LinearCombinationFunction

Returns the linear combination of the functions

Example input syntax

In this input file, we show how a LinearCombinationFunction may be used to combine a variety of different functions, then compare the results to a manually computed linear combination.

[Functions]
  [./xtimes]
    type = ParsedFunction
    expression = 1.1*x
  [../]

  [./twoxplus1]
    type = ParsedFunction
    expression = 2*x+1
  [../]

  [./xsquared]
    type = ParsedFunction
    expression = (x-2)*x
  [../]

  [./tover2]
    type = ParsedFunction
    expression = 0.5*t
  [../]

  [./the_linear_combo]
    type = LinearCombinationFunction
    functions = 'xtimes twoxplus1 xsquared tover2'
    w = '3 -1.2 0.4 3'
  [../]

  [./should_be_answer]
    type = ParsedFunction
    expression = 3*1.1*x-1.2*(2*x+1)+0.4*(x-2)*x+3*0.5*t
  [../]
[]

Input Parameters

functionsThis function will return Sum_over_i(w_i * functions_i)
C++ Type:std::vector<FunctionName>
Controllable:No
Description:This function will return Sum_over_i(w_i * functions_i)
wThis function will return Sum_over_i(w_i * functions_i)
C++ Type:std::vector<double>
Controllable:No
Description:This function will return Sum_over_i(w_i * functions_i)

Required Parameters

execute_onLINEARThe list of flag(s) indicating when this object should be executed, the available options include FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM.
Default:LINEAR
C++ Type:ExecFlagEnum
Options:FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed, the available options include FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

Input Files

(test/tests/functions/linear_combination_function/except1.i)
(python/peacock/tests/common/lcf1.i)
(modules/xfem/test/tests/nucleation_uo/nucleate_2edge_cracks_2d.i)
(test/tests/functions/linear_combination_function/lcf_grad.i)
(test/tests/functions/linear_combination_function/lcf_vector.i)
(python/peacock/tests/input_tab/InputTree/gold/lcf1.i)
(test/tests/functions/linear_combination_function/lcf1.i)

(test/tests/functions/linear_combination_function/lcf1.i)

# LinearCombinationFunction function test
# See [Functions] block for a description of the tests

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 2
  nx = 10
[]

[Variables]
  [./dummy]
  [../]
[]

[Kernels]
  [./dummy_u]
    type = TimeDerivative
    variable = dummy
  [../]
[]


[AuxVariables]
  [./the_linear_combo]
  [../]
[]

[AuxKernels]
  [./the_linear_combo]
    type = FunctionAux
    variable = the_linear_combo
    function = the_linear_combo
  [../]
[]


[Functions]
  [./xtimes]
    type = ParsedFunction
    expression = 1.1*x
  [../]

  [./twoxplus1]
    type = ParsedFunction
    expression = 2*x+1
  [../]

  [./xsquared]
    type = ParsedFunction
    expression = (x-2)*x
  [../]

  [./tover2]
    type = ParsedFunction
    expression = 0.5*t
  [../]

  [./the_linear_combo]
    type = LinearCombinationFunction
    functions = 'xtimes twoxplus1 xsquared tover2'
    w = '3 -1.2 0.4 3'
  [../]

  [./should_be_answer]
    type = ParsedFunction
    expression = 3*1.1*x-1.2*(2*x+1)+0.4*(x-2)*x+3*0.5*t
  [../]
[]

[Postprocessors]
  [./should_be_zero]
    type = NodalL2Error
    function = should_be_answer
    variable = the_linear_combo
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.5
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = lcf1
  hide = dummy
  exodus = false
  csv = true
[]

(test/tests/functions/linear_combination_function/except1.i)

# LinearCombinationFunction function test
# See [Functions] block for a description of the tests

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 2
  nx = 10
[]

[Variables]
  [./dummy]
  [../]
[]

[Kernels]
  [./dummy_u]
    type = TimeDerivative
    variable = dummy
  [../]
[]


[AuxVariables]
  [./the_linear_combo]
  [../]
[]

[AuxKernels]
  [./the_linear_combo]
    type = FunctionAux
    variable = the_linear_combo
    function = the_linear_combo
  [../]
[]


[Functions]
  [./twoxplus1]
    type = ParsedFunction
    expression = 2*x+1
  [../]

  [./xsquared]
    type = ParsedFunction
    expression = x*x
  [../]

  [./the_linear_combo]
    type = LinearCombinationFunction
    functions = 'x twoxplus1 xsquared'
    w = '0.5 5 0.4 0.3'
  [../]

  [./should_be_answer]
    type = ParsedFunction
    expression = 0.5*x+5*(2*x+1)*0.4*x*x+0.3*7
  [../]
[]

[Postprocessors]
  [./should_be_zero]
    type = NodalL2Error
    function = should_be_answer
    variable = the_linear_combo
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.5
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  hide = dummy
  exodus = false
  csv = true
[]

(python/peacock/tests/common/lcf1.i)

# LinearCombinationFunction function test
# See [Functions] block for a description of the tests

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 2
  nx = 10
[]

[Variables]
  [./dummy]
  [../]
[]

[Kernels]
  [./dummy_u]
    type = TimeDerivative
    variable = dummy
  [../]
[]


[AuxVariables]
  [./the_linear_combo]
  [../]
[]

[AuxKernels]
  [./the_linear_combo]
    type = FunctionAux
    variable = the_linear_combo
    function = the_linear_combo
  [../]
[]


[Functions]
  [./xtimes]
    type = ParsedFunction
    expression = 1.1*x
  [../]

  [./twoxplus1]
    type = ParsedFunction
    expression = 2*x+1
  [../]

  [./xsquared]
    type = ParsedFunction
    expression = (x-2)*x
  [../]

  [./tover2]
    type = ParsedFunction
    expression = 0.5*t
  [../]

  [./the_linear_combo]
    type = LinearCombinationFunction
    functions = 'xtimes twoxplus1 xsquared tover2'
    w = '3 -1.2 0.4 3'
  [../]

  [./should_be_answer]
    type = ParsedFunction
    expression = 3*1.1*x-1.2*(2*x+1)+0.4*(x-2)*x+3*0.5*t
  [../]
[]

[Postprocessors]
  [./should_be_zero]
    type = NodalL2Error
    function = should_be_answer
    variable = the_linear_combo
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.5
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = lcf1
  hide = dummy
  exodus = false
  csv = true
[]

(modules/xfem/test/tests/nucleation_uo/nucleate_2edge_cracks_2d.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[XFEM]
  geometric_cut_userobjects = 'cut_mesh2'
  qrule = volfrac
  output_cut_plane = true
[]

[Mesh]
[gen]
  type = GeneratedMeshGenerator
  dim = 2
  nx = 30
  ny = 15
  xmin = -2
  xmax = -.2
  ymin = 0.0
  ymax = 1.0
  elem_type = QUAD4
[]
[dispBlock_top]
  type = BoundingBoxNodeSetGenerator
  new_boundary = pull_top_y
  bottom_left = '-2.1 0.99 0'
  top_right = '-1.9 1.01 0'
  input = gen
[]
[dispBlock_bot]
  type = BoundingBoxNodeSetGenerator
  new_boundary = pull_bot_y
  bottom_left = '-2.1 -.01 0'
  top_right = '-1.9 0.01 0'
  input = dispBlock_top
[]
[]

[DomainIntegral]
  integrals = 'Jintegral InteractionIntegralKI InteractionIntegralKII'
  displacements = 'disp_x disp_y'
  crack_front_points_provider = cut_mesh2
  2d=true
  number_points_from_provider = 1
  crack_direction_method = CurvedCrackFront
  radius_inner = '0.15'
  radius_outer = '0.45'
  poissons_ratio = 0.3
  youngs_modulus = 207000
  block = 0
  incremental = true
  used_by_xfem_to_grow_crack = true
[]

[UserObjects]
  #fixme, nucleate has to be before cut_mesh2 in the input file or cut_mesh2 can't finde the nucleate_uo
  [nucleate]
    type = MeshCut2DRankTwoTensorNucleation
    tensor = stress
    scalar_type = MaxPrincipal
    nucleation_threshold = nucleation_threshold
    initiate_on_boundary = 'left bottom'
    average = true
    nucleation_length = .1
  []
  [cut_mesh2]
    type = MeshCut2DFractureUserObject
    mesh_file = make_edge_crack_in.e
    k_critical=80
    growth_increment = 0.1
    nucleate_uo = nucleate
  []
[]
[AuxVariables]
  [nucleation_threshold]
    order = CONSTANT
    family = MONOMIAL
  []
[]
[ICs]
   [nucleation]
     type = FunctionIC
     function =  nucleation_x_y
     variable = nucleation_threshold
   []
  # [nucleation]
  #   type = VolumeWeightedWeibull
  #   variable = nucleation_threshold
  #   reference_volume = 0.01 #This is the volume of an element for a 100x100 mesh
  #   weibull_modulus = 2
  #   median = 5000.0
  # []
[]

[Functions]
  [nucleation_y]
    type = ParsedFunction
    expression = 'if(y>0.7,10000,if(y<0.5,10000,4000*(1-y)^2-10000))'
  []
  [nucleation_x]
    type = ParsedFunction
    expression = 'if(x>-0.9,10000,if(x<-1.1,10000,1000*(x)^2-10000))'
  []
  [nucleation_x_y]
    type = LinearCombinationFunction
    functions = 'nucleation_x nucleation_y'
    w = '1 1'
  []
[]

[Modules/TensorMechanics/Master]
  [./all]
    strain = FINITE
    planar_formulation = plane_strain
    add_variables = true
    generate_output = 'stress_xx stress_yy vonmises_stress max_principal_stress'
  [../]
[]

[Functions]
  [bc_pull_top]
    type = ParsedFunction
    expression = 'if(t<6,0.0008*t,0.0008*5+0.0004*(t-6))'
  []
  [bc_pull_bot]
    type = ParsedFunction
    expression = 0.0004*t
  []
[]

[BCs]
  [top_left]
      type = FunctionDirichletBC
      boundary = pull_top_y
      variable = disp_y
      function = bc_pull_top
  []
  [bot_left]
    type = FunctionDirichletBC
    boundary = pull_bot_y
    variable = disp_y
    function = bc_pull_bot
[]
  [bottom_x]
    type = DirichletBC
    boundary = right
    variable = disp_x
    value = 0.0
  []
  [bottom_y]
    type = DirichletBC
    boundary = right
    variable = disp_y
    value = 0.0
  []
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 207000
    poissons_ratio = 0.3
    block = 0
  [../]
  [./stress]
    type = ComputeFiniteStrainElasticStress
    block = 0
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      8'

  line_search = 'none'

  [./Predictor]
    type = SimplePredictor
    scale = 1.0
  [../]

# controls for linear iterations
  l_max_its = 100
  l_tol = 1e-2

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9

# time control
  start_time = 0.0
  dt = 1.0
  end_time = 55
  max_xfem_update = 2
[]

[Outputs]
  # csv=true
  exodus = true
  execute_on = TIMESTEP_END
  # [xfemcutter]
  #   type=XFEMCutMeshOutput
  #   xfem_cutter_uo=cut_mesh2
  # []
  # console = false
  [./console]
    type = Console
    output_linear = false
    output_nonlinear = false
  [../]
[]

(test/tests/functions/linear_combination_function/lcf_grad.i)

# LinearCombinationFunction function test
# See [Functions] block for a description of the tests

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  nx = 3
  ny = 3
[]

[Variables]
  [./dummy]
  [../]
[]

[Kernels]
  [./dummy_u]
    type = TimeDerivative
    variable = dummy
  [../]
[]


[AuxVariables]
  [./the_linear_combo_x]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./the_linear_combo_y]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./the_linear_combo_x]
    type = FunctionDerivativeAux
    component = x
    variable = the_linear_combo_x
    function = the_linear_combo
  [../]
  [./the_linear_combo_y]
    type = FunctionDerivativeAux
    component = y
    variable = the_linear_combo_y
    function = the_linear_combo
  [../]
[]


[Functions]
  [./xtimes]
    type = ParsedGradFunction
    value = '1.1*x+y'
    grad_x = '1.1'
    grad_y = '1'
  [../]

  [./twoxplus1]
    type = ParsedGradFunction
    value = '2*x+1'
    grad_x = '2'
  [../]

  [./tover2]
    type = ParsedGradFunction
    value = '0.5*t-y*7'
    grad_y = '-7'
  [../]

  [./the_linear_combo]
    type = LinearCombinationFunction
    functions = 'xtimes twoxplus1 tover2'
    w = '3 -1.2 3'
  [../]

  [./should_be_answer_x]
    type = ParsedFunction
    expression = '3*1.1-1.2*2'
  [../]
  [./should_be_answer_y]
    type = ParsedFunction
    expression = '3*1+3*(-7)'
  [../]
[]

[Postprocessors]
  [./should_be_zero_x]
    type = ElementL2Error
    function = should_be_answer_x
    variable = the_linear_combo_x
  [../]
  [./should_be_zero_y]
    type = ElementL2Error
    function = should_be_answer_y
    variable = the_linear_combo_y
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.5
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = lcf_grad
  hide = dummy
  exodus = false
  csv = true
[]

(test/tests/functions/linear_combination_function/lcf_vector.i)

# use the vectorValue of a LinearCombinationFunction
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  uniform_refine = 1
[]

[Variables]
  [./u]
  [../]
[]

[Functions]
  [./conductivity_1]
    type = ParsedVectorFunction
    expression_y = '0.1+x'
    expression_x = '0.5*(1+x*y)'
  [../]
  [./conductivity_2]
    type = ParsedVectorFunction
    expression_y = '0.1+2*x'
    expression_x = '0.2+x*y'
  [../]
  [./conductivity]
    type = LinearCombinationFunction # yields value_y=0.1, value_x=0.8
    functions = 'conductivity_1 conductivity_2'
    w = '2 -1'
  [../]
[]

[Kernels]
  [./diff]
    type = DiffTensorKernel
    variable = u
    conductivity = conductivity
  [../]
[]

[BCs]
  [./left]
    type = DirichletBC
    variable = u
    boundary = left
    value = 0
  [../]
  [./bottom]
    type = DirichletBC
    variable = u
    boundary = bottom
    value = 1
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  exodus = true
[]

(python/peacock/tests/input_tab/InputTree/gold/lcf1.i)

# LinearCombinationFunction function test
# See [Functions] block for a description of the tests
[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 2
  nx = 10
[]

[Variables]
  [dummy]
  []
[]

[Kernels]
  [dummy_u]
    type = TimeDerivative
    variable = dummy
  []
[]

[AuxVariables]
  [the_linear_combo]
  []
[]

[AuxKernels]
  [the_linear_combo]
    type = FunctionAux
    variable = the_linear_combo
    function = the_linear_combo
  []
[]

[Functions]
  [xtimes]
    type = ParsedFunction
    expression = '1.1*x'
  []
  [twoxplus1]
    type = ParsedFunction
    expression = '2*x+1'
  []
  [xsquared]
    type = ParsedFunction
    expression = '(x-2)*x'
  []
  [tover2]
    type = ParsedFunction
    expression = '0.5*t'
  []
  [the_linear_combo]
    type = LinearCombinationFunction
    functions = 'xtimes twoxplus1 xsquared tover2'
    w = '3 -1.2 0.4 3'
  []
  [should_be_answer]
    type = ParsedFunction
    expression = '3*1.1*x-1.2*(2*x+1)+0.4*(x-2)*x+3*0.5*t'
  []
[]

[Postprocessors]
  [should_be_zero]
    type = NodalL2Error
    function = should_be_answer
    variable = 'the_linear_combo'
  []
[]

[Executioner]
  type = Transient
  dt = 0.5
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = lcf1
  hide = 'dummy'
  exodus = false
  csv = true
[]

(test/tests/functions/linear_combination_function/lcf1.i)

# LinearCombinationFunction function test
# See [Functions] block for a description of the tests

[Mesh]
  type = GeneratedMesh
  dim = 1
  xmin = 0
  xmax = 2
  nx = 10
[]

[Variables]
  [./dummy]
  [../]
[]

[Kernels]
  [./dummy_u]
    type = TimeDerivative
    variable = dummy
  [../]
[]


[AuxVariables]
  [./the_linear_combo]
  [../]
[]

[AuxKernels]
  [./the_linear_combo]
    type = FunctionAux
    variable = the_linear_combo
    function = the_linear_combo
  [../]
[]


[Functions]
  [./xtimes]
    type = ParsedFunction
    expression = 1.1*x
  [../]

  [./twoxplus1]
    type = ParsedFunction
    expression = 2*x+1
  [../]

  [./xsquared]
    type = ParsedFunction
    expression = (x-2)*x
  [../]

  [./tover2]
    type = ParsedFunction
    expression = 0.5*t
  [../]

  [./the_linear_combo]
    type = LinearCombinationFunction
    functions = 'xtimes twoxplus1 xsquared tover2'
    w = '3 -1.2 0.4 3'
  [../]

  [./should_be_answer]
    type = ParsedFunction
    expression = 3*1.1*x-1.2*(2*x+1)+0.4*(x-2)*x+3*0.5*t
  [../]
[]

[Postprocessors]
  [./should_be_zero]
    type = NodalL2Error
    function = should_be_answer
    variable = the_linear_combo
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.5
  end_time = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = lcf1
  hide = dummy
  exodus = false
  csv = true
[]

Example input syntax
Input Parameters
Input Files