Scale-invariant multilevel Monte Carlo method

In this paper, the scale-invariant version of the mean and variance multi-level Monte Carlo estimate is proposed. The optimization of the computation cost over the grid levels is done with the help of a novel normalized error based on t-statistic. In this manner, the algorithm convergence is made invariant to the physical scale at which the estimate is computed. The novel algorithm is tested on the linear elastic example, the constitutive law of which is described by material uncertainty including both heterogeneity and anisotropy.