FAST UPDATING MULTIPOLE COULOMBIC POTENTIAL CALCULATION.

Area of Science:

• Computational physics
• Computational chemistry
• Molecular dynamics

Background:

• Calculating the Coulomb potential is computationally intensive, especially for large systems.
• Efficiently updating potentials after particle movement is crucial for simulations.

Purpose of the Study:

• To develop a numerical method for efficient and accurate re-computation of Coulomb potentials after particle positional changes.
• To ensure bounded errors for practical application in iterative simulation techniques.

Main Methods:

• Utilizes truncated multipole expansions of the potential energy functional.
• Employs a tree decomposition of the computational domain to reduce complexity.
• Reduces computational costs to logarithmic scaling with problem size.

Main Results:

• The method demonstrates bounded errors even after numerous particle shifts.
• Numerical experiments confirm the method's scaling, accuracy, and efficiency.
• Outperforms direct calculation methods for moderate problem sizes.

Conclusions:

• The presented numerical method offers a practical and efficient solution for Coulomb potential re-computation.
• Its logarithmic scaling and bounded errors make it ideal for Monte Carlo Markov chain methods.
• Applicable across diverse fields including molecular dynamics, astrophysics, and chemistry.