The Metropolis Monte Carlo Finite Element Algorithm for Electrostatic Interactions

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.