FourierTransform

Compute the Fourier transform of a given variable field.

This user object computes a Fourier transform of a selected variable field using the FFT library FFTW3 (needs to be installed prior to building Magpie). Internally a _Real to Real_ transform is computed. The fransform is computed as a discrete Fourier transform (DFT)_ on a regular orthogonal grid. This grid is either specified using the grid parameter or can be auto-detected when a MyTRIMMesh is used in the simulation.

The fourier transform data is used by the following objects:

FourierLengthScale Postprocessor - Extracts a scalar average lenghth scale from the transform
FourierPowerSpectrum VectorPostprocessor - Extracts a radially (in frequency space) averaged power spectrum from the transform

Input Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
gridNumber of grid cells in each dimension to compute the FFT on (can be omitted when using MyTRIMMesh)
C++ Type:std::vector<int>
Controllable:No
Description:Number of grid cells in each dimension to compute the FFT on (can be omitted when using MyTRIMMesh)
max_h_level0Further grid refinement to apply when using MyTRIMMesh with adaptivity
Default:0
C++ Type:unsigned int
Controllable:No
Description:Further grid refinement to apply when using MyTRIMMesh with adaptivity
variableVariable field to compute the transform of
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Variable field to compute the transform of

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
Controllable:No
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).
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling 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:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
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
Controllable:No
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

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Installing FFTW3

Ubuntu


sudo apt install libfftw3-dev pkg-config

macOS

Using homebrew do


brew install fftw

Input Files

(examples/fft.i)
(tests/postprocessors/fourierlengthscale.i)
(tests/vectorpostprocessors/fourierpowerspectrum.i)

References

No citations exist within this document.

(examples/fft.i)

[Mesh]
  type = MyTRIMMesh
  dim = 2
  xmax = 100
  ymax = 100
  nx = 100
  ny = 100
[]

[Variables]
  [c]
    [InitialCondition]
      type = RandomIC
      min = 0.49
      max = 0.51
    []
  []
  [w]
  []
[]

[Kernels]
  [cres]
    type = SplitCHParsed
    variable = c
    property_name = fbulk
    kappa_name = kappa_c
    w = w
  []
  [wres]
    type = SplitCHWRes
    variable = w
    mob_name = M
  []
  [time]
    type = CoupledTimeDerivative
    variable = w
    v = c
  []
[]

[Materials]
  [const]
    type = GenericConstantMaterial
    prop_names = 'kappa_c M'
    prop_values = '8       1'
  []
  [F]
    type = DerivativeParsedMaterial
    coupled_variables = c
    property_name = fbulk
    constant_names = 'A B'
    constant_expressions = '1 0.5'
    function = '-A * (2*c-1)^2 + B * (2*c-1)^4'
  []
[]

[BCs]
  [Periodic]
    [all]
      auto_direction = 'x y'
    []
  []
[]

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

[Executioner]
  type = Transient
  num_steps = 100
  l_max_its = 100
  nl_max_its = 15

  [TimeStepper]
    type = IterationAdaptiveDT
    optimal_iterations = 7
    iteration_window = 2
    growth_factor = 1.5
    cutback_factor = 0.8
    dt = 0.1
  []
[]

[UserObjects]
  [fft]
    type = FourierTransform
    variable = c
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[VectorPostprocessors]
  [power]
    type = FourierPowerSpectrum
    fourier_transform = fft
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Postprocessors]
  [length]
    type = FourierLengthScale
    fourier_transform = fft
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Outputs]
  exodus = true
  csv = true
  print_linear_residuals = false
  [perf]
    type = PerfGraphOutput
    level = 2
  []
[]

(tests/postprocessors/fourierlengthscale.i)

[Mesh]
  type = MyTRIMMesh
  dim = 2
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'sin(x*3*(2*pi))*sin(y*2*(2*pi))'
    [../]
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 0
[]

[Problem]
  kernel_coverage_check = false
[]

[UserObjects]
  [./fft]
    type = FourierTransform
    variable = c
    execute_on = 'INITIAL'
  [../]
[]

[Postprocessors]
  [./length]
    type = FourierLengthScale
    fourier_transform = fft
    execute_on = 'INITIAL'
  [../]
[]

[Outputs]
  csv = true
  execute_on = INITIAL
[]

(tests/vectorpostprocessors/fourierpowerspectrum.i)

[Mesh]
  type = MyTRIMMesh
  dim = 2
  nx = 30
  ny = 20
[]

[Variables]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'sin(x*3*(2*pi))*sin(y*2*(2*pi))'
    [../]
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 0
[]

[Problem]
  kernel_coverage_check = false
[]

[UserObjects]
  [./fft]
    type = FourierTransform
    variable = c
    execute_on = 'INITIAL'
  [../]
[]

[VectorPostprocessors]
  [./power]
    type = FourierPowerSpectrum
    fourier_transform = fft
    execute_on = 'INITIAL'
  [../]
[]

[Outputs]
  csv = true
  exodus = true
  execute_on = INITIAL
[]

Input Parameters
Installing FFTW 3
Input Files
References