ParsedGradFunction

Defines a function and its gradient using input file parameters.

The ParsedGradFunction is similar to the ParsedFunction, differing only in that it also defines the gradient of the function. Inputs for defining each component of the gradient follow the same rules as outlined in ParsedFunction.

Example input syntax

In this input, the ParsedGradFunction is used for using the Method of Manufactured Solutions. This method verifies the convergence of the finite element method to known analytical solutions of a simple problem. u_func is used in the PostProcessors block to compute the H1 error, or the error on both the solution and its gradient, between u and this known solution.

[Functions]
  active = 'forcing_func u_func'

  [forcing_func]
    type = ParsedFunction
    expression = alpha*alpha*pi*pi*sin(alpha*pi*x)
    symbol_names = 'alpha'
    symbol_values = '4'
  []

  [u_func]
    type = ParsedGradFunction
    expression = sin(alpha*pi*x)
    grad_x = alpha*pi*sin(alpha*pi*x)
    symbol_names = 'alpha'
    symbol_values = '4'
  []
[]

Input Parameters

expressionUser defined function.
C++ Type:std::string
Unit:(no unit assumed)
Controllable:No
Description:User defined function.
grad_x0Partial derivative with respect to x.
Default:0
C++ Type:std::string
Unit:(no unit assumed)
Controllable:No
Description:Partial derivative with respect to x.
grad_y0Partial derivative with respect to y.
Default:0
C++ Type:std::string
Unit:(no unit assumed)
Controllable:No
Description:Partial derivative with respect to y.
grad_z0Partial derivative with respect to z.
Default:0
C++ Type:std::string
Unit:(no unit assumed)
Controllable:No
Description:Partial derivative with respect to z.
symbol_namesSymbols (excluding t,x,y,z) that are bound to the values provided by the corresponding items in the vals vector.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Symbols (excluding t,x,y,z) that are bound to the values provided by the corresponding items in the vals vector.
symbol_valuesConstant numeric values, postprocessor names, function names, and scalar variables corresponding to the symbols in symbol_names.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Constant numeric values, postprocessor names, function names, and scalar variables corresponding to the symbols in symbol_names.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
Controllable:No
Description:Set the enabled status of the MooseObject.

Advanced Parameters

(moose/test/tests/postprocessors/mms_slope/mms_slope_test.i)

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  []

  #  do not use uniform refine, we are using adaptive refining
  #  uniform_refine = 6
[]

[Variables]
  active = 'u'

  [u]
    order = FIRST
    family = LAGRANGE
  []
[]

[Functions]
  active = 'forcing_func u_func'

  [forcing_func]
    type = ParsedFunction
    expression = alpha*alpha*pi*pi*sin(alpha*pi*x)
    symbol_names = 'alpha'
    symbol_values = '4'
  []

  [u_func]
    type = ParsedGradFunction
    expression = sin(alpha*pi*x)
    grad_x = alpha*pi*sin(alpha*pi*x)
    symbol_names = 'alpha'
    symbol_values = '4'
  []
[]

[Kernels]
  active = 'diff forcing'

  [diff]
    type = Diffusion
    variable = u
  []

  [forcing]
    type = BodyForce
    variable = u
    function = forcing_func
  []
[]

[BCs]
  active = 'left right'

  [left]
    type = DirichletBC
    variable = u
    boundary = '3'
    value = 0
  []

  [right]
    type = DirichletBC
    variable = u
    boundary = '1'
    value = 0
  []
[]

[Executioner]
  type = Steady

  solve_type = NEWTON

  nl_abs_tol = 1e-14

  [Adaptivity]
    # if the refine fraction is 1 it will refine every element
    # remember < 1 means only refine that percentage of elements
    refine_fraction = 1

    steps = 6

    # do not coarsen at all
    coarsen_fraction = 0

    # maximum level of refinement steps, make sure this is > max_r_steps
    max_h_level = 10

    # leave this as is
    error_estimator = KellyErrorEstimator
  []
[]

# print l2 and h1 errors from the Postprocessors too so I can compare
[Postprocessors]
  active = 'l2_error h1_error dofs'
  #  active = ' '

  [l2_error]
    type = ElementL2Error
    variable = u
    function = u_func
  []

  [h1_error]
    type = ElementH1Error
    variable = u
    function = u_func
  []

  [dofs]
    type = NumDOFs
  []
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = out
  exodus = true
[]

Example input syntax
Input Parameters