diffusion.xmds

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

<?xml version="1.0"?>
<!-- Example simulation: Diffusion Equation -->

<!-- $Id: diffusion.xmds,v 1.7 2004/06/15 01:30:03 paultcochrane Exp $ -->

<!--  Copyright (C) 2000-2004                                           -->
<!--                                                                    -->
<!--  Code contributed by Greg Collecutt, Joseph Hope and Paul Cochrane -->
<!--                                                                    -->
<!--  This file is part of xmds.                                        -->
<!--                                                                    -->
<!--  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.            -->
<!--                                                                    -->
<!--  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     -->
<!--  GNU General Public License for more details.                      -->
<!--                                                                    -->
<!--  You should have received a copy of the GNU General Public License -->
<!--  along with this program; if not, write to the Free Software       -->
<!--  Foundation, Inc., 59 Temple Place - Suite 330, Boston,            -->
<!--  MA  02111-1307, USA.                                              -->

<simulation>

  <!-- Global system parameters and functionality -->
  <name>diffusion</name>

  <author> Paul Cochrane </author>
  <description>
    Solves the one-dimensional diffusion equation for an initial
    Gaussian pulse.
  </description>

  <prop_dim>t</prop_dim>
  <error_check>yes</error_check>
  <stochastic>no</stochastic>
  <use_wisdom>yes</use_wisdom>  <!-- Default is no -->

  <!-- Global variables for the simulation -->
  <globals>
  <![CDATA[
    const double sigma = 0.1;
    const double kappa = 0.1;
    const double x0 = 0.0;
  ]]>
  </globals>

  <!-- Field to be integrated over -->
  <field>
    <name>main</name>
    <dimensions>  x   </dimensions>
    <lattice>    128  </lattice>
    <domains>  (-1,1) </domains>

    <samples>1</samples>
    <vector>
      <name>main</name>
      <type>complex</type>
      <components>T</components>
      <fourier_space>no</fourier_space>
      <![CDATA[
        T = rcomplex(exp(-(x - x0)*(x - x0)/(2.0*sigma*sigma))/(sigma*sqrt(2.0*M_PI)),0.0);
      ]]>
    </vector>
  </field>

  <!-- The sequence of integrations to perform -->
  <sequence>
    <integrate>

      <algorithm>RK4EX</algorithm>
      <interval>1</interval>
      <lattice>10000</lattice>
      <samples>50</samples>
      <k_operators>
        <constant>yes</constant>
        <operator_names>L</operator_names>
        <![CDATA[
          L = -kappa*kx*kx;
        ]]>
      </k_operators>
      <vectors>main</vectors>
        <![CDATA[
          dT_dt =  L[T];
        ]]>
    </integrate>
  </sequence>

  <!-- The output to generate -->
  <output>
    <filename>diffusion.xsil</filename>
    <group>
      <sampling>
        <fourier_space> no </fourier_space>
        <lattice>       50 </lattice>
        <moments>temp</moments>
	<![CDATA[
	  temp = T;
	]]>
      </sampling>
    </group>
  </output>

</simulation>