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Qiyuan Zhao1, Jiuyang Liang2, Zhenli Xu3

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|September 9, 2018
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We developed a harmonic surface mapping algorithm (HSMA) to efficiently calculate electrostatic interactions for infinite image charges. This method accurately and quickly computes Madelung constants and ion energies, benefiting large-scale simulations.

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Area of Science:

  • Computational physics
  • Electrostatics
  • Numerical methods

Background:

  • Calculating electrostatic interactions in systems with infinite image charges is computationally intensive.
  • Existing methods struggle with non-periodic boundary conditions and large numbers of sources.

Purpose of the Study:

  • To introduce a novel algorithm, the harmonic surface mapping algorithm (HSMA), for efficient electrostatic pairwise sums.
  • To address challenges posed by infinite image charges and non-periodic boundary conditions.

Main Methods:

  • The HSMA approximates image charge contributions outside an auxiliary surface using least-squares spherical harmonics.
  • It transforms approximations into surface charges and dipoles via numerical integration, creating point images.
  • The method integrates with the fast multipole method for linear scaling.

Main Results:

  • HSMA accurately calculates the Madelung constant for crystalline lattices.
  • It efficiently determines the electrostatic energy of ions in metallic cavities.
  • Demonstrated fast computation times for large-scale systems.

Conclusions:

  • The HSMA provides an accurate and fast solution for electrostatic pairwise sums involving infinite image charges.
  • Its low complexity and efficiency make it suitable for diverse computational applications.
  • HSMA offers a significant advancement in handling complex electrostatic boundary value problems.