lane_emden.xmds

XMDS is a code generator that integrates equations. You write them down in human readable form in a

<?xml version="1.0"?>
<simulation>

<!-- $Id: lane_emden.xmds,v 1.1 2004/05/31 03:15:40 paultcochrane Exp $ -->

<!--  Copyright (C) 2000-2004                                           -->
<!--                                                                    -->
<!--  Code contributed by Greg Collecutt, Joseph Hope and Paul Cochrane -->
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<!--  This file is part of xmds.                                        -->
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<!--  This program is free software; you can redistribute it and/or     -->
<!--  modify it under the terms of the GNU General Public License       -->
<!--  as published by the Free Software Foundation; either version 2    -->
<!--  of the License, or (at your option) any later version.            -->
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<!--  This program is distributed in the hope that it will be useful,   -->
<!--  but WITHOUT ANY WARRANTY; without even the implied warranty of    -->
<!--  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the     -->
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<!--  MA  02111-1307, USA.                                              -->
  
  <name> lane_emden </name>      <!-- the name of the simulation -->
  
  <author> Paul Cochrane </author>  <!-- the author of the simulation -->
  <description>
    Example simulation of the Lane-Emden equation.
    This equation models stellar polytropes.
    Taken from the UQ Physics Astrophysics course notes.
  </description>
  
  <!-- Global system parameters and functionality -->
  <prop_dim> xi </prop_dim>    <!-- name of main propagation dim -->
  
  <error_check> yes </error_check>   <!-- defaults to yes -->
  <use_wisdom> yes </use_wisdom>     <!-- defaults to no -->
  <benchmark> yes </benchmark>       <!-- defaults to no -->
  <use_prefs> yes </use_prefs>       <!-- defaults to yes -->
  
  <argv>
    <arg>
      <!-- polytropic index -->
      <name> n </name>
      <type> double </type>
      <default_value> 0.0 </default_value>
    </arg>
  </argv>

  <!-- Global variables for the simulation -->
  <globals>
  <![CDATA[
    // initial values of variables
    const double theta0 = 1.0;       // 
  ]]>
  </globals>
  
  <!-- Field to be integrated over -->
  <field>
    <name> main </name>
    <samples> 1 </samples>       <!-- sample 1st point of dim? -->
    
    <vector>
      <name> main </name>
      <type> complex </type>           <!-- data type of vector -->
      <components> theta DthetaDxi </components>       <!-- names of components -->
      <fourier_space> no </fourier_space> <!-- defined in k-space? -->
      <![CDATA[
        theta = theta0;
        DthetaDxi = 0.0;   // the derivative of theta to xi
      ]]>
    </vector>
  </field>
  
  <!-- The sequence of integrations to perform -->
  <sequence>
    <integrate>
      <algorithm> RK4EX </algorithm> <!-- RK4EX, RK4IP, SIEX, SIIP -->
      <interval> 10 </interval>   <!-- how far in main dim? -->
      <lattice> 1000 </lattice>     <!-- no. points in main dim -->
      <samples> 100 </samples> <!-- no. pts in output moment group -->
      <![CDATA[
        dtheta_dxi = DthetaDxi;
	dDthetaDxi_dxi = -(2.0/(xi+1e-10))*DthetaDxi - pow(theta,n);          
      ]]>
    </integrate>
  </sequence>
  
  <!-- The output to generate -->
  <output format="ascii">
    <group>
      <sampling>
        <fourier_space> no </fourier_space> <!-- sample in k-space? -->
        <lattice> 100 </lattice>           <!-- no. points to sample -->
        <moments> thetaOut </moments> <!-- names of moments -->
        <![CDATA[
          thetaOut = theta;
        ]]>
      </sampling>
    </group>
  </output>
  
</simulation>