Vergleich von parallelen Verfahren zur Vorkonditionierung fuer die Methode der konjugierten Gradienten

This report presents preconditioning techniques for the conjugate gradient method (CG), an iterative method for the solution of large sparse symmetric positive definite systems. The availability of massively parallel processors draws attention to parallel preconditioners. In this context, polynomial preconditioning is shown to be suitable. The preconditioner increases the number of matrix-vector products, whereas the total number of iterations and therefore the number of dot products decreases. The parallel computation of matrix-vector products usually results in communication with a small number of processors. Dot products, however, require global synchronisation. This reduction also results in better stability of the CG-method because fewer orthogonalizations are executed. The implementation is based on Chebyshev polynomials; performance tests were carried out on two massively parallel computer systems of the Research Centre Juelich (KFA). (orig.)SIGLEAvailable from TIB Hannover: RA 831(2913) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman