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tests/burgers_mms_steady_adjoint_gradient_src_revolve/mms_A.bml
 
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<?xml version='1.0' encoding='utf-8'?>
 
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<burgers_equation>
 
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  <simulation_name>
 
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    <string_value lines="1">mms_adjoint_A</string_value>
 
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  </simulation_name>
 
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  <geometry>
 
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    <dimension>
 
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      <integer_value rank="0">1</integer_value>
 
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    </dimension>
 
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    <mesh name="CoordinateMesh">
 
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      <from_file file_name="mms_A">
 
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        <format name="triangle"/>
 
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        <stat>
 
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          <include_in_stat/>
 
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        </stat>
 
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      </from_file>
 
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    </mesh>
 
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    <mesh name="VelocityMesh">
 
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      <from_mesh>
 
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        <mesh name="CoordinateMesh"/>
 
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        <stat>
 
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          <exclude_from_stat/>
 
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        </stat>
 
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      </from_mesh>
 
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    </mesh>
 
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    <quadrature>
 
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      <degree>
 
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        <integer_value rank="0">4</integer_value>
 
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      </degree>
 
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    </quadrature>
 
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  </geometry>
 
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  <io>
 
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    <dump_format>vtk</dump_format>
 
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    <dump_period_in_timesteps>
 
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      <constant>
 
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        <integer_value rank="0">1</integer_value>
 
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      </constant>
 
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    </dump_period_in_timesteps>
 
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    <output_mesh name="VelocityMesh"/>
 
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  </io>
 
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  <timestepping>
 
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    <current_time>
 
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      <real_value rank="0">0</real_value>
 
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    </current_time>
 
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    <timestep>
 
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      <real_value rank="0">0.1</real_value>
 
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    </timestep>
 
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    <finish_time>
 
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      <real_value rank="0">1</real_value>
 
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    </finish_time>
 
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    <nonlinear_iterations>
 
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      <integer_value rank="0">2</integer_value>
 
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    </nonlinear_iterations>
 
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  </timestepping>
 
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  <material_phase name="Fluid">
 
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    <scalar_field name="Velocity" rank="0">
 
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      <prognostic>
 
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        <mesh name="VelocityMesh"/>
 
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        <temporal_discretisation>
 
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          <theta>
 
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            <real_value rank="0">0.5</real_value>
 
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          </theta>
 
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          <relaxation>
 
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            <real_value rank="0">0.5</real_value>
 
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          </relaxation>
 
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        </temporal_discretisation>
 
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        <solver>
 
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          <iterative_method name="preonly"/>
 
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          <preconditioner name="lu"/>
 
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          <relative_error>
 
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            <real_value rank="0">1e-16</real_value>
 
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          </relative_error>
 
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          <absolute_error>
 
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            <real_value rank="0">1e-12</real_value>
 
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          </absolute_error>
 
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          <max_iterations>
 
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            <integer_value rank="0">10000</integer_value>
 
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          </max_iterations>
 
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          <never_ignore_solver_failures/>
 
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          <diagnostics>
 
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            <monitors/>
 
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          </diagnostics>
 
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        </solver>
 
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        <remove_advection_term/>
 
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        <initial_condition name="WholeMesh">
 
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          <python>
 
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            <string_value lines="20" type="python">def val(X, t):
 
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  from math import sin, cos
 
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  x = X[0]
 
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  return sin(x) + cos(x)</string_value>
 
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          </python>
 
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        </initial_condition>
 
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        <boundary_conditions name="bc">
 
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          <surface_ids>
 
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            <integer_value shape="2" rank="1">1 2</integer_value>
 
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          </surface_ids>
 
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          <type name="dirichlet">
 
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            <python>
 
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              <string_value lines="20" type="python">def val(X, t):
 
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  from math import sin, cos
 
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  x = X[0]
 
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  return sin(x) + cos(x)</string_value>
 
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            </python>
 
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          </type>
 
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        </boundary_conditions>
 
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        <viscosity>
 
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          <real_value rank="0">1</real_value>
 
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        </viscosity>
 
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        <stat/>
 
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        <adjoint_storage>
 
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          <exists_in_both/>
 
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        </adjoint_storage>
 
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        <scalar_field name="Source" rank="0">
 
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          <prescribed>
 
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            <value name="WholeMesh">
 
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              <python>
 
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                <string_value lines="20" type="python">def val(X, t):
 
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  from math import sin, cos
 
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  x = X[0]
 
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  y = sin(x) + cos(x)
 
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  return y</string_value>
 
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              </python>
 
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            </value>
 
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          </prescribed>
 
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        </scalar_field>
 
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      </prognostic>
 
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    </scalar_field>
 
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    <scalar_field name="AnalyticalSolution" rank="0">
 
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      <prescribed>
 
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        <mesh name="VelocityMesh"/>
 
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        <value name="WholeMesh">
 
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          <python>
 
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            <string_value lines="20" type="python">def val(X, t):
 
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  from math import sin, cos
 
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  x = X[0]
 
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  return sin(x) + cos(x)</string_value>
 
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          </python>
 
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        </value>
 
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        <adjoint_storage>
 
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          <exists_in_forward/>
 
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        </adjoint_storage>
 
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      </prescribed>
 
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    </scalar_field>
 
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    <scalar_field name="Error" rank="0">
 
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      <diagnostic>
 
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        <mesh name="VelocityMesh"/>
 
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        <algorithm name="scalar_python_diagnostic" material_phase_support="single">
 
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          <string_value lines="20" type="python">soln = state.scalar_fields["Velocity"]
 
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exact = state.scalar_fields["AnalyticalSolution"]
 
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for i in range(field.node_count):
 
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  field.set(i, abs(soln.node_val(i) - exact.node_val(i)))</string_value>
 
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        </algorithm>
 
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        <stat/>
 
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        <adjoint_storage>
 
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          <exists_in_forward/>
 
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        </adjoint_storage>
 
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      </diagnostic>
 
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    </scalar_field>
 
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    <scalar_field name="funct_derivative" rank="0">
 
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      <diagnostic>
 
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        <mesh name="VelocityMesh"/>
 
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        <algorithm name="scalar_python_diagnostic" material_phase_support="single">
 
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          <string_value lines="20" type="python">field.val[:] = 0.0
 
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if time == 1.0:
 
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  coord = state.vector_fields['Coordinate']
 
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  adj_u = state.scalar_fields['AdjointVelocity']
 
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  #print "Adjoint velocity(t=1.0): ", adj_u.val
 
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  for ele in range(coord.element_count):
 
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    t = Transform(ele, coord)
 
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    shape = adj_u.ele_shape(ele)
 
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    mass = t.shape_shape(shape, shape)
 
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    field.addto(adj_u.ele_nodes(ele), numpy.dot(mass, adj_u.ele_val(ele)))
 
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#print "Funct_derivative (diagnostic): ", field.val</string_value>
 
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        </algorithm>
 
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        <stat/>
 
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        <adjoint_storage>
 
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          <exists_in_adjoint/>
 
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        </adjoint_storage>
 
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      </diagnostic>
 
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    </scalar_field>
 
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  </material_phase>
 
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  <adjoint>
 
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    <checkpointing>
 
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      <max_memory_checkpoints>
 
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        <integer_value rank="0">5</integer_value>
 
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      </max_memory_checkpoints>
 
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      <max_disk_checkpoints>
 
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        <integer_value rank="0">0</integer_value>
 
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      </max_disk_checkpoints>
 
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    </checkpointing>
 
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    <functional name="time_integral_ad">
 
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      <functional_value>
 
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        <algorithm name="functional_value">
 
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          <string_value lines="20" type="python">import numpy
 
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J = 0.0
 
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eps = 0.00000000001
 
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if time &gt; 1.0-eps:
 
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  coord = states[n]["Fluid"].vector_fields["Coordinate"]
 
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  u = states[n]["Fluid"].scalar_fields["Velocity"]
 
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204
  #print "u(t=0): ", states[0]["Fluid"].scalar_fields["Velocity"].val
 
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  #print "u(t=1): ", states[1]["Fluid"].scalar_fields["Velocity"].val
 
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  for ele in range(coord.element_count):
 
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    t = Transform(ele, coord)
 
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    shape = u.ele_shape(ele)
 
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    mass = t.shape_shape(shape, shape)
 
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    J = J + 0.5 * numpy.dot(u.ele_val(ele), numpy.dot(mass, u.ele_val(ele)))
 
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#  print "Got functional value: ", J
 
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#if hasattr(J, "nominal_value"):
 
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#  print "u.val: ", u.val
 
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#  print "delJ/delu: ", [J.derivatives[x] for x in u.val]
 
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#  print "J.nominal_value: ", J.nominal_value</string_value>
 
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        </algorithm>
 
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        <reduction>
 
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          <sum/>
 
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        </reduction>
 
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      </functional_value>
 
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      <functional_dependencies>
 
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        <algorithm name="functional_dependencies">
 
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          <string_value lines="20" type="python">def dependencies(times, timestep):
 
226
  if times[0] &lt;= 1.0 &lt;= times[1]:
 
227
    return {"Fluid::Coordinate": [timestep],
 
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            "Fluid::Velocity": [timestep]}
 
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  else:
 
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    return {}</string_value>
 
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        </algorithm>
 
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      </functional_dependencies>
 
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    </functional>
 
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    <controls>
 
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      <control name="Source">
 
236
        <type field_name="Fluid::VelocitySource" name="source_term"/>
 
237
      </control>
 
238
    </controls>
 
239
    <debug>
 
240
      <html_output/>
 
241
      <check_action_transposes/>
 
242
    </debug>
 
243
  </adjoint>
 
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</burgers_equation>