Update step-10 for 9.0.

This commit changes the output (which was altered as a result of the new
TFI scheme for placing new vertices) and the manifold handling (which
was altered by the 'attach default manifolds to triangulations' change
in GridGenerator).

diff --git a/doc/doxygen/stylesheet.css b/doc/doxygen/stylesheet.css
index 9f4191b68b1c25188904d83feea5fb3119ba5de7..9e4f9f201f7f4b5bfe14c14277c094cd7f421cb1 100644 (file)
--- a/doc/doxygen/stylesheet.css
+++ b/doc/doxygen/stylesheet.css
@@ -45,3 +45,15 @@ div.image img[src="fe_enriched_1d.png"] {
 div.image img[src="fe_enriched_h-refinement.png"] {
     width:500px;
 }
+
+/*
+ * environment for aligning pictures in two columns.
+ */
+.twocolumn {
+  display: grid;
+  grid-template-columns: 1fr 1fr;
+  grid-column-gap: 5%;
+  grid-row-gap: 5%;
+  margin-left: auto;
+  margin-right: auto;
+}

diff --git a/examples/step-10/doc/results.dox b/examples/step-10/doc/results.dox
index a81bf44e410174ef0143664c039e0caa991b6f01..7f4a5c6b3447591a003140416ebca4818630d03a 100644 (file)
--- a/examples/step-10/doc/results.dox
+++ b/examples/step-10/doc/results.dox
@@ -8,54 +8,58 @@ graphics. They are generated in Gnuplot format, and can be viewed with
 the commands
 @code
 set style data lines
-set size 0.721, 1
+set size ratio -1
 unset key
-plot [-1:1][-1:1] "ball_0_mapping_q_1.dat"
+unset xtics
+unset ytics
+plot [-1:1][-1:1] "ball_0_mapping_q_1.dat" lw4 lt rgb "black"
 @endcode
 or using one of the other filenames. The second line makes sure that
 the aspect ratio of the generated output is actually 1:1, i.e. a
 circle is drawn as a circle on your screen, rather than as an
 ellipse. The third line switches off the key in the graphic, as that
 will only print information (the filename) which is not that important
-right now.
-
-
-
-The following table shows the triangulated computational domain for
-Q1, Q2, and Q3 mappings, for the original coarse grid (left), and a
-once uniformly refined grid (right). If your browser does not display
-these pictures in acceptable quality, view them one by one.
-
-<table style="width:80%" align="center">
-  <tr>
-    <td><img src="https://www.dealii.org/images/steps/developer/step-10.ball_mapping_q1_ref0.png" alt=""></td>
-    <td><img src="https://www.dealii.org/images/steps/developer/step-10.ball_mapping_q1_ref1.png" alt=""></td>
-  </tr>
-
-  <tr>
-    <td><img src="https://www.dealii.org/images/steps/developer/step-10.ball_mapping_q2_ref0.png" alt=""></td>
-    <td><img src="https://www.dealii.org/images/steps/developer/step-10.ball_mapping_q2_ref1.png" alt=""></td>
-  </tr>
-
-  <tr>
-    <td><img src="https://www.dealii.org/images/steps/developer/step-10.ball_mapping_q3_ref0.png" alt=""></td>
-    <td><img src="https://www.dealii.org/images/steps/developer/step-10.ball_mapping_q3_ref1.png" alt=""></td>
-  </tr>
-</table>
-
-These pictures show the obvious advantage of higher order mappings:
-they approximate the true boundary quite well also on rather coarse
-meshes. To demonstrate this a little further, the following table
-shows the upper right quarter of the circle of the coarse mesh, and
-with dashed lines the exact circle:
-
-<table style="width:80%" align="center">
-  <tr>
-    <td><img src="https://www.dealii.org/images/steps/developer/step-10.quarter-q1.png" alt=""></td>
-    <td><img src="https://www.dealii.org/images/steps/developer/step-10.quarter-q2.png" alt=""></td>
-    <td><img src="https://www.dealii.org/images/steps/developer/step-10.quarter-q3.png" alt=""></td>
-  </tr>
-</table>
+right now. Similarly, the third and fourth disable tic marks.
+
+The following table shows the triangulated computational domain for $Q_1$,
+$Q_2$, and $Q_3$ mappings, for the original coarse grid (left), and a once
+uniformly refined grid (right).
+
+<div class="twocolumn" style="width: 80%">
+  <div>
+    <img src="https://www.dealii.org/images/steps/developer/step_10_ball_0_q1.svg">
+  </div>
+  <div>
+    <img src="https://www.dealii.org/images/steps/developer/step_10_ball_1_q1.svg">
+  </div>
+  <div>
+    <img src="https://www.dealii.org/images/steps/developer/step_10_ball_0_q2.svg">
+  </div>
+  <div>
+    <img src="https://www.dealii.org/images/steps/developer/step_10_ball_1_q2.svg">
+  </div>
+  <div>
+    <img src="https://www.dealii.org/images/steps/developer/step_10_ball_0_q3.svg">
+  </div>
+  <div>
+    <img src="https://www.dealii.org/images/steps/developer/step_10_ball_1_q3.svg">
+  </div>
+</div>
+
+These pictures show the obvious advantage of higher order mappings: they
+approximate the true boundary quite well also on rather coarse meshes. To
+demonstrate this a little further, here is part of the upper right quarter
+circle of the coarse meshes with $Q_2$ and $Q_3$ mappings, where the dashed
+red line marks the actual circle:
+
+<div class="twocolumn" style="width: 80%">
+  <div>
+    <img src="https://www.dealii.org/images/steps/developer/step_10_exact_vs_interpolate_q2.svg">
+  </div>
+  <div>
+    <img src="https://www.dealii.org/images/steps/developer/step_10_exact_vs_interpolate_q3.svg">
+  </div>
+</div>
 
 Obviously the quadratic mapping approximates the boundary quite well,
 while for the cubic mapping the difference between approximated domain
@@ -73,81 +77,93 @@ cells.
 The second purpose of the program was to compute the value of pi to
 good accuracy. This is the output of this part of the program:
 @code
+Output of grids into gnuplot files:
+===================================
+Refinement level: 0
+Degree = 1
+Degree = 2
+Degree = 3
+
+Refinement level: 1
+Degree = 1
+Degree = 2
+Degree = 3
+
 Computation of Pi by the area:
 ==============================
 Degree = 1
-cells      eval.pi            error      
-    5 1.9999999999999993 1.1416e+00    - 
-   20 2.8284271247461894 3.1317e-01 1.87 
-   80 3.0614674589207178 8.0125e-02 1.97 
-  320 3.1214451522580520 2.0148e-02 1.99 
- 1280 3.1365484905459393 5.0442e-03 2.00 
- 5120 3.1403311569547534 1.2615e-03 2.00 
+cells      eval.pi            error
+    5 1.9999999999999993 1.1416e+00    -
+   20 2.8284271247461890 3.1317e-01 1.87
+   80 3.0614674589207174 8.0125e-02 1.97
+  320 3.1214451522580511 2.0148e-02 1.99
+ 1280 3.1365484905459380 5.0442e-03 2.00
+ 5120 3.1403311569547516 1.2615e-03 2.00
 
 Degree = 2
-cells      eval.pi            error      
-    5 3.1045694996615865 3.7023e-02    - 
-   20 3.1391475703122271 2.4451e-03 3.92 
-   80 3.1414377167038303 1.5494e-04 3.98 
-  320 3.1415829366419015 9.7169e-06 4.00 
- 1280 3.1415920457576911 6.0783e-07 4.00 
- 5120 3.1415926155921139 3.7998e-08 4.00 
+cells      eval.pi            error
+    5 3.1045694996615860 3.7023e-02    -
+   20 3.1391475703122267 2.4451e-03 3.92
+   80 3.1414377167038290 1.5494e-04 3.98
+  320 3.1415829366419006 9.7169e-06 4.00
+ 1280 3.1415920457576898 6.0783e-07 4.00
+ 5120 3.1415926155921117 3.7998e-08 4.00
 
 Degree = 3
-cells      eval.pi            error      
-    5 3.1410033851499310 5.8927e-04    - 
-   20 3.1415830393583861 9.6142e-06 5.94 
-   80 3.1415925017363837 1.5185e-07 5.98 
-  320 3.1415926512106722 2.3791e-09 6.00 
- 1280 3.1415926535525962 3.7197e-11 6.00 
- 5120 3.1415926535892140 5.7923e-13 6.00 
+cells      eval.pi            error
+    5 3.1410033851499288 5.8927e-04    -
+   20 3.1415830393583839 9.6142e-06 5.94
+   80 3.1415925017363797 1.5185e-07 5.98
+  320 3.1415926512106696 2.3791e-09 6.00
+ 1280 3.1415926535525927 3.7200e-11 6.00
+ 5120 3.1415926535892100 5.8302e-13 6.00
 
 Degree = 4
-cells      eval.pi            error       
-    5 3.1415871927401127 5.4608e-06     - 
-   20 3.1415926314742437 2.2116e-08  7.95 
-   80 3.1415926535026228 8.7170e-11  7.99 
-  320 3.1415926535894529 3.4036e-13  8.00 
- 1280 3.1415926535897927 2.9187e-16 10.19 
- 5120 3.1415926535897944 1.3509e-15 -2.21 
+cells      eval.pi            error
+    5 3.1415871927401131 5.4608e-06    -
+   20 3.1415926314742428 2.2116e-08 7.95
+   80 3.1415926535026202 8.7173e-11 7.99
+  320 3.1415926535894498 3.4350e-13 7.99
+ 1280 3.1415926535897896 3.4671e-15 6.63
+ 5120 3.1415926535897909 2.4009e-15 0.53
 
 Computation of Pi by the perimeter:
 ===================================
 Degree = 1
-cells      eval.pi            error      
-    5 2.8284271247461898 3.1317e-01    - 
-   20 3.0614674589207178 8.0125e-02 1.97 
-   80 3.1214451522580520 2.0148e-02 1.99 
-  320 3.1365484905459393 5.0442e-03 2.00 
- 1280 3.1403311569547525 1.2615e-03 2.00 
- 5120 3.1412772509327729 3.1540e-04 2.00 
+cells      eval.pi            error
+    5 2.8284271247461898 3.1317e-01    -
+   20 3.0614674589207178 8.0125e-02 1.97
+   80 3.1214451522580520 2.0148e-02 1.99
+  320 3.1365484905459389 5.0442e-03 2.00
+ 1280 3.1403311569547525 1.2615e-03 2.00
+ 5120 3.1412772509327724 3.1540e-04 2.00
 
 Degree = 2
-cells      eval.pi            error      
-    5 3.1248930668550594 1.6700e-02    - 
-   20 3.1404050605605449 1.1876e-03 3.81 
-   80 3.1415157631807014 7.6890e-05 3.95 
-  320 3.1415878042798617 4.8493e-06 3.99 
- 1280 3.1415923498174534 3.0377e-07 4.00 
- 5120 3.1415926345932004 1.8997e-08 4.00 
+cells      eval.pi            error
+    5 3.1248930668550594 1.6700e-02    -
+   20 3.1404050605605449 1.1876e-03 3.81
+   80 3.1415157631807009 7.6890e-05 3.95
+  320 3.1415878042798613 4.8493e-06 3.99
+ 1280 3.1415923498174534 3.0377e-07 4.00
+ 5120 3.1415926345931995 1.8997e-08 4.00
 
 Degree = 3
-cells      eval.pi            error      
-    5 3.1414940401456057 9.8613e-05    - 
-   20 3.1415913432549156 1.3103e-06 6.23 
-   80 3.1415926341726914 1.9417e-08 6.08 
-  320 3.1415926532906893 2.9910e-10 6.02 
- 1280 3.1415926535851360 4.6571e-12 6.01 
- 5120 3.1415926535897203 7.2845e-14 6.00 
+cells      eval.pi            error
+    5 3.1414940401456048 9.8613e-05    -
+   20 3.1415913432549156 1.3103e-06 6.23
+   80 3.1415926341726910 1.9417e-08 6.08
+  320 3.1415926532906897 2.9910e-10 6.02
+ 1280 3.1415926535851355 4.6578e-12 6.00
+ 5120 3.1415926535897190 7.4216e-14 5.97
 
 Degree = 4
-cells      eval.pi            error      
-    5 3.1415921029432576 5.5065e-07    - 
-   20 3.1415926513737600 2.2160e-09 7.96 
-   80 3.1415926535810712 8.7218e-12 7.99 
-  320 3.1415926535897594 3.3668e-14 8.02 
- 1280 3.1415926535897922 1.0617e-15 4.99 
- 5120 3.1415926535897931 1.0061e-16 3.40 
+cells      eval.pi            error
+    5 3.1415921029432572 5.5065e-07     -
+   20 3.1415926513737595 2.2160e-09  7.96
+   80 3.1415926535810712 8.7222e-12  7.99
+  320 3.1415926535897576 3.5525e-14  7.94
+ 1280 3.1415926535897936 4.6729e-16  6.25
+ 5120 3.1415926535897918 1.4929e-15 -1.68
 @endcode
 
 
@@ -173,4 +189,3 @@ order 2<i>p</i>. Even though these points are here only used for interpolation
 of a <i>p</i>th order polynomial, we get a superconvergence effect when
 numerically evaluating the integral that actually gives this high order of
 convergence.
-

diff --git a/examples/step-10/step-10.cc b/examples/step-10/step-10.cc
index 23eee7aeb7cd89d9645e2896f7f68e48dd1c999d..88469c70f8ab53428233768519e2fff580af05f2 100644 (file)
--- a/examples/step-10/step-10.cc
+++ b/examples/step-10/step-10.cc
@@ -75,15 +75,13 @@ namespace Step10
     std::cout << "Output of grids into gnuplot files:" << std::endl
               << "===================================" << std::endl;
 
-    // So first generate a coarse triangulation of the circle and
-    // associate a suitable boundary description to it. Note that the
-    // default value of the argument to the SphericalManifold
-    // constructor is a center at the origin.
+    // So first generate a coarse triangulation of the circle and associate a
+    // suitable boundary description to it. By default,
+    // GridGenerator::hyper_ball attaches a SphericalManifold to the boundary
+    // (and uses FlatManifold for the interior) so we simply call that
+    // function and move on:
     Triangulation<dim> triangulation;
     GridGenerator::hyper_ball (triangulation);
-    static const SphericalManifold<dim> boundary;
-    triangulation.set_all_manifold_ids_on_boundary(0);
-    triangulation.set_manifold (0, boundary);
 
     // Next generate output for this grid and for a once refined grid. Note
     // that we have hidden the mesh refinement in the loop header, which might
@@ -134,7 +132,7 @@ namespace Step10
             // sufficient to give us the impression of seeing a curved line,
             // rather than a set of straight lines.
             GridOut grid_out;
-            GridOutFlags::Gnuplot gnuplot_flags(false, 30);
+            GridOutFlags::Gnuplot gnuplot_flags(false, 60);
             grid_out.set_flags(gnuplot_flags);
 
             // Finally, generate a filename and a file for output:
@@ -207,10 +205,6 @@ namespace Step10
         Triangulation<dim> triangulation;
         GridGenerator::hyper_ball (triangulation);
 
-        static const SphericalManifold<dim> boundary;
-        triangulation.set_all_manifold_ids_on_boundary (0);
-        triangulation.set_manifold(0, boundary);
-
         const MappingQ<dim> mapping (degree);
 
         // We now create a dummy finite element. Here we could choose any
@@ -344,10 +338,6 @@ namespace Step10
         Triangulation<dim> triangulation;
         GridGenerator::hyper_ball (triangulation);
 
-        static const SphericalManifold<dim> boundary;
-        triangulation.set_all_manifold_ids_on_boundary (0);
-        triangulation.set_manifold (0, boundary);
-
         const MappingQ<dim> mapping (degree);
         const FE_Q<dim>     fe (1);