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<?xml version="1.0"?>
<!-- Example simulation: Diffusion Equation -->
<!-- $Id: diffusion.xmds 1526 2007-08-21 17:30:14Z paultcochrane $ -->
<!-- Copyright (C) 2000-2007 -->
<!-- -->
<!-- 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., 51 Franklin St, Fifth Floor, Boston, -->
<!-- MA 02110-1301, 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.
Part 1 of 2: This simulation propagates the solution for 1 time unit,
and then saves the state of the field. The simulation can then be
continued in part 2.
</description>
<prop_dim>t</prop_dim>
<error_check>no</error_check>
<runtime_limit> 3 </runtime_limit>
<stochastic>no</stochastic>
<benchmark>yes</benchmark>
<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>ARK89EX</algorithm>
<interval>50</interval>
<lattice>10000</lattice>
<samples>50</samples>
<tolerance>1e-5</tolerance>
<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>
<breakpoint>
<filename>diffusion_break.xsil</filename>
<fourier_space> no </fourier_space>
<vectors> main </vectors>
</breakpoint>
</sequence>
<!-- The output to generate -->
<output>
<filename>diffusion.xsil</filename>
<group>
<sampling>
<fourier_space> no </fourier_space>
<lattice> 64 </lattice>
<moments>temp</moments>
<![CDATA[
temp = T;
]]>
</sampling>
</group>
</output>
</simulation>
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