HEJ, HU ISSN 1418-7108 Manuscript no.: ANM-980724-A

  
Numerical experiments

We apply the parallel preconditioned cg algorithm (ppcg) to model problem 1 and 2, respectively [12,13]. We utilize the preconditioner $C$ of (1)

$$C = \left( \begin{array}[c]{cc} {I_C} & {K_{CI}B_I^{-T}} \... ...\\ {B_I^{-1}K_{IC}} & {I_I} \\ \end{array} \right) \qquad ,$$

where $B_I$ is defined either by multigrid or full multigrid and $C_I$ and $C_C$ are given below.

After investigating $\mu\,=\,\varrho \,(S_C^{-1} T_C^{\phantom{\!\!\!\!-1}})$ in section 4 we now focus on the number of ppcg iterations that are required to reach a given relative accuracy ( $\varepsilon = 10^{-6}$). This number of iterations and $\mu$ are linked via the spectral condition number $\, \kappa(C^{-1}K) \,$ (cf. section 3 and equation (2) for the theoretical background).

Our experiments are twofold. The first part of this section is devoted solely to the verification of our model problem analysis. The remaining part contains the actual comparison of the ppcg iteration numbers for both the multigrid and full multigrid basis transformation.

Finally let MG and FMG denote multigrid and full multigrid.

HEJ, HU ISSN 1418-7108 Manuscript no.: ANM-980724-A