Krylov-based Deflation Solvers for Stochastic Flow in Porous Media

Hector Klie and Mary F. Wheeler

The University of Texas at Austin

Karhunen-Loeve Moment Equation (KLME) methods has emerged as an efficient and physical insightful alternative to conventional Monte Carlo simulations (MCS). Efficiency is particularly achieved by solving a deterministic set of PDE equations sharing the same differential operator but with different right-hand sides. This operator is described by a geometric average representation of the permeability field which makes the original problem suitable for using coarser meshes and generating linear algebraic systems with milder condition number than those produced by MCS that use the the original permeability field distribution. In this presentation, we illustrate how efficiency can be further exploited by using a Krylov-based deflation strategy to complement a preconditioner of choice. Moreover, the deflation strategy is combined with a block seed method to project residuals associated to unseed systems onto the Krylov subspace generated by the seed system. Numerical results are shown for highly heterogeneous permeability fields.