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<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
<testing>
<xsil_file name="nlse_sampling.xsil" expected="nlse_sampling_expected.xsil" absolute_tolerance="1e-6" relative_tolerance="1e-5" />
</testing>
<name>nlse_sampling</name>
<author>Joe Hope</author>
<description>
The nonlinear Schrodinger equation in one dimension,
which is a simple partial differential equation.
We introduce several new features in this script.
</description>
<features>
<benchmark />
<bing />
<fftw plan="patient" />
<auto_vectorise />
<globals>
<![CDATA[
const double energy = 4;
const double vel = 0.3;
const double hwhm = 1.0;
]]>
</globals>
</features>
<geometry>
<propagation_dimension> xi </propagation_dimension>
<transverse_dimensions>
<dimension name="tau" lattice="128" domain="(-6, 6)" />
</transverse_dimensions>
</geometry>
<vector name="wavefunction" type="complex" dimensions="tau">
<components> phi </components>
<initialisation>
<![CDATA[
const double w0 = hwhm*sqrt(2/log(2));
const double amp = sqrt(energy/w0/sqrt(M_PI/2));
phi = amp*exp(-tau*tau/w0/w0)*exp(i*vel*tau);
]]>
</initialisation>
</vector>
<vector name="dampingVector" type="real">
<components> Gamma </components>
<initialisation>
<![CDATA[
Gamma=1.0*(1-exp(-pow(tau*tau/4.0/4.0,10)));
]]>
</initialisation>
</vector>
<sequence>
<integrate algorithm="ARK45" interval="20.0" tolerance="1e-7">
<samples>10 100 10</samples>
<operators>
<integration_vectors>wavefunction</integration_vectors>
<operator kind="ex" constant="yes">
<operator_names>Ltt</operator_names>
<![CDATA[
Ltt = -i*ktau*ktau*0.5;
]]>
</operator>
<![CDATA[
dphi_dxi = Ltt[phi] - phi*Gamma + i*mod2(phi)*phi;
]]>
<dependencies>dampingVector</dependencies>
</operators>
</integrate>
</sequence>
<output>
<sampling_group basis="tau" initial_sample="yes">
<moments>density</moments>
<dependencies>wavefunction</dependencies>
<![CDATA[
density = mod2(phi);
]]>
</sampling_group>
<sampling_group basis="tau(0)" initial_sample="yes">
<moments>normalisation</moments>
<dependencies>wavefunction</dependencies>
<![CDATA[
normalisation = mod2(phi);
]]>
</sampling_group>
<sampling_group basis="ktau(1)" initial_sample="yes">
<moments>densityK</moments>
<dependencies>wavefunction</dependencies>
<![CDATA[
densityK = mod2(phi);
]]>
</sampling_group>
</output>
</simulation>
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