Block-Preconditioned Conjugate Gradient-Like Methods for Numerical Reservoir Simulation

摘要

In recent years, a collection of block-oriented preconditioners has been proposed for solving the sparse linear systems arising from the finite-difference discretization of elliptic partial differential equations. Each of these computes an incomplete factorization of the coefficient matrix in which either lines or planes are handled in an implicit manner. We describe a collection of block-preconditioners for use in solving large sparse linear systems of equations by iterative methods, and we compare their performance with several point-preconditioners in solving some systems arising in numerical reservoir simulation. We consider block-preconditioners that handle either lines or planes in an implicit manner, and pointwise incomplete LU factorizations combined with partial elimination preprocessors. Our conclusions are that the best of the pointwise methods are both more robust and faster, but that the best of the block methods are competitive for certain orderings of unknowns and require less storage.