The Metropolis Monte Carlo Finite Element Algorithm for Electrostatic Interactions

TL;DR

This paper introduces a Metropolis Monte Carlo finite element algorithm for electrostatic interactions that efficiently computes interaction energies, with computational time independent of the number of charges, enhancing simulation scalability.

Contribution

It presents a novel combination of Monte Carlo and finite element methods to efficiently evaluate electrostatic energies, reducing computational complexity for large systems.

Findings

Computing time for acceptance probability is independent of system size.

Finite Element method effectively integrates Poisson's equation.

Algorithm improves scalability for electrostatic simulations.

Abstract

The Metropolis Monte Carlo algorithm with the Finite Element method applied to compute electrostatic interaction energy between charge densities is described in this work. By using the Finite Element method to integrate numerically the Poisson's equation, it is shown that the computing time to obtain the acceptance probability of an elementary trial move does not, in principle, depend on the number of charged particles present in the system.