Multiscale deflation solvers for flow in porous media
Héctor Klíe, A. Rodríguez, Mary F. Wheeler · PAMM · 2007
Abstract This work describes a novel physics‐based deflation preconditioner approach for solving porous media flow problems characterized by highly heterogeneous media. The approach relies on high‐conductivity block solutions after rearranging the linear system coefficients into high‐conductive and low condutive blocks from a given physically driven threshold value. This rearranging relies on the Hoshen‐Kopelman (H‐K) algorithm that is commonly used to determine percolation clusters. The resulting preconditioner may alternatively be combined with a deflation preconditioning stage. The proposed approach is coined as a physics‐based 2‐stage deflation preconditioner (P2SDP). Numerical experiments on different permeability distributions reveal that P2SDP is a powerful means to solve pressure systems when compared to more conventional algebraic approaches such as the incomplete Cholesky factorization. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)