Algebraic multigrid methods for uncertainty quantification of source-type flows through randomly heterogeneous porous media

We consider steady flow generated by a source through a porous medium where, due to its erratic variations in the space, the conductivity K is regarded as a random field. As a consequence, flow variables become stochastic, and we aim at quantifying their uncertainty. To this purpose, we use Monte Carlo simulations, where for each realization the governing flow equation is solved by a finite volume method. This yields a deterministic linear system solved by algebraic multigrid (AMG) techniques. By leveraging analytical solutions valid for homogeneous (constant K) formations, we first compare different AMG solvers, that are subsequently used as trial in order to extend our approach to heterogeneous porous media. Results demonstrate that AMG methods enable achieving, especially at higher iteration counts, an L2-error lower than other, Gaussian-type, approximations.