Renormalization based MLMC method for scalar elliptic SPDE

Previously the authors have presented MLMC algorithms exploiting Multiscale Finite Elements and Reduced Bases as a basis for the coarser levels in the MLMC algorithm. In this paper a Renormalization based Multilevel Monte Carlo algorithm is discussed. The advantage of the renormalization as a basis for the coarse levels in MLMC is that it allows in a cheap way to create a reduced dimensional space with a variation which is very close to the variation at the finest level. This leads to especially efficient MLMC algorithms. Parallelization of the proposed algorithm is also considered and results from numerical experiments are presented.