Iterative methods for the solution of linear equations based on incomplete block factorization of the matrix

This work presents a class of iterative methods for the solution of linear equations like those that arise in reservoir simulators. The methods are generalizations of the incomplete LU-factorization technique introduced earlier. It can be applied to equations generated by the usual 5- and 7-point finite difference approximations as well as to those generated by special 9-, 11-, 19- and 27-point approximations. Application of the method to equations where the band structure of the matrix has been spoiled is discussed and modifications for running efficiently on vector processors are given. Numeric examples for well-known test problems are presented and compared with results of other methods. 15 references.