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<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
<testing>
<xsil_file name="bessel_transform_rectangular.xsil" expected="bessel_transform_rectangular_expected.xsil" absolute_tolerance="1e-6" relative_tolerance="1e-5" />
</testing>
<name>bessel_transform_rectangular</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 Bessel function transform implicitly
assumes Dirichlet boundary conditions at the edge of the disk.
</description>
<features>
<benchmark />
<bing />
<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="x" lattice="100" spectral_lattice="50" domain="(0, 1)" transform="bessel" />
</transverse_dimensions>
</geometry>
<vector name="main" initial_basis="x" 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" tolerance="1e-6" interval="8e-3">
<samples>100 73</samples>
<operators>
<operator kind="ex" constant="yes" basis="kx">
<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="binary">
<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>
</simulation>
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