Abstract
Abstract The multigrid technique is compared with the incomplete Cholesky conjugate gradient/modified incomplete Cholesky gradient (ICCG/M1CCG) methods for solving implicit pressure, explicit saturation (IMPES)-type pressure equations. The numerical results of several test problems with widely varying transmissibilities are presented. The multigrid algorithm is enhanced by pattern relaxation and acceleration. Optimization of the ICCG/MICCG algorithms is investigated by high-order (up to tenth) decompositions and different ordering schemes. For large problems the multigrid method is superior in terms of scalar work. The multigrid scheme can also be highly vectorized, and is an O(N) algorithm even for problems with large jump discontinuities in equation coefficients. Results of the multigrid method applied to nonsymmetric problems are also presented.
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