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This study compares computational methods for particle systems, finding Fast Multipole Method (FMM) and Fast Fourier Transform (FFT) offer the best performance and stability for Coulomb interactions. These methods are efficient across various system sizes and accuracy requirements.

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Area of Science:

  • Computational Physics
  • Scientific Computing
  • Particle Systems Simulation

Background:

  • Accurate simulation of Coulomb interactions in particle systems is crucial for many scientific fields.
  • Existing methods like multigrid and Maxwell solvers have limitations in scalability and performance.

Purpose of the Study:

  • To compare the efficiency, scalability, performance, and accuracy of Fast Multipole Method (FMM), multigrid-based methods, Fast Fourier Transform (FFT)-based methods, and a Maxwell solver.
  • To identify the most suitable computational methods for three-dimensional periodic boundary conditions in particle systems.

Main Methods:

  • Development of a parallel scalable library for Coulomb interactions.
  • Direct comparison of FMM, multigrid, FFT-based methods, and Maxwell solver.
  • Testing on identical benchmark systems across multiple computers to ensure comparable conditions.

Main Results:

  • FMM and FFT-based methods demonstrate superior efficiency in performance and stability.
  • The choice between FMM and FFT depends on system size and desired accuracy.
  • All methods were evaluated under identical conditions for a fair comparison.

Conclusions:

  • Fast Multipole Method (FMM) and Fast Fourier Transform (FFT) are recommended for simulating Coulomb interactions in particle systems.
  • These methods provide a robust and efficient solution for three-dimensional periodic boundary conditions.
  • The study offers valuable insights for selecting appropriate computational techniques in physics and engineering.