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<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
<testing>
<xsil_file name="vibstring_dct.xsil" expected="vibstring_dct_expected.xsil" absolute_tolerance="1e-7" relative_tolerance="1e-5" />
</testing>
<name>vibstring_dct</name>
<author>Graham Dennis</author>
<description>
Vibrating string using a Discrete Cosine transform (i.e. even boundary conditions on both sides)
</description>
<features>
<benchmark />
<error_check />
<bing />
<fftw plan="estimate" />
<openmp />
<globals>
<![CDATA[
const double T = 10.0;
const double mass = 1e-3;
const double length = 1.0;
const double mu = mass/length;
]]>
</globals>
</features>
<geometry>
<propagation_dimension> t </propagation_dimension>
<transverse_dimensions>
<dimension name="x" lattice="50" domain="(0.5, 1.0)" transform="dct"/>
</transverse_dimensions>
</geometry>
<vector name="main" initial_basis="x" type="double">
<components>
u uDot
</components>
<initialisation>
<![CDATA[
u = exp(-100.0*(x-0.5)*(x-0.5));
uDot = 0.0;
]]>
</initialisation>
</vector>
<sequence>
<integrate algorithm="RK4" interval="2e-3" steps="100">
<samples>50 50</samples>
<computed_vector name="moment_creator" dimensions="" type="double">
<components>moment</components>
<evaluation>
<dependencies fourier_space="kx"> main </dependencies>
<![CDATA[
moment = mod2(u);
]]>
</evaluation>
</computed_vector>
<operators>
<operator kind="ex" constant="yes">
<operator_names>L</operator_names>
<![CDATA[
L = -T*kx*kx/mu;
]]>
</operator>
<integration_vectors>main</integration_vectors>
<dependencies>moment_creator</dependencies>
<![CDATA[
du_dt = uDot;
duDot_dt = L[u];
moment;
]]>
</operators>
</integrate>
</sequence>
<output format="binary" filename="vibstring_dct.xsil">
<sampling_group initial_sample="yes">
<!-- Any dimension not mentioned is assumed to be in real space and its middle element will be sampled -->
<!-- Note that this is different default behaviour to the filter operator. To integrate, put in a dimension -->
<!-- with zero lattice points. -->
<!-- Note that dimensions can be in any order. Not that I can think of a reason why you would want to do that -->
<dimension name="x" lattice="50" fourier_space="no" />
<moments>amp</moments>
<dependencies>main</dependencies>
<![CDATA[
amp = u;
]]>
</sampling_group>
<sampling_group initial_sample="no">
<dimension name="x" lattice="50" fourier_space="yes" />
<moments>amp</moments>
<dependencies>main</dependencies>
<![CDATA[
amp = u;
]]>
</sampling_group>
</output>
<info>
Script compiled with xpdeint version VERSION_PLACEHOLDER (SUBVERSION_REVISION_PLACEHOLDER)
See http://www.xmds.org for more information.
</info>
<XSIL Name="moment_group_1">
<Param Name="n_independent">2</Param>
<Array Name="variables" Type="Text">
<Dim>4</Dim>
<Stream><Metalink Format="Text" Delimiter=" \n"/>
t x amp error_amp
</Stream>
</Array>
<Array Name="data" Type="double">
<Dim>51</Dim>
<Dim>50</Dim>
<Dim>4</Dim>
<Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="LittleEndian"/>
vibstring_dct_expected_mg0.dat
</Stream>
</Array>
</XSIL>
<XSIL Name="moment_group_2">
<Param Name="n_independent">2</Param>
<Array Name="variables" Type="Text">
<Dim>4</Dim>
<Stream><Metalink Format="Text" Delimiter=" \n"/>
t kx amp error_amp
</Stream>
</Array>
<Array Name="data" Type="double">
<Dim>50</Dim>
<Dim>50</Dim>
<Dim>4</Dim>
<Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="LittleEndian"/>
vibstring_dct_expected_mg1.dat
</Stream>
</Array>
</XSIL>
</simulation>
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