Title: Optimization of mesh hierarchies in Multilevel Monte Carlo samplers

Abstract:

We perform a general optimization of the parameters in the Multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. We optimize hierarchies with geometric and non-geometric sequences of mesh sizes and show that geometric hierarchies are nearly optimal and have the same asymptotic computational complexity as non-geometric optimal hierarchies. To provide numerical grounds for our theoretical results, we test our hierarchies with the Continuation MLMC Algorithm.​