Masters Thesis - TU Delft

10−1log10( Residual / norm(b) )−2−3−4−5−6Wihout1st layer2nd layer3rd layer1st 3rd layers1st 2nd 3rd LayerSubdomain−7−8−90 20 40 60 80 100 120 140Iteration stepFigure 6.4: Problem 3 with ASM preconditioning and Incomplete Cholesky FactorizationThe drop tolerance in Incomplete Cholesky is set to10 −3 and we use the same preconditioneras before. We now observe, that the Deflation is now making a difference in the speed of ourmethod. Once again, we see that the best choice is to take the stiff layers for the DeflationVectors, and once again we see that the addition of soft layers, if we already took the stiffones does not drastically improve the rate of convergence. Nevertheless, we observe, that thedifference in the number of iteration of DPCG with only stiff layers and PCG without anyDeflation is equal 16. This may be regarded as not much, however the size of the problem isalso small. We may expect that, for larger problems this number will be more perceptible.Let us now check the same for the second problem used in this section, i.e. Problem 4.39