5.7.2.2 Restriction

Choosing the restriction as transposed interpolation, i.e., $I_{q}^{q-1} = \left(I_{q-1}^{q}\right)^T\enspace$, we achieve a block triangular structure of the restriction matrix as in (4.10).

$\Longrightarrow$

Restriction matrix is accumulated : ${\ensuremath{\color{red}\mathfrak{I}}}_{q}^{q-1}$ .

$\Longrightarrow$

Vector  $\underline{{\ensuremath{\color{green}{\sf d}}}}_{q-1}$ is distributed stored, $\underline{{\ensuremath{\color{green}{\sf d}}}}_{q}$ is distributed in any case.

Again, it would be also possible to define the restriction matrix as distributed but in that case an additional type conversion with communication has to be performed on  $\underline{{\ensuremath{\color{green}{\sf d}}}}_{q}$ previously to the restriction.
Using the injection as restriction does not change anything of the previous statements.

No communication in restriction !