]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
Add step-3.
authorwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Mon, 20 Dec 1999 14:53:35 +0000 (14:53 +0000)
committerwolf <wolf@0785d39b-7218-0410-832d-ea1e28bc413d>
Mon, 20 Dec 1999 14:53:35 +0000 (14:53 +0000)
git-svn-id: https://svn.dealii.org/trunk@2088 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/doc/tutorial/chapter-2.step-by-step/navbar.html
deal.II/doc/tutorial/chapter-2.step-by-step/step-3.data/solution-1.jpg [new file with mode: 0644]
deal.II/doc/tutorial/chapter-2.step-by-step/step-3.data/solution-2.jpg [new file with mode: 0644]
deal.II/doc/tutorial/chapter-2.step-by-step/step-3.intro [new file with mode: 0644]
deal.II/doc/tutorial/chapter-2.step-by-step/step-3.results [new file with mode: 0644]
deal.II/doc/tutorial/chapter-2.step-by-step/toc.html

index e717a6de485bdcb1788ed013061d91e591efa2a4..a25e1268cba1c99b9015023af3648f7de1f68222 100644 (file)
          <a href="toc.html" target="body">Step-by-Step overview</a>
        </p>
       </li>
+
       <li>
        <p>
          <a href="step-1.html" target="body">Step 1</a>
        </p>
       </li>
+
       <li>
        <p>
          <a href="step-2.html" target="body">Step 2</a>
        </p>
       </li>
+
+      <li>
+       <p>
+         <a href="step-3.html" target="body">Step 3</a>
+       </p>
+      </li>
     </ol>
     <p>
       <a href="../index.html" target="_top">Back to the tutorial index</a>
diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.data/solution-1.jpg b/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.data/solution-1.jpg
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.data/solution-2.jpg b/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.data/solution-2.jpg
new file mode 100644 (file)
index 0000000..15f44e3
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diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.intro b/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.intro
new file mode 100644 (file)
index 0000000..e8f16db
--- /dev/null
@@ -0,0 +1,14 @@
+<a name="Intro"></a>
+<h1>Introduction</h1>
+
+This is the first example, where we actually use finite elements. We
+will solve a simple version of Laplace's equation witht zero boundary
+values, but a nonzero right hand side. This example is still quite
+simple, but it already shows the basic structure of most finite
+element programs, which are along the following lines:
+<ul>
+  <li> grid generation;
+  <li> assembling matrices and vectors of the discrete system;
+  <li> solving the linear system of equations;
+  <li> writing results to disk.
+</ul>
diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.results b/deal.II/doc/tutorial/chapter-2.step-by-step/step-3.results
new file mode 100644 (file)
index 0000000..6815f67
--- /dev/null
@@ -0,0 +1,57 @@
+<a name="Results"></a>
+<h1>Results</h1>
+
+The output of the program looks as follows:
+<pre>
+<code>
+Number of active cells: 1024
+Total number of cells: 1365
+Number of degrees of freedom: 1089
+DEAL:cg::Starting value 0.121094
+DEAL:cg::Starting value 0.323075
+DEAL:cg::Convergence step 47 value 5.33692e-13
+</code>
+</pre>
+
+The first three lines is what we wrote to <code>cout</code>. The last
+three lines were generated without our interaction by the CG
+solver. The first two lines state the residual at the start of the
+iteration, while the last line tells us that the solver needed 47
+iterations to bring the norm of the residual to 5.3e-13, i.e. below
+the threshold 1e-12 which we have set in the `solve' function. We will
+show in the next program how to suppress this output, which is
+sometimes useful for debugging purposes, but often clutters up the
+screen display.
+
+<p>
+
+Apart from the output shown above, the program generated the file
+<code>solution.gpl</code>, which is in GNUPLOT format. It can be
+viewed as follows: invoke GNUPLOT and enter the following sequence of
+commands at its prompt:
+<pre>
+<code>
+gnuplot> set data style lines
+gnuplot> splot "solution.gpl"
+</code>
+</pre>
+This produces the picture of the solution below left. Alternatively,
+you can order GNUPLOT to do some hidden line removal by the command
+<pre>
+<code>
+gnuplot> set hidden3d
+</code>
+</pre>
+to get the result at the right:
+<p>
+<TABLE WIDTH="100%">
+<tr>
+<td>
+<IMG SRC="step-3.data/solution-1.jpg" ALT="solution-1" WIDTH="400">
+</td>
+<td>
+<IMG SRC="step-3.data/solution-2.jpg" ALT="solution-2" WIDTH="400">
+</td>
+</tr>
+</table>
+<p>
index df36f194b5287229d99cb7d2825b55fb903ec141..1e16ec2e09351a26f0f5a7d9795a060a9ab4c2e8 100644 (file)
@@ -40,17 +40,23 @@ At present, the following programs exist:
 
 <dl>
       <dt><a href="step-1.html">Step 1</a></dt> 
-      <dd>What's new: everything. We create a grid and show a simple
+      <dd><strong>What's new:</strong> everything. We create a grid and show a simple
       way to write it to a file.
       </dd>
     
       <dt><a href="step-2.html">Step 2</a></dt> 
-      <dd>What's new: Associate degrees of freedom to each vertex
+      <dd><strong>What's new:</strong> Associate degrees of freedom to each vertex
       and compute the resulting sparsity pattern of matrices. Show
       that renumbering reduces the bandwidth of matrices
       significantly, i.e. clusters nonzero entries around the
       diagonal. 
       </dd>
+
+      <dt><a href="step-3.html">Step 3</a></dt> 
+      <dd><strong>What's new:</strong> Actually solve Laplace's
+      problem. Object-orientation. Assembling matrices and
+      vectors. Boundary values.
+      </dd>
 </dl>
 
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