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<?xml version="1.0" ?><simulation xmds-version="2">
<testing>
<xsil_file absolute_tolerance="1e-6" expected="bessel_neumann_wave_equation_expected.xsil" name="bessel_neumann_wave_equation.xsil" relative_tolerance="1e-5"/>
</testing>
<name>bessel_neumann_wave_equation</name>
<author>Graham Dennis</author>
<description>
Solve the wave equation on a disk of radius 1 utilising cylindrical symmetry
by using the Bessel function transform. The boundary condition at r=1 is d/dr u = 0
</description>
<features>
<benchmark/>
<bing/>
<validation kind="run-time"/>
<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>
<!-- Volume prefactor = 2 \pi is to cover the suppressed integration over \theta -->
<!-- transform="bessel-neumann" means cylindrical symmetry with zero derivative boundary conditions at the outer boundary -->
<dimension domain="(0, 1)" lattice="100" name="x" order="0" transform="bessel-neumann" volume_prefactor="2.0*M_PI"/>
</transverse_dimensions>
</geometry>
<vector initial_basis="x" name="main" type="complex">
<components>
u uDot
</components>
<initialisation>
<![CDATA[
u = exp(-100.0*(x-0.25)*(x-0.25));
uDot = 0.0;
]]>
</initialisation>
</vector>
<sequence>
<integrate algorithm="ARK45" interval="40e-3" steps="400" tolerance="1e-6">
<samples>100 100</samples>
<operators>
<operator basis="kx" kind="ex" type="real">
<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>
</integrate>
</sequence>
<output format="hdf5">
<sampling_group basis="x" initial_sample="yes">
<moments>amp</moments>
<dependencies>main</dependencies>
<![CDATA[
amp = u.Re();
]]>
</sampling_group>
<sampling_group basis="kx" initial_sample="no">
<moments>amp</moments>
<dependencies>main</dependencies>
<![CDATA[
amp = u.Re();
]]>
</sampling_group>
</output>
<info>
Script compiled with XMDS2 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>3</Dim>
<Stream><Metalink Format="Text" Delimiter=" \n"/>
t x amp
</Stream>
</Array>
<Array Name="data" Type="double">
<Dim>101</Dim>
<Dim>100</Dim>
<Dim>3</Dim>
<Stream><Metalink Format="HDF5" Type="Remote" Group="/1"/>
bessel_neumann_wave_equation_expected.h5
</Stream>
</Array>
</XSIL>
<XSIL Name="moment_group_2">
<Param Name="n_independent">2</Param>
<Array Name="variables" Type="Text">
<Dim>3</Dim>
<Stream><Metalink Format="Text" Delimiter=" \n"/>
t kx amp
</Stream>
</Array>
<Array Name="data" Type="double">
<Dim>100</Dim>
<Dim>100</Dim>
<Dim>3</Dim>
<Stream><Metalink Format="HDF5" Type="Remote" Group="/2"/>
bessel_neumann_wave_equation_expected.h5
</Stream>
</Array>
</XSIL>
</simulation>
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