> I did some further testing and can give the following update. Instead > of choosing initial guess as zero (for Inv(M) as well as for the Schur > complement system) if I take that as a random vector, defined as > follows: > > #define frand()((double) rand()/(RAND_MAX+1.0)) > > the number of iterations for Identity preconditioner has increased > substantially. The number of iterations are increased for approximate > Schur complement preconditioner too, but they are somewhat bounded. > However, now the cost of the approximate Schur complement > preconditioner approach is almost half of the Identity preconditioner > approach. Moreover, now the same choice of tolerance for Inv(M) and S > (I finally settled at 1e-08) gives the favorable results as compared > to the altered choices (like those observed from zero initial guess). > I'm not sure if it has to do something with the data of the problem > which I chose such that the analytic solution is Sin(pi*x)Sin(pi*y).
I don't know how to interpret this. If I understand correctly, then both approach become worse if you choose random initial vectors, but one becomes "more worse" than the other. I suppose a reasonable answer would be "don't do that" -- why would you choose a worse initial guess? Best W. ------------------------------------------------------------------------- Wolfgang Bangerth email: [email protected] www: http://www.math.tamu.edu/~bangerth/ _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
