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<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
<name>vibstring3</name>
<author>Joe Hope</author>
<description>
Vibrating string
</description>
<features>
<benchmark />
<error_check />
<bing />
<fftw />
<globals>
<![CDATA[
const real T = 10.0;
const real mass = 1e-3;
const real length = 1.0;
const real mu = mass/length;
]]>
</globals>
</features>
<geometry>
<propagation_dimension> t </propagation_dimension>
<transverse_dimensions>
<dimension name="q" type="integer" lattice="2" domain="(0, 1)" />
<dimension name="x" lattice="100" domain="(0, 1)" />
<dimension name="y" lattice="100" domain="(0, 1)" />
<dimension name="z" lattice="100" domain="(0, 1)" />
<dimension name="w" type="integer" domain="(-3, 3)" />
</transverse_dimensions>
</geometry>
<vector name="main" dimensions="x y" initial_basis="x y" type="complex">
<components>
u uDot
</components>
<initialisation>
<![CDATA[
u = exp(-100.0*(x-0.5)*(x-0.5));
uDot = 0.0;
]]>
</initialisation>
</vector>
<vector name="integrated_u" dimensions="" type="complex">
<components>
mom
</components>
</vector>
<computed_vector name="filter1" dimensions="" type="complex">
<components>moment</components>
<!-- If the moments are of type 'real', then all dimensions that aren't integrated
must be evaluated in 'x' space. -->
<evaluation>
<dependencies basis="kx ky">integrated_u main</dependencies>
<![CDATA[
moment = mod2(u);
]]>
</evaluation>
</computed_vector>
<sequence>
<integrate algorithm="RK9" interval="2e-3" steps="100">
<samples>50 50</samples>
<computed_vector name="filter2" dimensions="" type="complex">
<components>sparemoment</components>
<!-- If the moments are of type 'real', then all dimensions that aren't integrated
must be evaluated in 'x' space. -->
<evaluation>
<dependencies basis="kx ky">integrated_u main</dependencies>
<![CDATA[
sparemoment = mod2(u);
]]>
</evaluation>
</computed_vector>
<operators> <!-- For the x y dimensions -->
<operator kind="ex">
<operator_names>L</operator_names>
<![CDATA[
L = -T*kx*kx/mu;
]]>
</operator>
<integration_vectors>main</integration_vectors>
<![CDATA[
du_dt = uDot;
duDot_dt = L[u /**/];
]]>
</operators>
<operators> <!-- For the zero-dimensional field -->
<integration_vectors>integrated_u</integration_vectors>
<dependencies>filter1</dependencies>
<![CDATA[
dmom_dt = moment;
]]>
</operators>
<filters>
<filter>
<dependencies>filter1 main</dependencies>
<![CDATA[
u = 1.0 * u;
]]>
</filter>
</filters>
</integrate>
</sequence>
<output>
<sampling_group basis="x y" initial_sample="yes">
<computed_vector name="filter3" dimensions="" type="complex">
<components>sparemomentagain</components>
<!-- If the moments are of type 'real', then all dimensions that aren't integrated
must be evaluated in 'x' space. -->
<evaluation>
<dependencies basis="kx ky">integrated_u main</dependencies>
<![CDATA[
sparemomentagain = mod2(u);
]]>
</evaluation>
</computed_vector>
<operator kind="ex">
<operator_names>L</operator_names>
<![CDATA[
L = -T*kx*kx/mu;
]]>
</operator>
<moments>amp ke</moments>
<dependencies>main filter1</dependencies>
<![CDATA[
amp = mod2(u + moment);
ke = mod2(L[u]);
]]>
</sampling_group>
<sampling_group initial_sample="no">
<moments>momR momentR</moments>
<dependencies>integrated_u filter1</dependencies>
<![CDATA[
momR = mom.Re();
momentR = moment.Re();
]]>
</sampling_group>
</output>
</simulation>
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