Multilevel Monte Carlo method for simulations of fluids

TL;DR

This paper introduces a multilevel Monte Carlo method that improves fluid simulations by addressing scale limitations and long equilibration times, demonstrated through a one-dimensional fluid test case.

Contribution

The paper presents a novel multilevel Monte Carlo approach that enhances fluid simulation efficiency by combining coarse and fine level computations.

Findings

Reduces equilibration times in fluid simulations

Enables larger scale simulations beyond traditional limits

Demonstrates effectiveness on a 1D fluid test case

Abstract

Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical calculation. This means that scales larger than or comparable to the one that can be simulated are not taken into account. The second difficulty is the locality of the conventional Monte Carlo algorithms which leads to very (sometimes unreasonably) long equilibration times. These obstacles can be eliminated in the framework of the multilevel Monte Carlo method described here. The basic approach is to describe the system at increasingly coarser levels defined on increasingly large domains, and transfer information back and forth between the levels in order to obtain a selfconsistent result. The method is illustrated for a test case of one-dimensional fluids.