]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
Doxygenize
authorwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Tue, 28 Mar 2006 14:45:58 +0000 (14:45 +0000)
committerwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Tue, 28 Mar 2006 14:45:58 +0000 (14:45 +0000)
git-svn-id: https://svn.dealii.org/trunk@12716 0785d39b-7218-0410-832d-ea1e28bc413d

26 files changed:
deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/error.gif [deleted file]
deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/intro.dox [moved from deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/intro.html with 95% similarity]
deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/pix-kelly/grid-kelly-8.gif [deleted file]
deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/pix-kelly/solution-kelly-0.jpg [deleted file]
deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/pix-kelly/solution-kelly-1.jpg [deleted file]
deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/pix-kelly/solution-kelly-2.jpg [deleted file]
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deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/pix-kelly/solution-kelly-4.jpg [deleted file]
deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/pix-kelly/solution-kelly-5.jpg [deleted file]
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deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/results.dox [moved from deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/results.html with 76% similarity]
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deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/step-13.grid-kelly-8.png [new file with mode: 0644]
deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/step-13.solution-kelly-0.png [new file with mode: 0644]
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/error.gif b/deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/error.gif
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rename from deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/intro.html
rename to deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/intro.dox
index cd167e2b26748411c5a5407e1a83ca7a4de1943d..7362602221836eb4e32e53be527662103282ed7d 100644 (file)
@@ -3,7 +3,7 @@
 
 <h3>Background and purpose</h3>
 
-<p>
+
 In this example program, we will not so much be concerned with
 describing new ways how to use deal.II and its facilities, but rather
 with presenting methods of writing modular and extensible finite
@@ -21,13 +21,13 @@ program:
 <li> a wave equation solver: 21,020 lines of code.
 </ol>
 (The library proper - without example programs and
-test suite - has slightly more than 150,000 lines of code.) In
-the opinion of the author of this example program, the sizes of these
+test suite - has slightly more than 150,000 lines of code as of spring 2002.)
+In the opinion of the author of this example program, the sizes of these
 applications are at the edge of what one person, even an experienced
 programmer, can manage. 
-</p>
 
-<p>
+
+
 The numbers above make one thing rather clear: monolithic programs that
 are not broken up into smaller, mostly independent pieces have no way
 of surviving, since even the author will quickly lose the overview of
@@ -39,9 +39,9 @@ absolute prerequisite if more than one person is developing a program,
 since otherwise confusion will quickly prevail as one developer
 would need to know if another changed something about the internals of
 a different module if they were not cleanly separated.
-</p>
 
-<p>
+
+
 In previous examples, you have seen how the library itself is broken
 up into several complexes each building atop the underying ones, but
 relatively independent of the other ones:
@@ -60,10 +60,10 @@ course the following ``tool'' modules:
 <li>output in various graphical formats;
 <li>linear algebra classes.
 </ol>
-</p>
 
 
-<p>
+
+
 The goal of this program is now to give an example of how a relatively
 simple finite element program could be structured such that we end up
 with a set of modules that are as independent of each other as
@@ -71,9 +71,9 @@ possible. This allows to change the program at one end, without having to
 worry that it might break at the other, as long as we do not touch the
 interface through which the two ends communicate. The interface in
 C++, of course, is the declaration of abstract base classes.
-</p>
 
-<p>
+
+
 Here, we will implement (again) a Laplace solver, although with a
 number of differences compared to previous example programs:
 <ol>
@@ -106,9 +106,9 @@ number of differences compared to previous example programs:
 <li>Separate the description of the test case with which we will
     present the program, from the rest of the program.
 </ol>
-</p>
 
-<p>
+
+
 The things the program does are not new. In fact, this is more like a
 melange of previous programs, cannibalizing various parts and
 functions from earlier examples. It is the way they are arranged in
@@ -123,9 +123,9 @@ practice, and is not necessarily a style that you have to adopt in
 order to write successful numerical software if you feel uncomfortable
 with the chosen ways. It should serve as a case study, however,
 inspiring the reader with ideas to the desired end.
-</p>
 
-<p>
+
+
 Once you have worked through the program, you will remark that it is
 already somewhat complex in its structure. Nevertheless, it
 only has about 850 lines of code, without comments. In real
@@ -136,9 +136,9 @@ the applications listed above, this is still small, as they are 20 to
 the start is thus indispensible. Otherwise, it will have to be
 redesigned at one point in its life, once it becomes too large to be
 manageable.
-</p>
 
-<p>
+
+
 Despite of this, all three programs listed above have undergone major
 revisions, or even rewrites. The wave program, for example, was once
 entirely teared to parts when it was still significantly smaller, just
@@ -154,34 +154,34 @@ without flaws in its design, and in particular might not be suited for
 an application where the objective is different. It should serve as an
 inspiration for writing your own application in a modular way, to
 avoid the pitfalls of too closely coupled codes.
-</p>
+
 
 
 <h3>What the program does</h3>
 
-<p>
+
 What the program actually does is not even the main point of this
 program, the structure of the program is more important. However, in a
 few words, a description would be: solve the Laplace equation for a
 given right hand side such that the solution is the function 
-  <em> u(x,t)=exp(x+sin(10y+5x<sup>2</sup>)) </em>. The goal of the
+$u(x,t)=\exp(x+\sin(10y+5x^2))$. The goal of the
 computation is to get the value of the solution at the point
-<em>x<sub>0</sub>=(0.5,0.5)</em>, and to compare the accuracy with
+$x_0=(0.5,0.5)$, and to compare the accuracy with
 which we resolve this value for two refinement criteria, namely global
 refinement and refinement by the error indicator by Kelly et al. which
 we have already used in previous examples.
-</p>
 
-<p>
+
+
 The results will, as usual, be discussed in the respective section of
 this document. In doing so, we will find a slightly irritating
 observation about the relative performance of the two refinement
 criteria. In a later example program, building atop this one, we will
 devise a different method that should hopefully perform better than
 the techniques discussed here.
-</p>
 
-<p>
+
+
 So much now for all the theoretical and anecdotal background. The best
 way of learning about a program is to look at it, so here it is:
-</p>
+
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rename from deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/results.html
rename to deal.II/doc/tutorial/chapter-2.step-by-step/step-13.data/results.dox
index 66b921aab8c684fa9312c96ed3ad4350521a947f..c45718de00b7d1af6402dfecd823b6ad205ae2f1 100644 (file)
@@ -2,22 +2,21 @@
 <h1>Results</h1>
 
 
-<p>
+
 The results of this program are not that interesting - after all
 its purpose was not to demonstrate some new mathematical idea, and
 also not how to program with deal.II, but rather to use the material
 which we have developed in the previous examples to form something
 which demonstrates a way to build modern finite element software in a
 modular and extensible way.
-</p>
 
-<p>
+
+
 Nevertheless, we of course show the results of the program. Of
 foremost interest is the point value computation, for which we had
 implemented the corresponding evaluation class. The results (i.e. the
 output) of the program looks as follows:
-<code>
-<pre>
+@code
     Running tests with "global" refinement criterion:
     -------------------------------------------------
     Refinement cycle: 0 1 2 3 4 5 6
@@ -46,124 +45,107 @@ output) of the program looks as follows:
      7100 1.5876
     13059 1.5942
     24749 1.5933
-</pre>
-</code>
-</p>
+@endcode
+
 
-<p>
 What surprises here is that the the exact value is 1.59491554..., and that
 it is obviously suprisingly complicated to compute the solution even to
 only one per cent accuracy, although the solution is smooth (in fact
 infinite often differentiable). This smoothness is shown in the
 graphical output generated by the program, here coarse grid and the
 first 9 refinement steps of the Kelly refinement indicator:
-</p>
+
 
 <table width="80%" align="center">
   <tr>
     <td>
-      <img src="step-13.data/pix-kelly/solution-kelly-0.jpg" 
-       alt="Solution Kelly, coarse grid">
+      @image html step-13.solution-kelly-0.png
     </td>
     <td>
-      <img src="step-13.data/pix-kelly/solution-kelly-1.jpg" 
-       alt="Solution Kelly, 1 refinement steps">
+      @image html step-13.solution-kelly-1.png
     </td>
   </tr>
 
   <tr>
     <td>
-      <img src="step-13.data/pix-kelly/solution-kelly-2.jpg" 
-       alt="Solution Kelly, 2 refinement steps">
+      @image html step-13.solution-kelly-2.png
     </td>
     <td>
-      <img src="step-13.data/pix-kelly/solution-kelly-3.jpg" 
-       alt="Solution Kelly, 3 refinement steps">
+      @image html step-13.solution-kelly-3.png
     </td>
   </tr>
 
   <tr>
     <td>
-      <img src="step-13.data/pix-kelly/solution-kelly-4.jpg" 
-       alt="Solution Kelly, 4 refinement steps">
+      @image html step-13.solution-kelly-4.png
     </td>
     <td>
-      <img src="step-13.data/pix-kelly/solution-kelly-5.jpg" 
-       alt="Solution Kelly, 5 refinement steps">
+      @image html step-13.solution-kelly-5.png
     </td>
   </tr>
 
   <tr>
     <td>
-      <img src="step-13.data/pix-kelly/solution-kelly-6.jpg" 
-       alt="Solution Kelly, 6 refinement steps">
+      @image html step-13.solution-kelly-6.png
     </td>
     <td>
-      <img src="step-13.data/pix-kelly/solution-kelly-7.jpg" 
-       alt="Solution Kelly, 7 refinement steps">
+      @image html step-13.solution-kelly-7.png
     </td>
   </tr>
 
   <tr>
     <td>
-      <img src="step-13.data/pix-kelly/solution-kelly-8.jpg" 
-       alt="Solution Kelly, 8 refinement steps">
+      @image html step-13.solution-kelly-8.png
     </td>
     <td>
-      <img src="step-13.data/pix-kelly/solution-kelly-9.jpg" 
-       alt="Solution Kelly, 9 refinement steps">
+      @image html step-13.solution-kelly-9.png
     </td>
   </tr>
 </table>
 
-<p>
+
 While we're already at watching pictures, this is the eighth grid, as
 viewed from top:
-</p>
 
-<p align="center">
-  <img src="step-13.data/pix-kelly/grid-kelly-8.gif" alt="Kelly, grid 8">
-</p>
 
+@image html step-13.kelly-grid-8.png
 
 
-<p>
 However, we are not yet finished with evaluation the point value
 computation. In fact, plotting the error
-<em>e=|u(x<sub>h</sub>)-u<sub>h</sub>(x<sub>0</sub>)|</em> for the two
+$e=|u(x_0)-u_h(x_0)|$ for the two
 refinement criteria yields the following picture:
-</p>
 
-<p align="center">
-  <img src="step-13.data/error.gif" alt="error" width="80%">
-</p>
+
+@image html step-13.error.png
+
+
 
 
-<p>
 What <em>is</em> disturbing about this picture is that not only is the
 adaptive mesh refinement not better than global refinement as one
 would usually expect, it is even significantly worse since its
 convergence is irregular, preventing all extrapolation techniques when
 using the values of subsequent meshes! On the other hand, global
-refinement provides a perfect <em>1/N</em> or <em>h<sup>-2</sup></em>
+refinement provides a perfect $1/N$ or $h^{-2}$
 convergence history and provides every opportunity to even improve on
 the point values by extrapolation. Global mesh refinement must
 therefore be considered superior in this example! This is even more
 surprising as the evaluation point is not somewhere in the left part
 where the mesh is coarse, but rather to the right and the adaptive
 refinement should refine the mesh around the evaluation point as well.
-</p>
 
-<p>
+
+
 We thus close the discussion of this example program with a question:
-</p>
+
 <p align="center">
   <strong><em>What is wrong with adaptivity if it is not better than
   global refinement?</em></strong>
-</p>
 
 
-<p>
+
+
 <em>Exercise at the end of this example:</em> There is a simple reason
 for the bad and irregular behavior of the adapted mesh solutions. It
 is simple to find out by looking at the mesh around the evaluation
@@ -174,15 +156,15 @@ avoided. The second exercise is to check whether the results are then
 better than global refinement, and if so if even a better order of
 convergence (in terms of the number of degrees of freedom) is
 achieved, or only by a better constant.
-</p>
 
-<p>
+
+
 (<em>Very brief answers for the impatient:</em> at steps with larger
 errors, the mesh is not regular at the point of evaluation, i.e. some
 of the adjacent cells have hanging nodes; this destroys some
 superapproximation effects of which the globally refined mesh can
 profit. Answer 2: this quick hack
-<code><pre>
+@code
     bool refinement_indicated = false;
     typename Triangulation<dim>::active_cell_iterator cell;
     for (cell=triangulation->begin_active();
@@ -199,10 +181,10 @@ profit. Answer 2: this quick hack
        for (unsigned int v=0; v<GeometryInfo<dim>::vertices_per_cell; ++v)
          if (cell->vertex(v) == Point<dim>(.5,.5))
            cell->set_refine_flag ();
-</pre></code>
+@endcode
 in the refinement function of the Kelly refinement class right before
 executing refinement would improve the results (exercise: what does
 the code do?), making them consistently better than global
 refinement. Behavior is still irregular, though, so no results about
 an order of convergence are possible.)
-</p>
+
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