the full machine with 304,128 cores of the Intel Xeon Skylake architecture and
an arithmetic performance of around 5 PFlop/s for a geometric multigrid solver
with polynomials of degree 4 has been reached. Compared to the official
-LINPACK performance of the machine of 19.5 PFlop (the machine is listed on
+LINPACK performance of the machine of 19.5 PFlop/s (the machine is listed on
position 8 of the top-500 list of November 2018), this can be considered an
extremely good value for a PDE solver which have classically only reached a
few percent of the LINPACK performance, and given the optimization steps
trillion unknowns (or 7.1 million unknowns per MPI rank) and was solved in 3.5
seconds. Also, CFD production runs with up to $10^{11}$ unknowns and $10^5$
time steps have been completed in less than seven hours, demonstrating the
-capabilities of \dealii for large-scale parallel computations. The tests
+capabilities of \dealii for large-scale parallel computations. The scaling tests
also revealed several relatively expensive operations in the setup of the
multigrid unknowns in \dealii's \texttt{DoFHandler} and \texttt{MGTransfer}
classes. While a few bottlenecks have already been resolved, we plan several