Minor text edits on step-67.

diff --git a/examples/step-67/doc/intro.dox b/examples/step-67/doc/intro.dox
index e89f3f8ecc4571f8bc637f995c9250a2de33bcf4..4470ed139a578fab8fd8ef66ef0c942027414bce 100644 (file)
--- a/examples/step-67/doc/intro.dox
+++ b/examples/step-67/doc/intro.dox
@@ -710,7 +710,9 @@ back to the standard nodal Gauss-Lobatto basis.
 The advantage of this particular way of applying the inverse mass matrix is
 the fact that it is of similar cost as the forward application of a mass
 matrix, and cheaper than the evaluation of the spatial operator $\mathcal L_h$
-which is more costly due to over-integration and face integrals. In fact, it
+which is more costly due to over-integration and face integrals. (We
+will demonstrate this with detailed timing information in the
+<a href="#Results">results section</a>.) In fact, it
 is so cheap that it is limited by the bandwidth of reading the source vector,
 reading the diagonal, and writing into the destination vector on most modern
 architectures. The hardware used for the result section allows to do the

diff --git a/examples/step-67/doc/results.dox b/examples/step-67/doc/results.dox
index 3aae440bd89cdacf40675894df4f78a9a8393763..6b0c5aa7cc88502c7d0853c3772bafbdff28faea 100644 (file)
--- a/examples/step-67/doc/results.dox
+++ b/examples/step-67/doc/results.dox
@@ -42,10 +42,21 @@ that we use a relatively fine mesh of $32^2$ cells with polynomials of degree
 step size: whereas it is 0.0069 up to time 5, it increases to 0.0096 for later
 times. The step size increases once the vortex with some motion on top of the
 speed of sound (and thus faster propagation) leaves the computational domain
-between times 5 and 6.5. Our time step formula recognizes this and only
-detects the acoustic limit in the last part of the simulation.
-
-The summary of wall clock times shows that 1283 time steps have been performed
+between times 5 and 6.5. After that point, the flow is simply uniform
+in the same direction, and the maximum velocity of the gas is reduced
+compared to the previous state where the uniform velocity was overlaid
+by the vortex. Our time step formula recognizes this and only
+uses the acoustic limit in the last part of the simulation when
+determining the time step size.
+
+The final block of output shows detailed information about the timing
+of individual parts of the programs; it breaks this down by showing
+the time taken by the fastest and the slowest processor, and the
+average time -- this is often useful in very large computations to
+find whether there are processors that are consistently overheated
+(and consequently are throttling their clock speed) or consistently
+slow for other reasons.
+The summary shows that 1283 time steps have been performed
 in 1.02 seconds (looking at the average time among all MPI processes), while
 the output of 11 files has taken additional 0.96 seconds. Broken down per time
 step and into the five Runge--Kutta stages, the compute time per evaluation is
@@ -102,8 +113,8 @@ processed per second and Runge--Kutta stage, we obtain @f[ \text{throughput} =
 \frac{n_\mathrm{time steps} n_\mathrm{stages}
 n_\mathrm{dofs}}{t_\mathrm{compute}} = \frac{10258 \cdot 5 \cdot
 9.4\,\text{MDoFs}}{205s} = 2360\, \text{MDoFs/s} @f] This throughput number is
-very high, given that simply copying one vector to another one runs at around
-10,000 MDoFs/s.
+very high, given that simply copying one vector to another one runs at
+only around 10,000 MDoFs/s.
 
 If we go to the next-larger size with 37.7 million DoFs, the overall
 simulation time is 2196 seconds, with 1978 seconds spent in the time