<?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>
