Comparison of Preconditioners for the Conjugate Gradient Method in Reservoir Simulation

ABSTRACT Five methods of partial decomposition are compared as preconditioners for the conjugate gradient method for solving the pressure matrix equation of a sequential mode reservoir simulator. Three unsymmetric decompositions, Strongly Implicit Procedure; Dupont, Kendall, Rachford method; and Additional Bands (AB) proved effective and comparable, with AB being the most efficient when used on a scalar computer. The two symmetric Incomplete Cholesky methods did not prove as effective as the three unsymmetric methods. On the CRAY-1 computer, the SIP-conjugate gradient method was most efficient because it could be vectorized, and in comparison to Red-Black LSOR it was far superior for the example problem considered here. The insensitivity of the SIP-conjugate gradient method to the iteration parameter was an additional advantage of the method.