More edits.

21_distributed-memory.tex

@@ -392,12 +392,12 @@ metric if you switch this feature on (\texttt{hotspot}, e.g.).
 
 \subsection{Meshes for weak and strong scaling}
 
-\exahype distributes work by decomposing the tripartitioned spacetree into
+\exahype\ distributes work by decomposing the tripartitioned spacetree into
 subtrees that are deployed to worker processes.
 Only subtrees that overlap with the computational domain are deployed.
 This constraint can be used to steer work distribution.
 
-\exahype can scale the bounding box such that \texttt{outside\_cells\_left} and/or \\
+\exahype\ can scale the bounding box such that \texttt{outside\_cells\_left} and/or \\
 \texttt{outside\_cells\_right} cells are placed outside of the 
 domain while the latter is still resolved as accurately as specified in the spec file.
 
@@ -427,10 +427,9 @@ on the left side and 12 ranks per dimension. The mesh
 is interesting since it can be perfectly distributed among
 $2^d$, $4^d$, and $12^d$ processes.
 
-The same mesh refined by a factor $3^i$, $i \leq 0$ can be constructed if $3^i \times 9$ bounding box outside cells
-are placed to the left of the domain. The $36^d$ mesh requires a maximum-mesh-size of 
-$\frac{1}{36} \approx 0.03$.
-The uniformly refined variants must scale this mesh size with a factor $3^{-i}$.
+The same mesh refined by a factor $3^i$, $i \leq 0$, is constructed by placing $3^i \times 9$ bounding box 
+cells left to the domain. The $36^d$ mesh requires a maximum-mesh-size of $\frac{1}{36} \approx 0.03$.
+For further uniform refinement, this mesh size must be scaled by a factor $3^{-i}$.
 
 Another family of interesting uniform meshes are the ones with $3^i \times 48^d$ cells that are shifted
 by $3^i \times 3$ cells. They can be created by choosing $\texttt{ranks\_per\_dimension}=16$