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The grid-based fast multipole method--a massively parallel numerical scheme for calculating two-electron interaction

Elias A Toivanen1, Sergio A Losilla1, Dage Sundholm1

  • 1Department of Chemistry, University of Helsinki, A. I. Virtanens plats 1, P. O. Box 55, FI-00014, Finland. eatoivan@chem.helsinki.fi Dage.Sundholm@helsinki.fi.

Physical Chemistry Chemical Physics : PCCP
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Summary

A new grid-based fast multipole method (GB-FMM) efficiently calculates electrostatic interactions. This computational chemistry approach scales linearly, achieving high accuracy for large molecular systems.

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Area of Science:

  • Computational chemistry
  • Electrostatics
  • Algorithm development

Background:

  • Accurate calculation of electrostatic interactions is crucial in computational chemistry.
  • Existing methods often face challenges with computational scaling for large systems.

Purpose of the Study:

  • To develop and implement a grid-based fast multipole method (GB-FMM) for efficient electrostatic calculations.
  • To achieve linear scaling computational complexity for large molecular systems.

Main Methods:

  • Dividing the computational domain into a hierarchical tree of cubic subdomains.
  • Employing numerical integration for neighboring subdomains and multipole expansions for distant ones.
  • Utilizing general-purpose graphics processing units (GPGPUs) for parallel computation of electrostatic interaction energies.

Main Results:

  • The developed GB-FMM achieves linear scaling, with computational cost largely independent of system size.
  • High accuracy (parts per billion) was maintained for systems ranging from C20 to C720 fullerenes.
  • Demonstrated scalability and parallel performance using one CPU and 20 GPGPUs.

Conclusions:

  • The GB-FMM provides an efficient and accurate method for calculating electrostatic interactions in large systems.
  • The parallel implementation on GPGPUs significantly enhances computational performance.
  • This method offers a scalable solution for complex molecular simulations.