The Communication Patterns of Nested Preconditionings for Massively Parallel Architectures

Preconditioned Iterative methods are used to solve sparse linear systems from discrete convection dominated diffusion problems. The preconditionings are based on nested incomplete factorization with approximate tridiagonal inverses using a two color line ordering of the discretization grid. These preconditionings can be described in terms of vector-vector to vector operations of dimension equal to half the total of grid points. We discuss the communication patterns of these preconditionings for exploitation of massively parallel architectures.