Multi-level Monte Carlo acceleration of computations on multi-layer materials with random defects
This work addresses the computational bottleneck of Monte Carlo simulations for multi-layer materials with random defects, offering a faster method for materials science applications.
The paper proposes a Multi-level Monte Carlo technique to accelerate Monte Carlo sampling for approximating properties of materials with random defects, achieving significant computational time reductions for tight-binding models of graphene and MoS₂.
We propose a Multi-level Monte Carlo technique to accelerate Monte Carlo sampling for approximation of properties of materials with random defects. The computational efficiency is investigated on test problems given by tight-binding models of a single layer of graphene or of $MoS_2$ where the integrated electron density of states per unit area is taken as a representative quantity of interest. For the chosen test problems the multi-level Monte Carlo estimators significantly reduce the computational time of standard Monte Carlo estimators to obtain a given accuracy.