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<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
<name>vibstring_circle</name>
<author>Graham Dennis</author>
<description>
Vibrating string with Dirichlet boundary conditions on a circle.
</description>
<features>
<benchmark />
<error_check />
<bing />
<fftw plan="patient" />
<globals>
<![CDATA[
const real T = 10.0;
const real mass = 1e-3;
const real length = 1.0;
const real mu = mass/length;
const real T_mu = T/mu;
const real xmax = _max_x;
const real width = 0.1;
const real absorb = 80.0;
]]>
</globals>
</features>
<geometry>
<propagation_dimension> t </propagation_dimension>
<transverse_dimensions>
<dimension name="x" lattice="256" domain="(-1, 1)" />
<dimension name="y" lattice="256" 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="real">
<components>
bc
</components>
<initialisation>
<![CDATA[
real r = sqrt(x*x + y*y);
real rright = xmax-width;
real 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="2e-2" steps="1000">
<samples>50</samples>
<operators>
<operator kind="ex">
<operator_names>L</operator_names>
<![CDATA[
L = -T_mu*(kx*kx + ky*ky);
]]>
</operator>
<integration_vectors>main</integration_vectors>
<dependencies>boundary</dependencies>
<![CDATA[
du_dt = uDot;
duDot_dt = bc*L[u];
]]>
</operators>
</integrate>
</sequence>
<output>
<sampling_group basis="x y" initial_sample="yes">
<moments>amp</moments>
<dependencies>main</dependencies>
<![CDATA[
amp = u.Re();
]]>
</sampling_group>
</output>
</simulation>
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