Parallelizable incomplete factorization perconditioning methods

Two classes of parallelizable preconditioning iteration methods for the solution of finite difference or finite element matrix problems are presented. The first class is developed with regard to massively parallel computers and we discuss various methods to construct completely parallel preconditioners. The second class is intended for computers with a smaller number of parallel processors and uses a blockwise parallel incomplete factorization. Both types of methods are based on the calculation of approximate inverses. The speed of the methods may be increased by making the approximation of the inverses more accurate. Problems with constant as well as strongly varying orthotropy are examined and the methods are compared with respect to the computational complexity.