]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
Get rid of unneeded pictures. Write the results section.
authorbangerth <bangerth@0785d39b-7218-0410-832d-ea1e28bc413d>
Mon, 13 Feb 2012 10:08:33 +0000 (10:08 +0000)
committerbangerth <bangerth@0785d39b-7218-0410-832d-ea1e28bc413d>
Mon, 13 Feb 2012 10:08:33 +0000 (10:08 +0000)
git-svn-id: https://svn.dealii.org/trunk@25058 0785d39b-7218-0410-832d-ea1e28bc413d

37 files changed:
deal.II/examples/step-41/doc/results.dox
deal.II/examples/step-41/doc/step-41.active-set.01.png [deleted file]
deal.II/examples/step-41/doc/step-41.active-set.02.png [deleted file]
deal.II/examples/step-41/doc/step-41.active-set.04.png [deleted file]
deal.II/examples/step-41/doc/step-41.active-set.05.png [deleted file]
deal.II/examples/step-41/doc/step-41.active-set.07.png [deleted file]
deal.II/examples/step-41/doc/step-41.active-set.08.png [deleted file]
deal.II/examples/step-41/doc/step-41.active-set.10.png [deleted file]
deal.II/examples/step-41/doc/step-41.active-set.11.png [deleted file]
deal.II/examples/step-41/doc/step-41.active-set.13.png [deleted file]
deal.II/examples/step-41/doc/step-41.active-set.14.png [deleted file]
deal.II/examples/step-41/doc/step-41.active-set.16.png [deleted file]
deal.II/examples/step-41/doc/step-41.active-set.17.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.01.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.02.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.04.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.05.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.07.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.08.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.10.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.11.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.13.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.14.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.16.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.17.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.3d.01.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.3d.02.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.3d.04.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.3d.05.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.3d.07.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.3d.08.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.3d.10.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.3d.11.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.3d.13.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.3d.14.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.3d.16.png [deleted file]
deal.II/examples/step-41/doc/step-41.displacement.3d.17.png [deleted file]

index f4c6feefb5b45452a5c65244ed85a736a8fb7390..15abbbf7de442c2bed2d2543bc069f140cff0c96 100644 (file)
@@ -1 +1,193 @@
 <h1>Results</h1>
+
+Running the program produces output like this:
+@code
+Number of active cells: 16384
+Total number of cells: 21845
+Number of degrees of freedom: 16641
+
+Newton iteration 0
+   Assembling system...
+   Solving system...
+      Error: 0.310059 -> 5.16619e-05 in 5 CG iterations.
+   Updating active set...
+      Size of active set: 13164
+   Residual of the non-contact part of the system: 1.61863e-05
+   Writing graphical output...
+
+Newton iteration 1
+   Assembling system...
+   Solving system...
+      Error: 1.11987 -> 0.00109377 in 6 CG iterations.
+   Updating active set...
+      Size of active set: 12363
+   Residual of the non-contact part of the system: 3.9373
+   Writing graphical output...
+
+...
+
+Newton iteration 17
+   Assembling system...
+   Solving system...
+      Error: 0.00713308 -> 2.29249e-06 in 4 CG iterations.
+   Updating active set...
+      Size of active set: 5399
+   Residual of the non-contact part of the system: 0.000957525
+   Writing graphical output...
+
+Newton iteration 18
+   Assembling system...
+   Solving system...
+      Error: 0.000957525 -> 2.8033e-07 in 4 CG iterations.
+   Updating active set...
+      Size of active set: 5399
+   Residual of the non-contact part of the system: 2.8033e-07
+   Writing graphical output...
+@endcode
+
+The iterations end once the active set doesn't change any more (it has
+5,399 constrained degrees of freedom at that point). More revealing is
+to look at a sequence of graphical output files (every third step is
+shown, with the number of the iteration in the leftmost column):
+
+<table align="center">
+  <tr>
+    <td valign="top">
+      0 &nbsp;
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.00.png
+    </td>
+    <td valign="top">
+      @image html step-41.active-set.00.png
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.3d.00.png
+    </td>
+  </tr>
+
+  <tr>
+    <td valign="top">
+      3 &nbsp;
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.03.png
+    </td>
+    <td valign="top">
+      @image html step-41.active-set.03.png
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.3d.03.png
+    </td>
+  </tr>
+
+  <tr>
+    <td valign="top">
+      6 &nbsp;
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.06.png
+    </td>
+    <td valign="top">
+      @image html step-41.active-set.06.png
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.3d.06.png
+    </td>
+  </tr>
+
+  <tr>
+    <td valign="top">
+      9 &nbsp;
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.09.png
+    </td>
+    <td valign="top">
+      @image html step-41.active-set.09.png
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.3d.09.png
+    </td>
+  </tr>
+
+  <tr>
+    <td valign="top">
+      12 &nbsp;
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.12.png
+    </td>
+    <td valign="top">
+      @image html step-41.active-set.12.png
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.3d.12.png
+    </td>
+  </tr>
+
+  <tr>
+    <td valign="top">
+      15 &nbsp;
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.15.png
+    </td>
+    <td valign="top">
+      @image html step-41.active-set.15.png
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.3d.15.png
+    </td>
+  </tr>
+
+  <tr>
+    <td valign="top">
+      18 &nbsp;
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.18.png
+    </td>
+    <td valign="top">
+      @image html step-41.active-set.18.png
+    </td>
+    <td valign="top">
+      @image html step-41.displacement.3d.18.png
+    </td>
+  </tr>
+</table>
+
+The pictures show that in the first step, the solution (which has been
+computed without any of the constraints active) bends through so much
+that pretty much every interior point has to be bounced back to the
+stairstep function, producing a discontinuous solution. Over the
+course of the active set iterations, this unphysical membrane shape is
+smoothed out, the contact with the lower-most stair step disappears,
+and the solution stabilizes.
+
+
+<a name="extensions"></a>
+<h3>Possibilities for extensions</h3>
+
+As with any of the programs of this tutorial, there are a number of
+obvious possibilities for extensions and experiments. The first one is
+clear: introduce adaptivity. Contact problems are prime candidates for
+adaptive meshes because the solution has lines along which it is less
+regular (the places where contact is established between membrane and
+obstacle) and other areas where the solution is very smooth (or, in
+the present context, constant wherever it is in contact with the
+obstacle). Adding this to the current program should not pose too many
+difficulties.
+
+A more challenging task would be an extension to 3d. The problem here
+is not so much to simply make everything run in 3d. Rather, it is that
+when a 3d body is deformed and gets into contact with an obstacle,
+then the obstacle does not act as a constraining body force within the
+domain as is the case here. Rather, the contact force only acts on the
+boundary of the object. The inequality then is not in the differential
+equation but in fact in the (Neumann-type) boundary conditions, though
+this leads to a similar kind of variational
+inequality. Mathematically, this means that the Lagrange multiplier
+only lives on the surface, though it can of course be extended by zero
+into the domain if that is convenient. As in the current program, one
+does not need to form and store this Lagrange multiplier explicitly.
diff --git a/deal.II/examples/step-41/doc/step-41.active-set.01.png b/deal.II/examples/step-41/doc/step-41.active-set.01.png
deleted file mode 100644 (file)
index a17098d..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.active-set.01.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.active-set.02.png b/deal.II/examples/step-41/doc/step-41.active-set.02.png
deleted file mode 100644 (file)
index 8377723..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.active-set.02.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.active-set.04.png b/deal.II/examples/step-41/doc/step-41.active-set.04.png
deleted file mode 100644 (file)
index 6da88c0..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.active-set.04.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.active-set.05.png b/deal.II/examples/step-41/doc/step-41.active-set.05.png
deleted file mode 100644 (file)
index 2fec90e..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.active-set.05.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.active-set.07.png b/deal.II/examples/step-41/doc/step-41.active-set.07.png
deleted file mode 100644 (file)
index 3343a9f..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.active-set.07.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.active-set.08.png b/deal.II/examples/step-41/doc/step-41.active-set.08.png
deleted file mode 100644 (file)
index 0da55c1..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.active-set.08.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.active-set.10.png b/deal.II/examples/step-41/doc/step-41.active-set.10.png
deleted file mode 100644 (file)
index 43fe75f..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.active-set.10.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.active-set.11.png b/deal.II/examples/step-41/doc/step-41.active-set.11.png
deleted file mode 100644 (file)
index 8be8e59..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.active-set.11.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.active-set.13.png b/deal.II/examples/step-41/doc/step-41.active-set.13.png
deleted file mode 100644 (file)
index 84eec2e..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.active-set.13.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.active-set.14.png b/deal.II/examples/step-41/doc/step-41.active-set.14.png
deleted file mode 100644 (file)
index 6a712ea..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.active-set.14.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.active-set.16.png b/deal.II/examples/step-41/doc/step-41.active-set.16.png
deleted file mode 100644 (file)
index 0ca08b6..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.active-set.16.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.active-set.17.png b/deal.II/examples/step-41/doc/step-41.active-set.17.png
deleted file mode 100644 (file)
index 29b2929..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.active-set.17.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.01.png b/deal.II/examples/step-41/doc/step-41.displacement.01.png
deleted file mode 100644 (file)
index 924fd28..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.01.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.02.png b/deal.II/examples/step-41/doc/step-41.displacement.02.png
deleted file mode 100644 (file)
index bd866d4..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.02.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.04.png b/deal.II/examples/step-41/doc/step-41.displacement.04.png
deleted file mode 100644 (file)
index 487b54a..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.04.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.05.png b/deal.II/examples/step-41/doc/step-41.displacement.05.png
deleted file mode 100644 (file)
index 3f36962..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.05.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.07.png b/deal.II/examples/step-41/doc/step-41.displacement.07.png
deleted file mode 100644 (file)
index 3b8d04d..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.07.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.08.png b/deal.II/examples/step-41/doc/step-41.displacement.08.png
deleted file mode 100644 (file)
index c038127..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.08.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.10.png b/deal.II/examples/step-41/doc/step-41.displacement.10.png
deleted file mode 100644 (file)
index b03cb40..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.10.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.11.png b/deal.II/examples/step-41/doc/step-41.displacement.11.png
deleted file mode 100644 (file)
index 4c93791..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.11.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.13.png b/deal.II/examples/step-41/doc/step-41.displacement.13.png
deleted file mode 100644 (file)
index ebf423e..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.13.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.14.png b/deal.II/examples/step-41/doc/step-41.displacement.14.png
deleted file mode 100644 (file)
index 7bc23a0..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.14.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.16.png b/deal.II/examples/step-41/doc/step-41.displacement.16.png
deleted file mode 100644 (file)
index 17dd2d8..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.16.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.17.png b/deal.II/examples/step-41/doc/step-41.displacement.17.png
deleted file mode 100644 (file)
index 28452c4..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.17.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.3d.01.png b/deal.II/examples/step-41/doc/step-41.displacement.3d.01.png
deleted file mode 100644 (file)
index 1071335..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.3d.01.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.3d.02.png b/deal.II/examples/step-41/doc/step-41.displacement.3d.02.png
deleted file mode 100644 (file)
index 6182728..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.3d.02.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.3d.04.png b/deal.II/examples/step-41/doc/step-41.displacement.3d.04.png
deleted file mode 100644 (file)
index f6223ba..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.3d.04.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.3d.05.png b/deal.II/examples/step-41/doc/step-41.displacement.3d.05.png
deleted file mode 100644 (file)
index a59a728..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.3d.05.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.3d.07.png b/deal.II/examples/step-41/doc/step-41.displacement.3d.07.png
deleted file mode 100644 (file)
index a815c98..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.3d.07.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.3d.08.png b/deal.II/examples/step-41/doc/step-41.displacement.3d.08.png
deleted file mode 100644 (file)
index 6639470..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.3d.08.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.3d.10.png b/deal.II/examples/step-41/doc/step-41.displacement.3d.10.png
deleted file mode 100644 (file)
index d559319..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.3d.10.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.3d.11.png b/deal.II/examples/step-41/doc/step-41.displacement.3d.11.png
deleted file mode 100644 (file)
index 3e28e7f..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.3d.11.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.3d.13.png b/deal.II/examples/step-41/doc/step-41.displacement.3d.13.png
deleted file mode 100644 (file)
index 12eed29..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.3d.13.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.3d.14.png b/deal.II/examples/step-41/doc/step-41.displacement.3d.14.png
deleted file mode 100644 (file)
index 4478829..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.3d.14.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.3d.16.png b/deal.II/examples/step-41/doc/step-41.displacement.3d.16.png
deleted file mode 100644 (file)
index 0940d35..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.3d.16.png and /dev/null differ
diff --git a/deal.II/examples/step-41/doc/step-41.displacement.3d.17.png b/deal.II/examples/step-41/doc/step-41.displacement.3d.17.png
deleted file mode 100644 (file)
index 8b653cf..0000000
Binary files a/deal.II/examples/step-41/doc/step-41.displacement.3d.17.png and /dev/null differ

In the beginning the Universe was created. This has made a lot of people very angry and has been widely regarded as a bad move.

Douglas Adams


Typeset in Trocchi and Trocchi Bold Sans Serif.