Particle-particle, particle-scaling function algorithm for electrostatic problems in free boundary conditions.

Area of Science:

• Computational physics
• Molecular dynamics

Background:

• Accurate calculation of Coulombic forces is crucial for molecular dynamics simulations.
• Existing methods like direct summation (O(N^2)) and the fast multipole method have limitations in speed and efficiency.

Purpose of the Study:

• To propose a novel algorithm for the fast calculation of Coulombic forces and energies.
• To achieve a calculation time complexity of N log N for N particles.
• To offer a simpler and more efficient alternative to existing methods.

Main Methods:

• Development of a new algorithm for Coulombic force and energy calculations.
• Analysis of the algorithm's time complexity, showing an N log N scaling.
• Comparison of the algorithm's crossover point with direct summation and the fast multipole method.
• Ensuring energy conservation by deriving forces as analytical derivatives of energy.

Main Results:

• The proposed algorithm achieves N log N computational scaling.
• The crossover point with direct summation is lower than that of the fast multipole method.
• Forces calculated are analytical derivatives of energy, ensuring energy conservation in simulations.

Conclusions:

• The novel algorithm provides a computationally efficient and simple method for Coulombic force and energy calculations.
• This method is particularly beneficial for large-scale molecular dynamics simulations.
• A parallelized version of the code is available for public use under the GNU GPL.