas, C., Zhang, W., Chen, Y. (eds) High Performance Computing and Applications. HPCA 2015. Lecture Notes in Computer Science(), vol 9576. Springer, Cham. https://doi.org/10.1007/978-3-319-32557-6_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-32557-6_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32556-9

  • Online ISBN: 978-3-319-32557-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation