5.7.2 Parallel components of multigrid

It is obvious, that we can parallelize the whole multigrid algorithm if we can parallelize each single component of it, i.e., interpolation, restriction, smoothing and coarse grid solver. If we use the non-overlapping element distribution from Sec. 4.3.1 already on the coarsest grid  $\mathfrak{T}_{1}$ then this distribution is kept on all finer grids.

Figure 5.6: Non-overlapping element distribution on two nested grids

Again, we store the matrices  ${\ensuremath{\color{green}{\sf K}}}_q$ as distributed ones. From the experiences of previous sections (especially Sec. 5.1) the following classification of vectors from Alg. 5.20 into the two parallel vector types seems to be advantageous.

• Accumulated vectors : $\widehat{\underline{{\ensuremath{\color{red}\mathfrak{u}}}}} \makebox[0pt]{}_q$, $\widetilde{\underline{{\ensuremath{\color{red}\mathfrak{u}}}}} \makebox[0pt]{}_q$, $\widehat{\underline{{\ensuremath{\color{red}\mathfrak{w}}}}} \makebox[0pt]{}_q$ .
• Distributed vectors : $\underline{{\ensuremath{\color{green}{\sf f}}}}_q$, $\underline{{\ensuremath{\color{green}{\sf d}}}}_q$ .
• Not yet assigned : $\underline{u}_q$, $\underline{w}_{q-1}$, $\underline{w}_{q-1}^0$, $\underline{d}_{q-1}$ .