<h3>Results for a 2d circular shell testcase</h3>
-Next, we will run step-32 with the parameter file in the directory. Here we
-are using 50 processors. The command to launch is (note that step-32.prm is
-the default):
+Next, we will run step-32 with the parameter file in the directory with one
+change: we increase the final time to 1e9. Here we are using 16 processors. The
+command to launch is (note that step-32.prm is the default):
<code>
<pre>
-\$ mpirun -np 50 ./step-32
+\$ mpirun -np 16 ./step-32
</pre>
</code>
<code>
<pre>
+\$ mpirun -np 16 ./step-32
Number of active cells: 12,288 (on 6 levels)
Number of degrees of freedom: 186,624 (99,840+36,864+49,920)
Timestep 0: t=0 years
Rebuilding Stokes preconditioner...
- Solving Stokes system... 40 iterations.
+ Solving Stokes system... 41 iterations.
Maximal velocity: 60.4935 cm/year
Time step: 18166.9 years
17 CG iterations for temperature
Temperature range: 973 4273.16
-Number of active cells: 16,389 (on 7 levels)
-Number of degrees of freedom: 259,617 (140,300+49,167+70,150)
+Number of active cells: 15,921 (on 7 levels)
+Number of degrees of freedom: 252,723 (136,640+47,763+68,320)
Timestep 0: t=0 years
Rebuilding Stokes preconditioner...
- Solving Stokes system... 49 iterations.
- Maximal velocity: 60.5202 cm/year
- Time step: 10619.2 years
+ Solving Stokes system... 50 iterations.
+ Maximal velocity: 60.3223 cm/year
+ Time step: 10557.6 years
19 CG iterations for temperature
Temperature range: 973 4273.16
-Number of active cells: 20,124 (on 8 levels)
-Number of degrees of freedom: 323,145 (175,182+60,372+87,591)
+Number of active cells: 19,926 (on 8 levels)
+Number of degrees of freedom: 321,246 (174,312+59,778+87,156)
Timestep 0: t=0 years
Rebuilding Stokes preconditioner...
- Solving Stokes system... 51 iterations.
- Maximal velocity: 59.9101 cm/year
- Time step: 5334.14 years
+ Solving Stokes system... 50 iterations.
+ Maximal velocity: 57.8396 cm/year
+ Time step: 5453.78 years
18 CG iterations for temperature
- Temperature range: 973 4273.43
+ Temperature range: 973 4273.16
-Timestep 1: t=5334.14 years
+Timestep 1: t=5453.78 years
Solving Stokes system... 49 iterations.
- Maximal velocity: 61.0837 cm/year
- Time step: 5232.24 years
+ Maximal velocity: 59.0231 cm/year
+ Time step: 5345.86 years
18 CG iterations for temperature
- Temperature range: 973 4273.43
+ Temperature range: 973 4273.16
-Timestep 2: t=10566.4 years
+Timestep 2: t=10799.6 years
Solving Stokes system... 24 iterations.
- Maximal velocity: 62.265 cm/year
- Time step: 5133.56 years
- 18 CG iterations for temperature
- Temperature range: 973 4273.43
+ Maximal velocity: 60.2139 cm/year
+ Time step: 5241.51 years
+ 17 CG iterations for temperature
+ Temperature range: 973 4273.16
[...]
-Timestep 100: t=270918 years
+Timestep 100: t=272151 years
- Solving Stokes system... 22 iterations.
- Maximal velocity: 161.391 cm/year
- Time step: 1683.55 years
+ Solving Stokes system... 21 iterations.
+ Maximal velocity: 161.546 cm/year
+ Time step: 1672.96 years
17 CG iterations for temperature
- Temperature range: 973 4282.45
+ Temperature range: 973 4282.57
-Number of active cells: 54,717 (on 8 levels)
-Number of degrees of freedom: 880,626 (477,650+164,151+238,825)
+Number of active cells: 56,085 (on 8 levels)
+Number of degrees of freedom: 903,408 (490,102+168,255+245,051)
+---------------------------------------------+------------+------------+
-| Total wallclock time elapsed since start | 170s | |
+| Total wallclock time elapsed since start | 115s | |
| | | |
| Section | no. calls | wall time | % of total |
+---------------------------------+-----------+------------+------------+
-| Assemble Stokes system | 103 | 2.25s | 1.3% |
-| Assemble temperature matrices | 12 | 0.296s | 0.17% |
-| Assemble temperature rhs | 103 | 9.66s | 5.7% |
-| Build Stokes preconditioner | 12 | 1.78s | 1% |
-| Solve Stokes system | 103 | 149s | 88% |
-| Solve temperature system | 103 | 1.84s | 1.1% |
-| Postprocessing | 3 | 0.398s | 0.23% |
-| Refine mesh structure, part 1 | 12 | 0.599s | 0.35% |
-| Refine mesh structure, part 2 | 12 | 0.216s | 0.13% |
-| Setup dof systems | 13 | 2.15s | 1.3% |
+| Assemble Stokes system | 103 | 2.82s | 2.5% |
+| Assemble temperature matrices | 12 | 0.452s | 0.39% |
+| Assemble temperature rhs | 103 | 11.5s | 10% |
+| Build Stokes preconditioner | 12 | 2.09s | 1.8% |
+| Solve Stokes system | 103 | 90.4s | 79% |
+| Solve temperature system | 103 | 1.53s | 1.3% |
+| Postprocessing | 3 | 0.532s | 0.46% |
+| Refine mesh structure, part 1 | 12 | 0.93s | 0.81% |
+| Refine mesh structure, part 2 | 12 | 0.384s | 0.33% |
+| Setup dof systems | 13 | 2.96s | 2.6% |
+---------------------------------+-----------+------------+------------+
[...]
-Timestep 6946: t=1.00001e+08 years
-
- Solving Stokes system... 12 iterations.
- Maximal velocity: 8.94391 cm/year
- Time step: 31505.4 years
- 18 CG iterations for temperature
- Temperature range: 973 4273.04
-
-
-
+---------------------------------------------+------------+------------+
-| Total wallclock time elapsed since start | 8.86e+03s | |
+| Total wallclock time elapsed since start | 9.14e+04s | |
| | | |
| Section | no. calls | wall time | % of total |
+---------------------------------+-----------+------------+------------+
-| Assemble Stokes system | 6949 | 153s | 1.7% |
-| Assemble temperature matrices | 697 | 18.2s | 0.2% |
-| Assemble temperature rhs | 6949 | 600s | 6.8% |
-| Build Stokes preconditioner | 697 | 115s | 1.3% |
-| Solve Stokes system | 6949 | 7.56e+03s | 85% |
-| Solve temperature system | 6949 | 123s | 1.4% |
-| Postprocessing | 140 | 18.1s | 0.2% |
-| Refine mesh structure, part 1 | 696 | 34.6s | 0.39% |
-| Refine mesh structure, part 2 | 696 | 12.6s | 0.14% |
-| Setup dof systems | 697 | 130s | 1.5% |
+| Assemble Stokes system | 47045 | 2.05e+03s | 2.2% |
+| Assemble temperature matrices | 4707 | 310s | 0.34% |
+| Assemble temperature rhs | 47045 | 8.7e+03s | 9.5% |
+| Build Stokes preconditioner | 4707 | 1.48e+03s | 1.6% |
+| Solve Stokes system | 47045 | 7.34e+04s | 80% |
+| Solve temperature system | 47045 | 1.46e+03s | 1.6% |
+| Postprocessing | 1883 | 222s | 0.24% |
+| Refine mesh structure, part 1 | 4706 | 641s | 0.7% |
+| Refine mesh structure, part 2 | 4706 | 259s | 0.28% |
+| Setup dof systems | 4707 | 1.86e+03s | 2% |
+---------------------------------+-----------+------------+------------+
</pre>
</code>
-The simulation terminates when the time reaches the 100 million years
+The simulation terminates when the time reaches the 1 billion years
selected in the input file. You can extrapolate from this how long a
simulation would take for a different final time (the time step size
ultimately settles on somewhere around 20,000 years, so computing for
-one billion years will take 50,000 time steps, give or take 20%). As
+two billion years will take 100,000 time steps, give or take 20%). As
can be seen here, we spend most of the compute time in assembling
linear systems and — above all — in solving Stokes
systems.
-We can clearly not show all output files produced by this program when
-run for a longer period of time, so let us
-only show the output from every 2500th time step here (these figures
-are from a version of this tutorial program before the introduction of
-manifolds, when it was not yet possible to arrange vertices along
-circles; the figures may therefore look slightly different if you run
-the current version):
-<table>
- <tr>
- <td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.0000.png" alt="">
- </td>
-
- <td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.0100.png" alt="">
- </td>
-
- <td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.0200.png" alt="">
- </td>
- </tr>
-
- <tr>
- <td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.0300.png" alt="">
- </td>
-
- <td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.0400.png" alt="">
- </td>
-
- <td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.0500.png" alt="">
- </td>
- </tr>
-
- <tr>
- <td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.0600.png" alt="">
- </td>
-
- <td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.0700.png" alt="">
- </td>
-
- <td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.0800.png" alt="">
- </td>
- </tr>
+To demonstrate the output we show the output from every 1250th time step here:
+<table>
<tr>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.0900.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-000.png" alt="">
</td>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.1000.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-050.png" alt="">
</td>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.1100.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-100.png" alt="">
</td>
</tr>
<tr>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.1200.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-150.png" alt="">
</td>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.1300.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-200.png" alt="">
</td>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.1400.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-250.png" alt="">
</td>
</tr>
<tr>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.1500.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-300.png" alt="">
</td>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.1600.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-350.png" alt="">
</td>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.1700.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-400.png" alt="">
</td>
</tr>
<tr>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.1800.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-450.png" alt="">
</td>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.1900.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-500.png" alt="">
</td>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.2000.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-550.png" alt="">
</td>
</tr>
-
<tr>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.temperature.2100.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-time-600.png" alt="">
</td>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.grid.2100.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-cells.png" alt="">
</td>
<td>
- <img src="https://www.dealii.org/images/steps/developer/step-32.2d.partition.2100.png" alt="">
+ <img src="https://www.dealii.org/images/steps/developer/step-32-2d-partition.png" alt="">
</td>
</tr>
</table>
-The last two images show the grid as well as the partitioning of the
-mesh for a computation with 10 subdomains on 10 processors. The full dynamics
-of this simulation are really only visible by looking at
-an animation, for example the one <a
-href="http://www.math.colostate.edu/~bangerth/images/pictures/convection-outward/\step-32.2d.convection.gif">shown on
-this site</a>. Beware that this animation is
-about 20MB large, though it is well worth watching due to its almost
-artistic quality.
+The last two images show the grid as well as the partitioning of the mesh for
+the same computation with 16 subdomains and 16 processors. The full dynamics of
+this simulation are really only visible by looking at an animation, for example
+the one <a
+href="https://www.dealii.org/images/steps/developer/step-32-2d-temperature.webm">shown
+on this site</a>. This image is well worth watching due to its artistic quality
+and entrancing depiction of the evolution of the magma plumes.
If you watch the movie, you'll see that the convection pattern goes
through several stages: First, it gets rid of the instable temperature
projects / dealii.git / commitdiff