Eigenvalues

construction:Undocumented Class

The Eigenvalues has not been documented. The content listed below should be used as a starting point for documenting the class, which includes the typical automatic documentation associated with a MooseObject; however, what is contained is ultimately determined by what is necessary to make the documentation clear for users.


# Eigenvalues

!syntax description /VectorPostprocessors/Eigenvalues

## Overview

!! Replace these lines with information regarding the Eigenvalues object.

## Example Input File Syntax

!! Describe and include an example of how to use the Eigenvalues object.

!syntax parameters /VectorPostprocessors/Eigenvalues

!syntax inputs /VectorPostprocessors/Eigenvalues

!syntax children /VectorPostprocessors/Eigenvalues

Returns the Eigen values from the nonlinear Eigen system.

Input Parameters

contains_complete_historyFalseSet this flag to indicate that the values in all vectors declared by this VPP represent a time history (e.g. with each invocation, new values are added and old values are never removed). This changes the output so that only a single file is output and updated with each invocation
Default:False
C++ Type:bool
Options:
Description:Set this flag to indicate that the values in all vectors declared by this VPP represent a time history (e.g. with each invocation, new values are added and old values are never removed). This changes the output so that only a single file is output and updated with each invocation
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
inverse_eigenvalueFalseTrue to evaluate the inverse of eigenvalues
Default:False
C++ Type:bool
Options:
Description:True to evaluate the inverse of eigenvalues
parallel_typeREPLICATEDSet how the data is represented within the VectorPostprocessor (VPP); 'distributed' indicates that data within the VPP is distributed and no auto communication is preformed, this setting will result in parallel output within the CSV output; 'replicated' indicates that the data within the VPP is correct on processor 0, the data will automatically be broadcast to all processors unless the '_auto_broadcast' param is set to false within the validParams function.
Default:REPLICATED
C++ Type:MooseEnum
Options:DISTRIBUTED, REPLICATED
Description:Set how the data is represented within the VectorPostprocessor (VPP); 'distributed' indicates that data within the VPP is distributed and no auto communication is preformed, this setting will result in parallel output within the CSV output; 'replicated' indicates that the data within the VPP is correct on processor 0, the data will automatically be broadcast to all processors unless the '_auto_broadcast' param is set to false within the validParams function.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Options:
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
force_preauxFalseForces the GeneralUserObject to be executed in PREAUX
Default:False
C++ Type:bool
Options:
Description:Forces the GeneralUserObject to be executed in PREAUX
force_preicFalseForces the GeneralUserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Options:
Description:Forces the GeneralUserObject to be executed in PREIC during initial setup
outputsVector of output names were you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

Input Files

(test/tests/problems/eigen_problem/eigensolvers/ne_deficient_b.i)
(test/tests/problems/eigen_problem/eigensolvers/ne_hmg.i)
(test/tests/problems/eigen_problem/eigensolvers/dg_krylovschur.i)
(test/tests/problems/eigen_problem/eigensolvers/gipm_ibc.i)
(test/tests/problems/eigen_problem/preconditioners/ne_pbp.i)
(test/tests/problems/eigen_problem/eigensolvers/ipm.i)
(test/tests/problems/eigen_problem/initial_condition/ne_ic.i)
(test/tests/problems/eigen_problem/initial_condition/ne_ic_no_free.i)
(test/tests/problems/eigen_problem/eigensolvers/scalar.i)
(test/tests/problems/eigen_problem/eigensolvers/ne-coupled-resid-scaling.i)
(test/tests/problems/eigen_problem/arraykernels/ne_array_kernels.i)
(test/tests/problems/eigen_problem/eigensolvers/ne_coupled_picard_subT_sub.i)
(test/tests/problems/eigen_problem/eigensolvers/gipm.i)
(test/tests/problems/eigen_problem/eigensolvers/ane.i)
(test/tests/problems/eigen_problem/eigensolvers/ne-coupled-scaling.i)
(test/tests/problems/eigen_problem/eigensolvers/ne.i)
(test/tests/problems/eigen_problem/eigensolvers/ne_coupled.i)
(test/tests/problems/eigen_problem/arraykernels/ne_two_variables.i)
(test/tests/problems/eigen_problem/eigensolvers/ne_coupled_picard.i)

(test/tests/problems/eigen_problem/eigensolvers/ne_deficient_b.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
  [./v]
    order = FIRST
    family = LAGRANGE
    eigen = true
  [../]
[]

[Kernels]
  [./diff_u]
    type = Diffusion
    variable = u
  [../]
  [./diff_v]
    type = Diffusion
    variable = v
  [../]

  [./rhs]
    type = CoupledForce
    variable = u
    v = v
    extra_vector_tags = 'eigen'
  [../]
  [./src_v]
    type = CoupledForce
    variable = v
    v = u
  [../]
[]

[BCs]
  [./homogeneous_u]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]
  [./homogeneous_v]
    type = DirichletBC
    variable = v
    boundary = '0 1 2 3'
    value = 0
  [../]
  [./eigenBC_u]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]
  [./eigenBC_v]
    type = EigenDirichletBC
    variable = v
    boundary = '0 1 2 3'
  [../]

[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  file_base = ne_deficient_b
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/eigensolvers/ne_hmg.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

# the minimum eigenvalue of this problem is 2*(PI/a)^2;
# Its inverse is 0.5*(a/PI)^2 = 5.0660591821169. Here a is equal to 10.

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]

  [./diffv]
    type = Diffusion
    variable = v
  [../]

  [./rhsv]
    type = CoefReaction
    variable = v
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]
  [./eigen]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]

  [./homogeneousv]
    type = DirichletBC
    variable = v
    boundary = '0 1 2 3'
    value = 0
  [../]
  [./eigenv]
    type = EigenDirichletBC
    variable = v
    boundary = '0 1 2 3'
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
  petsc_options_iname = '-pc_type
                         -pc_hmg_use_subspace_coarsening'
  petsc_options_value = 'hmg true'
  petsc_options = '-eps_view'
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  file_base = monolith_newton
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/eigensolvers/dg_krylovschur.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 1
  nx = 10
  ny = 10
  elem_type = QUAD4
[]

[Variables]
  [./u]
    order = FIRST
    family = MONOMIAL
  [../]
[]

[DGKernels]
  [./dg_diff]
    type = DGDiffusion
    variable = u
    sigma = 6
    epsilon = -1
  []
[]

[Kernels]
  [./rhs]
    type = Reaction
    variable = u
    extra_vector_tags = 'eigen'
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = KRYLOVSCHUR
  eigen_problem_type = HERMITIAN
  which_eigen_pairs = LARGEST_MAGNITUDE
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/eigensolvers/gipm_ibc.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 100
  ymin = 0
  ymax = 100
  elem_type = QUAD4
  nx = 64
  ny = 64

  displacements = 'x_disp y_disp'
[]

[Variables]
  [./u]
    order = first
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./x_disp]
  [../]
  [./y_disp]
  [../]
[]

[AuxKernels]
  [./x_disp]
    type = FunctionAux
    variable = x_disp
    function = x_disp_func
  [../]
  [./y_disp]
    type = FunctionAux
    variable = y_disp
    function = y_disp_func
  [../]
[]

[Functions]
  [./x_disp_func]
    type = ParsedFunction
    value = 0
  [../]
  [./y_disp_func]
    type = ParsedFunction
    value = 0
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
    use_displaced_mesh = true
  [../]

  [./rea]
    type = CoefReaction
    variable = u
    coefficient = 2.0
    use_displaced_mesh = true
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    use_displaced_mesh = true
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]
[]

[BCs]
  [./nbc_homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0'
    value = 0
    use_displaced_mesh = true
  [../]

  [./nbc_eigen]
    type = EigenDirichletBC
    variable = u
    boundary = '0'
    use_displaced_mesh = true
  [../]

  [./ibc]
    type = VacuumBC
    variable = u
    boundary = '1 2 3'
    extra_vector_tags = 'eigen'
    use_displaced_mesh = true
  []
[]

[Executioner]
  type = Eigenvalue
  eigen_problem_type = gen_non_hermitian
  which_eigen_pairs = SMALLEST_MAGNITUDE
  n_eigen_pairs = 1
  n_basis_vectors = 18
  solve_type = jacobi_davidson
  petsc_options = '-eps_view'
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  execute_on = 'timestep_end'
  [./console]
    type = Console
    outlier_variable_norms = false
  [../]
[]

(test/tests/problems/eigen_problem/preconditioners/ne_pbp.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

# the minimum eigenvalue of this problem is 2*(PI/a)^2;
# Its inverse is 0.5*(a/PI)^2 = 5.0660591821169. Here a is equal to 10.

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diffu]
    type = Diffusion
    variable = u
  [../]

  [./difv]
    type = Diffusion
    variable = v
  [../]

  [./rhsu]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]

  [./rhsv]
    type = CoefReaction
    variable = v
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]
[]

[BCs]
  [./homogeneousu]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./homogeneousv]
    type = DirichletBC
    variable = v
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenu]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]

  [./eigenv]
    type = EigenDirichletBC
    variable = v
    boundary = '0 1 2 3'
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = JFNK
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  execute_on = 'timestep_end'
[]

[Preconditioning]
  [./PBP]
    type = PBP
    solve_order = 'u v'
    preconditioner  = 'LU LU'
  [../]
[]

(test/tests/problems/eigen_problem/eigensolvers/ipm.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 100
  ymin = 0
  ymax = 100
  elem_type = QUAD4
  nx = 8
  ny = 8

  uniform_refine = 0

  displacements = 'x_disp y_disp'
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./x_disp]
  [../]
  [./y_disp]
  [../]
[]

[AuxKernels]
  [./x_disp]
    type = FunctionAux
    variable = x_disp
    function = x_disp_func
  [../]
  [./y_disp]
    type = FunctionAux
    variable = y_disp
    function = y_disp_func
  [../]
[]

[Functions]
  [./x_disp_func]
    type = ParsedFunction
    value = 0
  [../]
  [./y_disp_func]
    type = ParsedFunction
    value = 0
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
    use_displaced_mesh = true
  [../]

  [./rea]
    type = CoefReaction
    variable = u
    coefficient = 2.0
    use_displaced_mesh = true
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
    use_displaced_mesh = true
  [../]
[]

[Executioner]
  type = Eigenvalue
  which_eigen_pairs = largest_magnitude
  eigen_problem_type = NON_HERMITIAN
  n_eigen_pairs = 5
  n_basis_vectors = 15
  solve_type = krylovschur
  petsc_options = '-eps_view'
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  execute_on = 'timestep_end'
  [./console]
    type = Console
    outlier_variable_norms = false
  [../]
[]

(test/tests/problems/eigen_problem/initial_condition/ne_ic.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

# the minimum eigenvalue of this problem is 2*(PI/a)^2;
# Its inverse is 0.5*(a/PI)^2 = 5.0660591821169. Here a is equal to 10.

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]
  [./eigen]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-6
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/initial_condition/ne_ic_no_free.i)

[Mesh]
  file = 'gold/ne_ic_out.e'
[]

# the minimum eigenvalue of this problem is 2*(PI/a)^2;
# Its inverse is 0.5*(a/PI)^2 = 5.0660591821169. Here a is equal to 10.

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    # Use a good initial so that Newton can converge when we do not use free power iterations
    initial_from_file_var = u
    initial_from_file_timestep = 1
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]
  [./eigen]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
  free_power_iterations = 0
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-6
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/eigensolvers/scalar.i)

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

[Variables]
  [./f1]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
  [./f2]
    family = SCALAR
    order = FIRST
    initial_condition = 1
  [../]
[]

[ScalarKernels]
  [./row1]
    type = ParsedODEKernel
    variable = f1
    function = '5*f1 + 2*f2'
    args = 'f2'
  [../]

  [./row2]
    type = ParsedODEKernel
    variable = f2
    function = '2*f1 + 5*f2'
    args = 'f1'
  [../]
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Eigenvalue
  which_eigen_pairs = LARGEST_MAGNITUDE
  eigen_problem_type = HERMITIAN
  n_eigen_pairs = 2
  n_basis_vectors = 4
  eigen_max_its = 10
  solve_type = KRYLOVSCHUR
  petsc_options = '-eps_view'
[]

[Outputs]
  csv = true
[]

(test/tests/problems/eigen_problem/eigensolvers/ne-coupled-resid-scaling.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [u]
    initial_condition = 1
  []
  [T]
    initial_condition = 1
  []
[]

[AuxVariables]
  [power][]
[]

[Kernels]
  [./diff]
    type = DiffMKernel
    variable = u
    mat_prop = diffusion
    offset = 0.0
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]

  [./diff_T]
    type = CoefDiffusion
    variable = T
    coef = 1e30
  [../]
  [./src_T]
    type = CoupledForce
    variable = T
    v = power
    coef = 1e30
  [../]
[]

[AuxKernels]
  [./power_ak]
    type = NormalizationAux
    variable = power
    source_variable = u
    normalization = unorm
    # this coefficient will affect the eigenvalue.
    normal_factor = 10
    execute_on = linear
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenU]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]

  [./homogeneousT]
    type = DirichletBC
    variable = T
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenT]
    type = EigenDirichletBC
    variable = T
    boundary = '0 1 2 3'
  [../]
[]

[Materials]
  [./dc]
    type = VarCouplingMaterial
    var = T
    block = 0
    base = 1.0
    coef = 1.0
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
  automatic_scaling = true
  petsc_options = '-pc_svd_monitor'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'svd'
  verbose = true
  resid_vs_jac_scaling_param = 1
[]

[Postprocessors]
  [./unorm]
    type = ElementIntegralVariablePostprocessor
    variable = u
    execute_on = linear
  [../]
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/arraykernels/ne_array_kernels.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

# the minimum eigenvalue of this problem is 2*(PI/a)^2;
# Its inverse is 0.5*(a/PI)^2 = 5.0660591821169. Here a is equal to 10.

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
    components = 2
  []
  [v]
    order = FIRST
    family = LAGRANGE
    components = 2
  []
[]

[Kernels]
  [diffu]
    type = ArrayDiffusion
    variable = u
    diffusion_coefficient = dc
  []

  [reactionu]
    type = ArrayReaction
    variable = u
    reaction_coefficient = rc
    extra_vector_tags = 'eigen'
  []

  [diffv]
    type = ArrayDiffusion
    variable = v
    diffusion_coefficient = dc
  []

  [reactionv]
    type = ArrayReaction
    variable = v
    reaction_coefficient = rc
    extra_vector_tags = 'eigen'
  []
[]

[Materials]
  [dc]
    type = GenericConstantArray
    prop_name = dc
    prop_value = '1. 1.'
  []
  [rc]
    type = GenericConstantArray
    prop_name = rc
    prop_value = '-1 -1'
  []
[]

[BCs]
  [hom_u]
    type = ArrayDirichletBC
    variable = u
    values = '0 0'
    boundary = '0 1 2 3'
  []

  [eigenhom_u]
    type = EigenArrayDirichletBC
    variable = u
    boundary = '0 1 2 3'
  []

  [hom_v]
    type = ArrayDirichletBC
    variable = v
    values = '0 0'
    boundary = '0 1 2 3'
  []

  [eigenhom_v]
    type = EigenArrayDirichletBC
    variable = v
    boundary = '0 1 2 3'
  []
[]

[Executioner]
  type = Eigenvalue
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/eigensolvers/ne_coupled_picard_subT_sub.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 10
  ny = 10
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./T]
    order = FIRST
    family = LAGRANGE
  [../]
  [./power]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = DiffMKernel
    variable = u
    mat_prop = diffusion
    offset = 0.0
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]
[]

[AuxKernels]
  [./power_ak]
    type = NormalizationAux
    variable = power
    source_variable = u
    normalization = unorm
    normal_factor = 10
    execute_on = timestep_end
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenU]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]
[]

[Materials]
  [./dc]
    type = VarCouplingMaterial
    var = T
    block = 0
    base = 1.0
    coef = 1.0
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-6
[]

[Postprocessors]
  [./power]
    type = ElementIntegralVariablePostprocessor
    variable = power
    execute_on = timestep_end
  [../]
  [./unorm]
    type = ElementIntegralVariablePostprocessor
    variable = u
    execute_on = linear
  [../]
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  exodus = true
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/eigensolvers/gipm.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 100
  ymin = 0
  ymax = 100
  elem_type = QUAD4
  nx = 64
  ny = 64

  displacements = 'x_disp y_disp'
[]

#The minimum eigenvalue for this problem is 2*(pi/a)^2 + 2 with a = 100.
#Its inverse will be 0.49950700634518.

[Variables]
  [./u]
    order = first
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./x_disp]
  [../]
  [./y_disp]
  [../]
[]

[AuxKernels]
  [./x_disp]
    type = FunctionAux
    variable = x_disp
    function = x_disp_func
  [../]
  [./y_disp]
    type = FunctionAux
    variable = y_disp
    function = y_disp_func
  [../]
[]

[Functions]
  [./x_disp_func]
    type = ParsedFunction
    value = 0
  [../]
  [./y_disp_func]
    type = ParsedFunction
    value = 0
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
    use_displaced_mesh = true
  [../]

  [./rea]
    type = CoefReaction
    variable = u
    coefficient = 2.0
    use_displaced_mesh = true
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    use_displaced_mesh = true
    extra_vector_tags = 'eigen'
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
    use_displaced_mesh = true
  [../]
  [./eigen_bc]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
    use_displaced_mesh = true
  [../]
[]

[Executioner]
  type = Eigenvalue
  eigen_problem_type = gen_non_hermitian
  which_eigen_pairs = SMALLEST_MAGNITUDE
  n_eigen_pairs = 1
  n_basis_vectors = 18
  solve_type = jacobi_davidson
  petsc_options = '-eps_view'
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  execute_on = 'timestep_end'
  [./console]
    type = Console
    outlier_variable_norms = false
  [../]
[]

(test/tests/problems/eigen_problem/eigensolvers/ane.i)

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 10
    ymin = 0
    ymax = 10
    nx = 8
    ny = 8
    elem_type = QUAD4
  []
[]

# the minimum eigenvalue is (2*PI*(p-1)^(1/p)/a/p/sin(PI/p))^p;
# Its inverse is 35.349726539758187. Here a is equal to 10.

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

# Set an random initial condition is necessary for this problem
# A constant initial condition will not work for this problem since
# the problem is ill-conditioned at a constant vector.
# We observed bad convergence when using a constant initial condition
[ICs]
  [./uic]
    type = RandomIC
    variable = u
  [../]
[]

[Kernels]
  [./diff]
    type = PHarmonic
    variable = u
    p = 3
  [../]

  [./rhs]
    type = PMassKernel
    extra_vector_tags = 'eigen'
    variable = u
    coefficient = -1.0
    p = 3
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 2'
    value = 0
  [../]
  [./eigen]
    type = EigenDirichletBC
    variable = u
    boundary = '0 2'
  [../]
[]

[Executioner]
  type = Eigenvalue
  free_power_iterations = 10
  solve_type = PJFNK
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  file_base = ane
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/eigensolvers/ne-coupled-scaling.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [u][]
  [T][]
[]

[AuxVariables]
  [power][]
[]

[Kernels]
  [./diff]
    type = DiffMKernel
    variable = u
    mat_prop = diffusion
    offset = 0.0
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]

  [./diff_T]
    type = CoefDiffusion
    variable = T
    coef = 1e30
  [../]
  [./src_T]
    type = CoupledForce
    variable = T
    v = power
    coef = 1e30
  [../]
[]

[AuxKernels]
  [./power_ak]
    type = NormalizationAux
    variable = power
    source_variable = u
    normalization = unorm
    # this coefficient will affect the eigenvalue.
    normal_factor = 10
    execute_on = linear
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenU]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]

  [./homogeneousT]
    type = DirichletBC
    variable = T
    boundary = '0 1 2 3'
    value = 0
  [../]
[]

[Materials]
  [./dc]
    type = VarCouplingMaterial
    var = T
    block = 0
    base = 1.0
    coef = 1.0
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
  automatic_scaling = true
  petsc_options = '-pc_svd_monitor'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'svd'
  verbose = true
[]

[Postprocessors]
  [./unorm]
    type = ElementIntegralVariablePostprocessor
    variable = u
    execute_on = linear
  [../]
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  exodus = true
  csv = true
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/eigensolvers/ne.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

# the minimum eigenvalue of this problem is 2*(PI/a)^2;
# Its inverse is 0.5*(a/PI)^2 = 5.0660591821169. Here a is equal to 10.

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = Diffusion
    variable = u
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]
  [./eigen]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  file_base = monolith_newton
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/eigensolvers/ne_coupled.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]

  [./T]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./power]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = DiffMKernel
    variable = u
    mat_prop = diffusion
    offset = 0.0
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]

  [./diff_T]
    type = Diffusion
    variable = T
  [../]
  [./src_T]
    type = CoupledForce
    variable = T
    v = power
  [../]
[]

[AuxKernels]
  [./power_ak]
    type = NormalizationAux
    variable = power
    source_variable = u
    normalization = unorm
    # this coefficient will affect the eigenvalue.
    normal_factor = 10
    execute_on = linear
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenU]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]

  [./homogeneousT]
    type = DirichletBC
    variable = T
    boundary = '0 1 2 3'
    value = 0
  [../]
[]

[Materials]
  [./dc]
    type = VarCouplingMaterial
    var = T
    block = 0
    base = 1.0
    coef = 1.0
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
[]

[Postprocessors]
  [./unorm]
    type = ElementIntegralVariablePostprocessor
    variable = u
    execute_on = linear
  [../]
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  file_base = ne_coupled
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/arraykernels/ne_two_variables.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

# the minimum eigenvalue of this problem is 2*(PI/a)^2;
# Its inverse is 0.5*(a/PI)^2 = 5.0660591821169. Here a is equal to 10.

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
  [../]
  [./v]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diffu]
    type = Diffusion
    variable = u
  [../]

  [./diffv]
    type = Diffusion
    variable = v
  [../]

  [./rhsu]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]

  [./rhsv]
    type = CoefReaction
    variable = v
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]
[]

[BCs]
  [./homogeneousu]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]
  [./homogeneousv]
    type = DirichletBC
    variable = v
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenu]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]
  [./eigenv]
    type = EigenDirichletBC
    variable = v
    boundary = '0 1 2 3'
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  execute_on = 'timestep_end'
[]

(test/tests/problems/eigen_problem/eigensolvers/ne_coupled_picard.i)

[Mesh]
  type = GeneratedMesh
  dim = 2
  xmin = 0
  xmax = 10
  ymin = 0
  ymax = 10
  elem_type = QUAD4
  nx = 8
  ny = 8
[]

[Variables]
  [./u]
    order = FIRST
    family = LAGRANGE
    # set this so that the Picard initial norm is not zero
    initial_condition = 1
  [../]
[]

[AuxVariables]
  [./T]
    order = FIRST
    family = LAGRANGE
    # set this so that the Picard initial norm is not zero
    initial_condition = 1
  [../]
  [./power]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./diff]
    type = DiffMKernel
    variable = u
    mat_prop = diffusion
    offset = 0.0
  [../]

  [./rhs]
    type = CoefReaction
    variable = u
    coefficient = -1.0
    extra_vector_tags = 'eigen'
  [../]
[]

[AuxKernels]
  [./power_ak]
    type = NormalizationAux
    variable = power
    source_variable = u
    normalization = unorm
    # this coefficient will affect the eigenvalue.
    normal_factor = 10
    execute_on = timestep_end
  [../]
[]

[BCs]
  [./homogeneous]
    type = DirichletBC
    variable = u
    boundary = '0 1 2 3'
    value = 0
  [../]

  [./eigenU]
    type = EigenDirichletBC
    variable = u
    boundary = '0 1 2 3'
  [../]
[]

[Materials]
  [./dc]
    type = VarCouplingMaterial
    var = T
    block = 0
    base = 1.0
    coef = 1.0
  [../]
[]

[Executioner]
  type = Eigenvalue
  solve_type = PJFNK
  nl_abs_tol = 1e-8
  nl_rel_tol = 1e-6
  picard_max_its = 10
  picard_rel_tol = 1e-6
[]

[Postprocessors]
  [./unorm]
    type = ElementIntegralVariablePostprocessor
    variable = u
    execute_on = linear
  [../]
[]

[VectorPostprocessors]
  [./eigenvalues]
    type = Eigenvalues
    execute_on = 'timestep_end'
  [../]
[]

[Outputs]
  csv = true
  exodus =true
  execute_on = 'timestep_end'
[]

[MultiApps]
  [./sub]
    type = FullSolveMultiApp
    input_files = ne_coupled_picard_sub.i
    execute_on = timestep_end
  [../]
[]

[Transfers]
  [./T_from_sub]
    type = MultiAppMeshFunctionTransfer
    direction = from_multiapp
    multi_app = sub
    source_variable = T
    variable = T
  [../]
  [./power_to_sub]
    type = MultiAppMeshFunctionTransfer
    direction = to_multiapp
    multi_app = sub
    source_variable = power
    variable = power
  [../]
[]

Input Parameters
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