<OpenGeoSysProject>
  <mesh>square_1x1_quad_1e4.vtu</mesh>
  <geometry>square_1x1.gml</geometry>
  <processes>
    <process>
      <name>HeatConduction</name>
      <type>HEAT_CONDUCTION</type>
      <integration_order>2</integration_order>
      <process_variables>
        <process_variable>temperature</process_variable>
      </process_variables>
      <secondary_variables>
        <secondary_variable name="heat_flux" />
      </secondary_variables>
    </process>
  </processes>
  <media>
    <medium>
      <phases />
      <properties>
        <property>
          <name>thermal_conductivity</name>
          <type>Constant</type>
          <value>1</value>
        </property>
        <property>
          <name>specific_heat_capacity</name>
          <type>Constant</type>
          <value>1</value>
        </property>
        <property>
          <name>density</name>
          <type>Constant</type>
          <value>1</value>
        </property>
      </properties>
    </medium>
  </media>
  <time_loop>
    <processes>
      <process ref="HeatConduction">
        <nonlinear_solver>NLS</nonlinear_solver>
        <convergence_criterion>
          <type>DeltaX</type>
          <norm_type>NORM2</norm_type>
          <reltol>1e-14</reltol>
        </convergence_criterion>
        <time_discretization>
          <type>BackwardEuler</type>
        </time_discretization>
        <time_stepping>
          <type>FixedTimeStepping</type>
          <t_initial>0</t_initial>
          <t_end>1</t_end>
          <timesteps>
            <pair>
              <repeat>1</repeat>
              <delta_t>0.1</delta_t>
            </pair>
            <pair>
              <repeat>2</repeat>
              <delta_t>0.2</delta_t>
            </pair>
            <pair>
              <repeat>2</repeat>
              <delta_t>0.25</delta_t>
            </pair>
          </timesteps>
        </time_stepping>
      </process>
    </processes>
    <output>
      <type>VTK</type>
      <prefix>{:meshname}</prefix>
      <variables>
        <variable>temperature</variable>
        <variable>v</variable>
      </variables>
      <suffix>t{:gtime}</suffix>
      <fixed_output_times>0 0.5 1</fixed_output_times>
      <timesteps>
        <pair>
          <repeat>1</repeat>
          <each_steps>100000</each_steps>
        </pair>
      </timesteps>
    </output>
  </time_loop>
  <parameters>
    <parameter>
      <name>solution</name>
      <type>Function</type>
      <expression>x^2 * sin(2*pi*y) * t</expression>
    </parameter>
    <parameter>
      <name>zero</name>
      <type>Constant</type>
      <value>0</value>
    </parameter>
    <parameter>
      <name>alpha</name>
      <type>Constant</type>
      <value>2</value>
    </parameter>
    <parameter>
      <name>dsolution_dx</name>
      <type>Function</type>
      <expression>2 * x * sin(2*pi*y) * t</expression>
    </parameter>
    <parameter>
      <name>ambient_temperature</name>
      <type>Function</type>
      <expression>2 * sin(2*pi*y) * t</expression>
    </parameter>
    <parameter>
      <name>source_term</name>
      <type>Function</type>
      <expression>(x^2 - 2 * t + 4 * pi^2 * x^2 * t) * sin(2*pi*y)</expression>
    </parameter>
  </parameters>
  <process_variables>
    <process_variable>
      <name>temperature</name>
      <order>1</order>
      <components>1</components>
      <initial_condition>solution</initial_condition>
      <boundary_conditions>
        <boundary_condition>
          <geometrical_set>square_1x1_geometry</geometrical_set>
          <geometry>bottom</geometry>
          <type>Dirichlet</type>
          <parameter>solution</parameter>
        </boundary_condition>
        <boundary_condition>
          <geometrical_set>square_1x1_geometry</geometrical_set>
          <geometry>top</geometry>
          <type>Dirichlet</type>
          <parameter>solution</parameter>
        </boundary_condition>
        <boundary_condition>
          <geometrical_set>square_1x1_geometry</geometrical_set>
          <geometry>right</geometry>
          <type>Robin</type>
          <alpha>alpha</alpha>
          <u_0>ambient_temperature</u_0>
        </boundary_condition>
        <boundary_condition>
          <geometrical_set>square_1x1_geometry</geometrical_set>
          <geometry>left</geometry>
          <type>Neumann</type>
          <parameter>dsolution_dx</parameter>
        </boundary_condition>
      </boundary_conditions>
      <source_terms>
        <source_term>
          <mesh>square_1x1_quad_1e4</mesh>
          <type>Volumetric</type>
          <parameter>source_term</parameter>
        </source_term>
      </source_terms>
    </process_variable>
  </process_variables>
  <nonlinear_solvers>
    <nonlinear_solver>
      <name>NLS</name>
      <type>Picard</type>
      <max_iter>10</max_iter>
      <linear_solver>general_linear_solver</linear_solver>
    </nonlinear_solver>
  </nonlinear_solvers>
  <linear_solvers>
    <linear_solver>
      <name>general_linear_solver</name>
      <eigen>
        <solver_type>BiCGSTAB</solver_type>
        <precon_type>DIAGONAL</precon_type>
        <max_iteration_step>10000</max_iteration_step>
        <error_tolerance>1e-16</error_tolerance>
      </eigen>
    </linear_solver>
  </linear_solvers>
  <test_definition>
    <vtkdiff>
      <regex>square_1x1_quad_1e4_t_.*.vtu</regex>
      <field>temperature</field>
      <absolute_tolerance>2e-14</absolute_tolerance>
      <relative_tolerance>0</relative_tolerance>
    </vtkdiff>
  </test_definition>
</OpenGeoSysProject>