This work introduces an efficient Krylov subspace strategy for the implementation of the Karhunen-Loève moment equation (KLME) method. The KLME method has recently emerged as a competitive alternative for subsurface uncertainty assessment since it involves simulations at a lower resolution level than Monte Carlo simulations. Algebraically, the KLME method reduces to the solution of a sequence of linear systems with multiple right-hand sides. We propose a Krylov subspace projection method to efficiently compute different stochastic orders and moments of the primary variable response from the zero-order solution. The Krylov basis is recycled to deflate and improve the initial guess for the block and seed treatment of right-hand sides. Numerical results are encouraging to extend the capabilities of the proposed stochastic framework to address more complex simulation models.


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