 <OpenGeoSysProject>

   <mesh axially_symmetric="true">square_1x1_quad_1e2.vtu</mesh>

   <geometry>square_1x1_axi.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 internal_name="heat_flux" output_name="heat_flux" />

       </secondary_variables>

     </process>

   </processes>

   <media>

     <medium id="0">

       <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>basic_picard</nonlinear_solver>

         <convergence_criterion>

           <type>DeltaX</type>

           <norm_type>NORM2</norm_type>

           <abstol>1e-14</abstol>

         </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>

           </timesteps>

         </time_stepping>

       </process>

     </processes>

     <output>

       <type>VTK</type>

       <prefix>square_1e2_axi</prefix>

       <timesteps>

         <pair>

           <repeat>1</repeat>

           <each_steps>10</each_steps>

         </pair>

       </timesteps>

       <variables>

         <variable>temperature</variable>

         <variable>heat_flux</variable>

       </variables>

       <suffix>ts{:timestep}_t_{:time}</suffix>

     </output>

   </time_loop>

   <parameters>

     <parameter>

       <name>solution</name>

       <type>Function</type>

       <expression>t * sin(2*pi*y) * x^2</expression>

     </parameter>

     <parameter>

       <name>dsolution_dy</name>

       <type>Function</type>

       <expression>-t * 2*pi*cos(2*pi*y) * x^2</expression>

     </parameter>

     <parameter>

       <name>heat_transfer_coefficient</name>

       <type>Constant</type>

       <value>1</value>

     </parameter>

     <parameter>

       <name>ambient_temperature</name>

       <type>Function</type>

       <expression>3 * t * sin(2*pi*y)</expression>

     </parameter>

     <parameter>

       <name>source_term</name>

       <type>Function</type>

       <expression>sin(2*pi*y) * ((1 + 4*pi^2*t)*x^2 - 4*t)</expression>

     </parameter>

   </parameters>

   <process_variables>

     <process_variable>

       <name>temperature</name>

       <components>1</components>

       <order>1</order>

       <initial_condition>solution</initial_condition>

       <boundary_conditions>

         <boundary_condition>

           <geometrical_set>geometry</geometrical_set>

           <geometry>bottom</geometry>

           <type>Neumann</type>

           <parameter>dsolution_dy</parameter>

         </boundary_condition>

         <boundary_condition>

           <geometrical_set>geometry</geometrical_set>

           <geometry>top</geometry>

           <type>Dirichlet</type>

           <parameter>ambient_temperature</parameter>

         </boundary_condition>

         <boundary_condition>

           <geometrical_set>geometry</geometrical_set>

           <geometry>outer</geometry>

           <type>Robin</type>

           <alpha>heat_transfer_coefficient</alpha>

           <u_0>ambient_temperature</u_0>

         </boundary_condition>

       </boundary_conditions>

       <source_terms>

         <source_term>

           <mesh>square_1x1_quad_1e2</mesh>

           <type>Volumetric</type>

           <parameter>source_term</parameter>

         </source_term>

       </source_terms>

     </process_variable>

   </process_variables>

   <nonlinear_solvers>

     <nonlinear_solver>

       <name>basic_picard</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>

       <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>

       <eigen>

         <solver_type>CG</solver_type>

         <precon_type>DIAGONAL</precon_type>

         <max_iteration_step>10000</max_iteration_step>

         <error_tolerance>1e-16</error_tolerance>

       </eigen>

       <petsc>

         <prefix>gw</prefix>

         <parameters>-gw_ksp_type cg -gw_pc_type bjacobi -gw_ksp_rtol 1e-16 -gw_ksp_max_it 10000</parameters>

       </petsc>

     </linear_solver>

   </linear_solvers>

 </OpenGeoSysProject>