Author:

Abstract:

Multilevel Monte Carlo methods are efficient variance reduction techniques that use a coarse to fine hierarchy of approximations to reduce the computational complexity in uncertainty quantification applications. We investigate how the coarse grids can be generated automatically in the partial differential equation setting by using the Algebraic Multigrid method. Furthermore, when using Full Multigrid to solve the underlying deterministic equation, we show how coarse solutions obtained by the solver can be reused as samples in the Multilevel Monte Carlo method. We present numerical results that show significant speedup, even in cases where the underlying coarse grids are hard to obtain.