<?xml version="1.0" encoding="UTF-8"?>
<simulation xmds-version="2">
  <name>vibstring_dirichlet_boundary2</name>
  <author>Graham Dennis</author>
  <description>
    Vibrating string with Dirichlet boundary conditions.
	
	This script is the second of two scripts that demonstrate how to refine or coarsen a grid between simulations.
	This simulation loads the final state of the previous simulation (vibstring_dirichlet_boundary.xmds) and initialises from
	the results of that simulation in Fourier space, but with a higher (spatial) resolution.  Because the spatial grid widths are
	the same, the step size in Fourier space is the same, and so the higher resolution simulation simply initialises the lower kx
	values from the results of the lower resolution simulation and all higher fourier components are set to zero.
  </description>
  
  <features>
    <benchmark />
    <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 xmax = _max_x;
      const real width = 0.1;
      ]]>
    </globals>
  </features>
  
  <geometry>
    <propagation_dimension> t </propagation_dimension>
    <transverse_dimensions>
      <dimension name="x" lattice="512"  domain="(-1, 1)" />
    </transverse_dimensions>
  </geometry>
  
  <vector name="main" initial_basis="kx" type="complex">
    <components>
      u uDot
    </components>
    <initialisation kind="hdf5" geometry_matching_mode="loose">
      <filename group="2">vibstring_dirichlet_boundary.h5</filename>
    </initialisation>
  </vector>
  
  <vector name="boundary" initial_basis="x" type="real">
    <components>
      bc
    </components>
    <initialisation>
      <![CDATA[
        real r = abs(x);
        real rright = xmax-width;

        if ( r > rright)
          bc = 0.0;
        else
          bc = 1.0;
          
        
      ]]>
    </initialisation>
  </vector>
  
  <sequence>
    <integrate algorithm="ARK89" tolerance="1e-8" interval="2e-2" steps="1000">
      <samples>500</samples>
      <operators>
        <operator kind="ex">
          <operator_names>L</operator_names>
          <![CDATA[
            L = -T*kx*kx/mu;
          ]]>
        </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" initial_sample="yes">
        <moments>amp</moments>
        <dependencies>main</dependencies>
        <![CDATA[
          amp = u.Re();
        ]]>
      </sampling_group>
  </output>
</simulation>