 <OpenGeoSysProject>

   <mesh axially_symmetric="true">unit-circle.vtu</mesh>

   <geometry>unit-circle.gml</geometry>

   <python_script>hertz_contact_bc.py</python_script>

   <processes>

     <process>

       <name>SD</name>

       <type>SMALL_DEFORMATION</type>

       <integration_order>2</integration_order>

       <constitutive_relation>

         <type>LinearElasticIsotropic</type>

         <youngs_modulus>E</youngs_modulus>

         <poissons_ratio>nu</poissons_ratio>

       </constitutive_relation>

       <specific_body_force>0 0</specific_body_force>

       <process_variables>

         <process_variable>displacement</process_variable>

       </process_variables>

       <secondary_variables>

         <secondary_variable internal_name="sigma" output_name="sigma" />

         <secondary_variable internal_name="epsilon" output_name="epsilon" />

       </secondary_variables>

     </process>

   </processes>

   <time_loop>

     <processes>

       <process ref="SD">

         <nonlinear_solver>basic_newton</nonlinear_solver>

         <convergence_criterion>

           <type>DeltaX</type>

           <norm_type>INFINITY_N</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>10</t_end>

           <timesteps>

             <pair>

               <repeat>1</repeat>

               <delta_t>1</delta_t>

             </pair>

           </timesteps>

         </time_stepping>

       </process>

     </processes>

     <output>

       <type>VTK</type>

       <prefix>hertz</prefix>

       <timesteps>

         <pair>

           <repeat>1</repeat>

           <each_steps>1</each_steps>

         </pair>

       </timesteps>

       <output_iteration_results>false</output_iteration_results>

       <variables>

         <variable>displacement</variable>

         <variable>sigma</variable>

         <variable>epsilon</variable>

       </variables>

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

     </output>

   </time_loop>

   <media>

     <medium>

       <phases>

         <phase>

           <type>Solid</type>

           <properties>

             <property>

               <name>density</name>

               <type>Constant</type>

               <value>1</value>

             </property>

           </properties>

         </phase>

       </phases>

     </medium>

   </media>

   <parameters>

     <parameter>

       <name>E</name>

       <type>Constant</type>

       <value>1</value>

     </parameter>

     <parameter>

       <name>nu</name>

       <type>Constant</type>

       <value>.3</value>

     </parameter>

     <parameter>

       <name>displacement0</name>

       <type>Constant</type>

       <values>0 0</values>

     </parameter>

     <parameter>

       <name>zero</name>

       <type>Constant</type>

       <value>0</value>

     </parameter>

   </parameters>

   <process_variables>

     <process_variable>

       <name>displacement</name>

       <components>2</components>

       <order>1</order>

       <initial_condition>displacement0</initial_condition>

       <boundary_conditions>

         <boundary_condition>

           <geometrical_set>geom</geometrical_set>

           <geometry>left</geometry>

           <type>Dirichlet</type>

           <component>0</component>

           <parameter>zero</parameter>

         </boundary_condition>

         <boundary_condition>

           <geometrical_set>geom</geometrical_set>

           <geometry>bottom</geometry>

           <type>Dirichlet</type>

           <component>1</component>

           <parameter>zero</parameter>

         </boundary_condition>

         <boundary_condition>

           <geometrical_set>geom</geometrical_set>

           <geometry>outer</geometry>

           <type>Python</type>

           <component>1</component>

           <bc_object>bc</bc_object>

           <flush_stdout>false</flush_stdout>

         </boundary_condition>

       </boundary_conditions>

     </process_variable>

   </process_variables>

   <nonlinear_solvers>

     <nonlinear_solver>

       <name>basic_newton</name>

       <type>Newton</type>

       <max_iter>50</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>sd</prefix>

         <parameters>-sd_ksp_type cg -sd_pc_type lu -sd_ksp_rtol 1e-16 -sd_ksp_max_it 10</parameters>

       </petsc>

     </linear_solver>

   </linear_solvers>

   <test_definition>

     <vtkdiff>

       <file>hertz_ts_5_t_5.000000.vtu</file>

       <field>displacement</field>

       <absolute_tolerance>1.2e-4</absolute_tolerance>

       <relative_tolerance>0</relative_tolerance>

     </vtkdiff>

     <vtkdiff>

       <file>hertz_ts_5_t_5.000000.vtu</file>

       <field>epsilon</field>

       <absolute_tolerance>4e-3</absolute_tolerance>

       <relative_tolerance>0</relative_tolerance>

     </vtkdiff>

     <vtkdiff>

       <file>hertz_ts_5_t_5.000000.vtu</file>

       <field>sigma</field>

       <absolute_tolerance>5.5e-3</absolute_tolerance>

       <relative_tolerance>0</relative_tolerance>

     </vtkdiff>

     <vtkdiff>

       <file>hertz_ts_10_t_10.000000.vtu</file>

       <field>displacement</field>

       <absolute_tolerance>6.1e-5</absolute_tolerance>

       <relative_tolerance>0</relative_tolerance>

     </vtkdiff>

     <vtkdiff>

       <file>hertz_ts_10_t_10.000000.vtu</file>

       <field>epsilon</field>

       <absolute_tolerance>2e-3</absolute_tolerance>

       <relative_tolerance>0</relative_tolerance>

     </vtkdiff>

     <vtkdiff>

       <file>hertz_ts_10_t_10.000000.vtu</file>

       <field>sigma</field>

       <absolute_tolerance>2.5e-3</absolute_tolerance>

       <relative_tolerance>0</relative_tolerance>

     </vtkdiff>

   </test_definition>

 </OpenGeoSysProject>