vibstring.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: Waves on a vibrating string -->

<!-- $Id: vibstring.xmds,v 1.8 2004/07/14 06:37:05 joehope 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.                      -->
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<!--  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.                                              -->

<!-- Adapted from the example in -->
<!-- "A first course in computational physics" -->
<!-- Paul L. DeVries, pg 348 -->

<simulation>

  <name>vibstring</name>

  <author>Paul Cochrane</author>
  <description>
    Example simulation of waves on a vibrating string.  Adapted from
    the example in "A first course in computational physics" by Paul
    L. Devries, page 348.
  </description>

  <!-- Global system parameters and functionality -->
  <prop_dim>t</prop_dim>
  <error_check>yes</error_check>
  <stochastic>no</stochastic>

  <!-- Global variables for the simulation -->
  <globals>
  <![CDATA[
    const double length = 1.0;      // 1 metre
    const double mass = 1e-3;       // 1 gram
    const double T = 10.0;          // (Tension) 10 Newtons
    const double mu = mass/length;  // mass density
    const double c = sqrt(T/mu);    // speed of wave propagation
  ]]>
  </globals>

  <!-- Field to be integrated over -->
  <field>
    <name>main</name>
    <dimensions>  x   </dimensions>
    <lattice>    100  </lattice>
    <domains>  (0,1) </domains>

    <samples>1</samples>
    <vector>
      <name>main</name>
      <type>complex</type>
      <components>u uDot</components>
      <fourier_space>no</fourier_space>
      <![CDATA[
        /* supposed to be 0 at the boundaries x=0 and x=1, but can't do this in xmds-1.2 */
	u = rcomplex(exp(-100.0*(x-0.5)*(x-0.5)),0.0);
	uDot = 0.0;
      ]]>
    </vector>
  </field>

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

      <algorithm>RK4EX</algorithm>
      <interval>0.002</interval>
      <lattice>1000</lattice>
      <samples>20</samples>
      <k_operators>
        <constant>yes</constant>
        <operator_names>L</operator_names>
        <![CDATA[
          L = -T*kx*kx/mu;
        ]]>
      </k_operators>
      <vectors>main</vectors>
        <![CDATA[
          du_dt = uDot;
	  duDot_dt = L[u];
        ]]>
    </integrate>
  </sequence>

  <!-- The output to generate -->
  <output format="ascii" precision="double">
    <filename>vibstring.xsil</filename>
    <group>
      <sampling>
        <fourier_space> no </fourier_space>
        <lattice>       50 </lattice>
        <moments>amp</moments>
	<![CDATA[
	  amp=u;
	]]>
      </sampling>
    </group>
  </output>

</simulation>