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<head>
<title>deal.II Development Information</title>
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+ <link href="../screen.css" type="text/css" rel="StyleSheet">
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- <meta name="copyright" content="Copyright (C) 1998, 1999, 2000, 2002, 2003, 2004, 2005 by the deal.II authors">
+ <meta name="copyright" content="Copyright (C) 1998, 1999, 2000, 2002, 2003, 2004, 2005, 2007 by the deal.II authors">
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- <link href="screen.css" rel="StyleSheet" media="screen">
+ <link href="screen.css" rel="StyleSheet" type="text/css">
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<meta name="copyright" content="Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 by the deal.II authors">
<p>
The documentation uses many of the features of Doxygen. In particular,
- the link takes you straight to a page that lists <it>modules</it>, a way
+ the link takes you straight to a page that lists <i>modules</i>, a way
to group classes with similar purposes. This may be what you are probably
interested in when you are not yet familiar with the library. If you
already know your way around and want to look up the signature of a
-->
<title>Step-by-Step Examples</title>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Tutorial" media="screen">
+ <link href="../../screen.css" rel="StyleSheet" type="text/css">
<meta name="author" content="the deal.II authors <authors@dealii.org>">
<meta name="keywords" content="deal.II,deal.II tutorial,deal II">
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-<frameset rows="70,*" border=0>
-
- <frame name="title" src="title.html" frameborder="1">
- <frameset cols="120,*" border=0>
- <frame name="navbar" src="navbar.html" frameborder="0">
- <frame name="body" src="toc.html" frameborder="0">
- </frameset>
-
+<frameset cols="120,*">
+ <frame name="navbar" src="navbar.html" frameborder="0">
+ <frame name="body" src="toc.html" frameborder="0">
</frameset>
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-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
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+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
+"http://www.w3.org/TR/html4/strict.dtd">
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<head>
-<!-- deal.II tutorial template
- Wolfgang Bangerth <deal@iwr.uni-heidelberg.de> 1999
--->
-
<title>Step-by-Step Examples</title>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Tutorial" media="screen">
- <meta name="author" content="the deal.II authors <authors@dealii.org>">
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+ <meta name="author" content="the deal.II authors <authors@dealii.org>">
+ <meta name="copyright" content="Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2008 by the deal.II authors">
+ <meta name="date" content="$Date$">
+ <meta name="svn_id" content="$Id$">
+ <meta name="keywords" content="deal.II,deal.II tutorial,deal II">
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<head>
-<!-- deal.II tutorial template
- Wolfgang Bangerth <deal@iwr.uni-heidelberg.de> 1999
--->
-
<title>Step-by-Step Examples</title>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Tutorial" media="screen">
- <meta name="author" content="the deal.II authors <authors@dealii.org>">
- <meta name="keywords" content="deal.II,deal.II tutorial,deal II">
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+ <link rel="SHORTCUT ICON" href="deal.ico">
+ <meta name="author" content="the deal.II authors <authors@dealii.org>">
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+ <meta name="keywords" content="deal.II,deal.II tutorial,deal II">
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+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
+"http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
-<!-- deal.II tutorial template
- Wolfgang Bangerth <deal@iwr.uni-heidelberg.de> 1999
--->
-
<title>Step-by-Step</title>
- <link href="../../screen.css" rel="StyleSheet" title="deal.II Tutorial" media="screen">
- <meta name="author" content="the deal.II authors <authors@dealii.org>">
- <meta name="keywords" content="deal.II,deal.II tutorial,deal II">
+ <meta name="author" content="the deal.II authors <authors@dealii.org>">
+ <meta name="copyright" content="Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2008 by the deal.II authors">
+ <meta name="date" content="$Date$">
+ <meta name="svn_id" content="$Id$">
+ <meta name="keywords" content="deal.II,deal.II tutorial,deal II">
</head>
<!-- Page Body -->
programs, each more
or less built atop of previous ones, which demonstrate various
aspects of the library. Each such example has the following structure
-follows:
+follows:</p>
<ol>
<li> <b>Introduction:</b>A brief description of what the program does and
what is new compared to the previous programs. This also includes a
program again, with all comments stripped off, to allow getting an
overview of it.
</ol>
-</p>
<p>
The programs can be found at a path which is indicated at
<p>
Below we will list the currently available tutorial programs twice, once
-<a href="#bynumber>in numerical order explaining what is new in each
+<a href="#bynumber">in numerical order explaining what is new in each
program</a> and once <a href="#bytopic">listed by topic</a> to facilitate
searching for programs for certain functionality.
</p>
<tr><td><a href="../../doxygen/deal.II/step_25.html">Step-25</a></td>
<td> The sine-Gordon
soliton equation, which is a nonlinear variant of the time
- dependent wave equation covered in step-23 and step-24. </td></tr>
+ dependent wave equation covered in step-23 and step-24.
</td></tr>
<tr><td><a href="../../doxygen/deal.II/step_27.html">Step-27</a></td>
-<a name="Results"></a>
<h1>Results</h1>
The program has, after having been run, produced two grids, which look
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
This is what the program outputs:
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
<h2>Point values</h2>
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
The program has, after having been run, produced two sparsity
-<a name="Results"></a>
<h1>Results</h1>
<h3>Output of the program and graphical visualization</h3>
-<a name="Results"></a> <h1>Results</h1>
+<h1>Results</h1>
If we run the program, we get the following kind of output:
@code
-<a name="Results"></a>
<h1>Results</h1>
When the program is run, it produces the following output:
-<a name="Results"></a>
<h1>Results</h1>
The program writes both graphical data for each time step as well as the
-<a name="Results"></a> <h1>Results</h1>
+<h1>Results</h1>
The explicit Euler time stepping scheme ($\theta=0$) performs adequately for the problems we wish to solve. Unfortunately, a rather small time step has to be chosen due to stability issues --- $k\sim h/10$ appears to work for most the simulations we performed. On the other hand, the Crank-Nicolson scheme ($\theta=\frac{1}{2}$) is unconditionally stable, and (at least for the case of the 1D breather) we can pick the time step to be as large as $25h$ without any ill effects on the solution. The implicit Euler scheme ($\theta=1$) is "exponentially damped," so it is not a good choice for solving the sine-Gordon equation, which is conservative. However, some of the damped schemes in the continuum that is offered by the $\theta$-method were useful for eliminating spurious oscillations due to boundary effects.
In the simulations below, we solve the sine-Gordon equation on the interval $\Omega =
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
In this section, we discuss a few results produced from running the
-<a name="Results"></a> <h1>Results</h1>
+<h1>Results</h1>
The output of this program consist of the console output, a file
-<a name="Results"></a>
<h1>Results</h1>
The output of the program looks as follows:
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
-<a name="Results"></a>
<h1>Results</h1>
projects / dealii-svn.git / commitdiff