THE EFFECTS ON COMMUNICATION OF DATA REPRESENTATION OF NESTED PRECONDITIONINGS FOR MASSIVELY-PARALLEL ARCHITECTURES

The effect which the representation of the data (matrices and vectors) has on the communication patterns of preconditionings for exploitatio n of massively parallel architectures is discussed. Preconditioned ite rative methods are used to solve the sparse linear systems generated b y discretizations of partial differential equations in many areas of s cience and engineering. The preconditionings considered are based on n ested incomplete factorization with approximate tridiagonal inverses u sing a two color line ordering of the discretization grid. These preco nditionings can be described in terms of vector-vector to vector opera tions of dimension equal to half the total number of grid points.