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

The Metropolis Monte Carlo Finite Element Algorithm for Electrostatic Interactions