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<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
<testing>
<xsil_file name="vibstring_circle_spectral.xsil" expected="vibstring_circle_spectral_expected.xsil" absolute_tolerance="1e-5" relative_tolerance="1e-5" />
</testing>
<name>vibstring_circle_spectral</name>
<author>Graham Dennis</author>
<description>
Vibrating string with Dirichlet boundary conditions on a circle.
Modification of vibstring_circle to calculate temporal derivatives in fourier (spectral) space.
This runs faster than vibstring_circle on the same grid.
</description>
<features>
<benchmark />
<!-- <error_check /> -->
<bing />
<fftw plan="patient" />
<openmp />
<globals>
<![CDATA[
const double T = 10.0;
const double mass = 1e-3;
const double length = 1.0;
const double mu = mass/length;
const double T_mu = T/mu;
const double xmax = _xy_max_x;
const double width = 0.1;
const double absorb = 80.0;
]]>
</globals>
</features>
<geometry>
<propagation_dimension> t </propagation_dimension>
<transverse_dimensions>
<dimension name="x" lattice="64" domain="(-1, 1)" />
<dimension name="y" lattice="64" domain="(-1, 1)" />
</transverse_dimensions>
</geometry>
<vector name="main" initial_basis="x y" type="complex">
<components>
u uDot
</components>
<initialisation>
<![CDATA[
u = exp(-100.0*((x-0.5)*(x-0.5) + y*y));
uDot = 0.0;
]]>
</initialisation>
</vector>
<vector name="boundary" initial_basis="x y" type="double">
<components>
bc
</components>
<initialisation>
<![CDATA[
double r = sqrt(x*x + y*y);
double rright = xmax-width;
double rdamping = r > rright ? absorb*(1-cos(M_PI*(r - rright)/width)) : 0.0;
bc = exp(-rdamping);
if (r > xmax)
bc = 0.0;
if ( r > rright)
bc = 0.0;
else
bc = 1.0;
]]>
</initialisation>
</vector>
<sequence>
<integrate algorithm="ARK89" tolerance="1e-7" interval="4e-2" steps="1000" home_space="k">
<samples>5 5 100</samples>
<operators>
<operator kind="ex" constant="yes" fourier_space="x y">
<operator_names>L</operator_names>
<![CDATA[
double r2 = x*x + y*y;
if (r2 > (_max_x - width)*(_max_x-width))
L = 0.0;
else
L = 1.0;
]]>
</operator>
<integration_vectors fourier_space="kx ky">main</integration_vectors>
<![CDATA[
du_dt = uDot;
duDot_dt = L[-T_mu*(kx*kx+ky*ky)*u];
]]>
</operators>
</integrate>
</sequence>
<output format="binary">
<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="32" fourier_space="no" />
<dimension name="y" lattice="32" fourier_space="no" />
<moments>amp</moments>
<dependencies>main</dependencies>
<![CDATA[
amp = u;
]]>
</sampling_group>
<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="32" fourier_space="yes" />
<dimension name="y" lattice="32" fourier_space="yes" />
<moments>amp</moments>
<dependencies>main</dependencies>
<![CDATA[
amp = u;
]]>
</sampling_group>
<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="0" fourier_space="no" />
<dimension name="y" lattice="0" fourier_space="no" />
<moments>energy</moments>
<dependencies>main</dependencies>
<operator kind="ex" constant="no">
<operator_names>Lx Ly</operator_names>
<![CDATA[
Lx = i*kx;
Ly = i*ky;
]]>
</operator>
<![CDATA[
energy = mod2(uDot) + T_mu*mod2(Lx[u]) + T_mu*mod2(Ly[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">3</Param>
<Array Name="variables" Type="Text">
<Dim>4</Dim>
<Stream><Metalink Format="Text" Delimiter=" \n"/>
t x y amp
</Stream>
</Array>
<Array Name="data" Type="double">
<Dim>6</Dim>
<Dim>32</Dim>
<Dim>32</Dim>
<Dim>4</Dim>
<Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="LittleEndian"/>
vibstring_circle_spectral_expected_mg0.dat
</Stream>
</Array>
</XSIL>
<XSIL Name="moment_group_2">
<Param Name="n_independent">3</Param>
<Array Name="variables" Type="Text">
<Dim>4</Dim>
<Stream><Metalink Format="Text" Delimiter=" \n"/>
t kx ky amp
</Stream>
</Array>
<Array Name="data" Type="double">
<Dim>6</Dim>
<Dim>32</Dim>
<Dim>32</Dim>
<Dim>4</Dim>
<Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="LittleEndian"/>
vibstring_circle_spectral_expected_mg1.dat
</Stream>
</Array>
</XSIL>
<XSIL Name="moment_group_3">
<Param Name="n_independent">1</Param>
<Array Name="variables" Type="Text">
<Dim>2</Dim>
<Stream><Metalink Format="Text" Delimiter=" \n"/>
t energy
</Stream>
</Array>
<Array Name="data" Type="double">
<Dim>101</Dim>
<Dim>2</Dim>
<Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="LittleEndian"/>
vibstring_circle_spectral_expected_mg2.dat
</Stream>
</Array>
</XSIL>
</simulation>
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