Multilevel Monte Carlo methods for highly heterogeneous media
For researchers in uncertainty quantification, this provides a rigorous extension of MLMC to more realistic coefficient models, but the contribution is incremental as it builds on existing MLMC theory.
The paper extends multilevel Monte Carlo methods to elliptic PDEs with highly heterogeneous random coefficients, including tensor-valued and log-normal cases, and provides numerical analysis under minimal assumptions.
We discuss the application of multilevel Monte Carlo methods to elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification in subsurface flow modeling. We give a brief review of recent advances in the numerical analysis of the multilevel algorithm under minimal assumptions on the random coefficient, and extend the analysis to cover also tensor--valued coefficients, as well as point evaluations. Our analysis includes as an example log--normal random coefficients, which are frequently used in applications.