Efficient Implementation of the Barnes-Hut Octree Algorithm for Monte Carlo Simulations of Charged Systems

TL;DR

This paper introduces an efficient Barnes-Hut octree algorithm tailored for Monte Carlo simulations of charged systems, significantly reducing computational costs for large-scale electrostatic calculations.

Contribution

The authors developed a novel Barnes-Hut treecode algorithm with fast local updates, enabling efficient electrostatic evaluations in Monte Carlo simulations of Coulomb systems.

Findings

Computational cost scales as log N per move.

Speed improved by two orders of magnitude for 10,000 particles.

Accurate evaluation of electric double layer near a spherical interface.

Abstract

Computer simulation with Monte Carlo is an important tool to investigate the function and equilibrium properties of many systems with biological and soft matter materials solvable in solvents. The appropriate treatment of long-range electrostatic interaction is essential for these charged systems, but remains a challenging problem for large-scale simulations. We have developed an efficient Barnes-Hut treecode algorithm for electrostatic evaluation in Monte Carlo simulations of Coulomb many-body systems. The algorithm is based on a divide-and-conquer strategy and fast update of the octree data structure in each trial move through a local adjustment procedure. We test the accuracy of the tree algorithm, and use it to perform computer simulations of electric double layer near a spherical interface. It has been shown that the computational cost of the Monte Carlo method with treecode acceleration scales as $\log N$ in each move. For a typical system with ten thousand particles, by using the new algorithm, the speed has been improved by two orders of magnitude from the direct summation.