This paper presents an incomplete LU factorization (ILU) technique coupled with generalized conjugate gradient acceleration especially designed for linear equations resulting from locally refined grids. The factorization is based on a special ordering scheme. This repeated red black (RRB) ordering can cope with grid irregularities introduced by local refinement in a natural way. Moreover, it is a very effective scheme on regular grids. In this case, the condition number (measure for the rate of convergence) of the preconditioned linear system increases asymptotically more slowly with the number of grid blocks than for conventional ILU preconditionings. For large linear systems, this results in a smaller number of iterations necessary to reach convergence. This makes the method highly competitive compared with other techniques even on regular grids, although the new ordering scheme causes more overhead data handling than standard orderings.
Results for several idealized test cases (IMPES-type equations) are given showing the new method to be faster than standard iterative methods.