DerivativeParsedMaterial

Parsed Function Material with automatic derivatives.

This material class does everything the ParsedMaterial does, plus automatic symbolic differentiation of the function expression. The function material property derivatives follow a naming scheme defined in DerivativeMaterialPropertyNameInterface. The maximum order of derivatives generated is set using the derivative_order parameter.

Only required derivatives will be evaluated (e.g. the split operator kernel does not require third order derivatives. Second-order derivatives are only required for the Jacobian, as discussed here).

Non linear and auxiliary variables declared in the "coupled_variables" parameter, constants declared in "constant_names" and "constant_expressions", material properties declared in "material_property_names", and postprocessors ("postprocessor_names") may be used in the parsed function expression. Note that the constants can be defined using parsed expressions as long as these expressions only use numbers and/or constants already defined to the left of the current constant, line in this example:


    constant_names       = 'T    kB         E'
    constant_expressions = '300  8.6173e-5  T*kB'

where E can be defined in terms of T and kB, as those constants are to the left of E.

If a material property M is listed in "material_property_names" a special syntax (M(c1,c2) where c1 and c2 are variables) can be used to declare variable dependencies as well as selecting derivatives of material properties (for example, d2M:=D[M(c1,c2),c2,c2] would make the second derivative of M with respect to c2 available as d2M in the parsed function expression). If variable dependencies are declared, the necessary derivatives of the coupled material properties will be automatically pulled in when constructing the derivatives of the parsed function.

In phase field, an application would be the definition of a mobility term

$var element = document.getElementById("moose-equation-220345b0-4a35-4c86-9fdb-3f9b52e88807");katex.render("M = \\frac D{\\frac{\\partial^2 F}{\\partial c^2}}", element, {displayMode:true,throwOnError:false});$

containing the second derivative of a function $var element = document.getElementById("moose-equation-122961a7-b46f-46bc-b9f6-bad29b8f3949");katex.render("F", element, {displayMode:false,throwOnError:false});$ , or a custom switching function derivative in a Grand potential model

[./coupled_eta_function]
  type = DerivativeParsedMaterial
  expression = '(cs - cl) * dh'
  coupled_variables = 'eta w'
  property_name = ft
  material_property_names = 'cs cl dh:=D[h,eta]'
  derivative_order = 1
  outputs = exodus
[../]

The ft defined above would have accurately constructed automatic derivatives w.r.t. $var element = document.getElementById("moose-equation-9ff4b8c2-4701-42d8-8bbb-f2ace6c9f22a");katex.render("\\eta", element, {displayMode:false,throwOnError:false});$ (eta), which contain second and higher derivatives of $var element = document.getElementById("moose-equation-969be4c9-b385-48a0-b417-6dac9fd49033");katex.render("h", element, {displayMode:false,throwOnError:false});$ (make sure to set the derivative_order of $var element = document.getElementById("moose-equation-b9cf15f6-2c69-42f1-8bae-f3e65f5dd168");katex.render("h", element, {displayMode:false,throwOnError:false});$ high enough!).

The "material_property_names" are parsed by the FunctionMaterialPropertyDescriptor class, which understands the following syntax:

Expression	Description
`F`	A material property called F with no declared variable dependencies (i.e. vanishing derivatives)
`F(c,phi)`	A material property called F with declared dependence on 'c' and 'phi' (uses `DerivativeFunctionMaterial` rules to look up the derivatives) using the round-bracket-notation
`d3x:=D[x(a,b),a,a,b]`	The third derivative $var element = document.getElementById("moose-equation-7fc58f56-90fe-4d9b-9039-59f3273698a0");katex.render("\\frac{\\partial^3x}{\\partial^2a\\partial b}", element, {displayMode:false,throwOnError:false});$ of the a,b-dependent material property x, which will be referred to as `d3x` in the function expression
`dF:=D[F,c]`	Derivative of F w.r.t. c. Although the c-dependence of F is not explicitly declared using the round-bracket-notation it is implicitly assumed as a derivative w.r.t. c is requested
`F_old:=Old[F]`	Old (previous time step) state of F. Note that no derivatives of this property are available.
`F_older:=Older[F]`	Older (two time steps ago) state of F. Note that no derivatives of this property are available.

Add outputs=exodus to the material block to automatically write all derivatives and the function to the exodus output.

Input Parameters

additional_derivative_symbolsA list of additional (non-variable) symbols (such as material property or postprocessor names) to take derivatives w.r.t.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:A list of additional (non-variable) symbols (such as material property or postprocessor names) to take derivatives w.r.t.
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Unit:(no unit assumed)
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_expressionsVector of values for the constants in constant_names (can be an FParser expression)
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Vector of values for the constants in constant_names (can be an FParser expression)
constant_namesVector of constants used in the parsed function (use this for kB etc.)
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Vector of constants used in the parsed function (use this for kB etc.)
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
coupled_variablesVector of variables used in the parsed function
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Vector of variables used in the parsed function
declare_suffixAn optional suffix parameter that can be appended to any declared 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 declared properties. The suffix will be prepended with a '_' character.
derivative_order3Maximum order of derivatives taken
Default:3
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:Maximum order of derivatives taken
epsilon1e-12Fuzzy comparison tolerance
Default:1e-12
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fuzzy comparison tolerance
error_on_missing_material_propertiesTrueThrow an error if any explicitly requested material property does not exist. Otherwise assume it to be zero.
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Throw an error if any explicitly requested material property does not exist. Otherwise assume it to be zero.
expressionParsed function (see FParser) expression for the parsed material
C++ Type:FunctionExpression
Unit:(no unit assumed)
Controllable:No
Description:Parsed function (see FParser) expression for the parsed material
extra_symbolsSpecial symbols, like point coordinates, time, and timestep size.
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Options:x, y, z, t, dt
Controllable:No
Description:Special symbols, like point coordinates, time, and timestep size.
functor_namesFunctors to use in the parsed expression
C++ Type:std::vector<MooseFunctorName>
Unit:(no unit assumed)
Controllable:No
Description:Functors to use in the parsed expression
functor_symbolsSymbolic name to use for each functor in 'functor_names' in the parsed expression. If not provided, then the actual functor names will be used in the parsed expression.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Symbolic name to use for each functor in 'functor_names' in the parsed expression. If not provided, then the actual functor names will be used in the parsed expression.
material_property_namesVector of material properties used in the parsed function
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Vector of material properties used in the parsed function
postprocessor_namesVector of postprocessor names used in the parsed function
C++ Type:std::vector<PostprocessorName>
Unit:(no unit assumed)
Controllable:No
Description:Vector of postprocessor names used in the parsed function
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.
property_nameFName of the parsed material property
Default:F
C++ Type:std::string
Unit:(no unit assumed)
Controllable:No
Description:Name of the parsed material property
tol_namesVector of variable names to be protected from being 0 or 1 within a tolerance (needed for log(c) and log(1-c) terms)
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:Vector of variable names to be protected from being 0 or 1 within a tolerance (needed for log(c) and log(1-c) terms)
tol_valuesVector of tolerance values for the variables in tol_names
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Vector of tolerance values for the variables in tol_names
upstream_materialsList of upstream material properties that must be evaluated when compute=false
C++ Type:std::vector<MaterialName>
Unit:(no unit assumed)
Controllable:No
Description:List of upstream material properties that must be evaluated when compute=false
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
Unit:(no unit assumed)
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.

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: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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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

disable_fpoptimizerFalseDisable the function parser algebraic optimizer
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Disable the function parser algebraic optimizer
enable_ad_cacheTrueEnable caching of function derivatives for faster startup time
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Enable caching of function derivatives for faster startup time
enable_auto_optimizeTrueEnable automatic immediate optimization of derivatives
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Enable automatic immediate optimization of derivatives
enable_jitTrueEnable just-in-time compilation of function expressions for faster evaluation
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Enable just-in-time compilation of function expressions for faster evaluation
evalerror_behaviornanWhat to do if evaluation error occurs. Options are to pass a nan, pass a nan with a warning, throw a error, or throw an exception
Default:nan
C++ Type:MooseEnum
Unit:(no unit assumed)
Options:nan, nan_warning, error, exception
Controllable:No
Description:What to do if evaluation error occurs. Options are to pass a nan, pass a nan with a warning, throw a error, or throw an exception

Parsed Expression Advanced Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Unit:(no unit assumed)
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

(moose/modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialPFM.i)

# this input file test the implementation of the grand-potential phase-field model based on M.Plapp PRE 84,031601(2011)
# in this simple example, the liquid and solid free energies are parabola with the same curvature and the material properties are constant
# Note that this example also test The SusceptibilityTimeDerivative kernels
[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 16
  ny = 16
  xmax = 32
  ymax = 32
[]

[GlobalParams]
  radius = 20.0
  int_width = 4.0
  x1 = 0
  y1 = 0
[]

[Variables]
  [./w]
  [../]
  [./eta]
  [../]
[]

[ICs]
  [./w]
    type = SmoothCircleIC
    variable = w
    # note w = A*(c-cleq), A = 1.0, cleq = 0.0 ,i.e., w = c (in the matrix/liquid phase)
    outvalue = -0.2
    invalue = 0.2
  [../]
  [./eta]
    type = SmoothCircleIC
    variable = eta
    outvalue = 0.0
    invalue = 1.0
  [../]
[]

[Kernels]
  [./w_dot]
    type = SusceptibilityTimeDerivative
    variable = w
    f_name = chi
    coupled_variables = '' # in this case chi (the susceptibility) is simply a constant
  [../]
  [./Diffusion]
    type = MatDiffusion
    variable = w
    diffusivity = D
    args = ''
  [../]
  [./coupled_etadot]
    type = CoupledSusceptibilityTimeDerivative
    variable = w
    v = eta
    f_name = ft
    coupled_variables = 'eta'
  [../]
  [./AC_bulk]
    type = AllenCahn
    variable = eta
    f_name = F
    coupled_variables = 'w'
  [../]
  [./AC_int]
    type = ACInterface
    variable = eta
  [../]
  [./e_dot]
    type = TimeDerivative
    variable = eta
  [../]
[]

[Materials]
  [./constants]
    type = GenericConstantMaterial
    prop_names  = 'kappa_op  D    L    chi  cseq   cleq   A'
    prop_values = '4.0       1.0  1.0  1.0  0.0  1.0  1.0'
  [../]

  [./liquid_GrandPotential]
    type = DerivativeParsedMaterial
    expression = '-0.5 * w^2/A - cleq * w'
    coupled_variables = 'w'
    property_name = f1
    material_property_names = 'cleq A'
  [../]
  [./solid_GrandPotential]
    type = DerivativeParsedMaterial
    expression = '-0.5 * w^2/A - cseq * w'
    coupled_variables = 'w'
    property_name = f2
    material_property_names = 'cseq A'
  [../]
  [./switching_function]
    type = SwitchingFunctionMaterial
    eta = eta
    h_order = HIGH
  [../]
  [./barrier_function]
    type = BarrierFunctionMaterial
    eta = eta
  [../]
  [./cs]
    type = DerivativeParsedMaterial
    coupled_variables = 'w'
    property_name = cs
    material_property_names = 'A cseq'
    expression = 'w/A + cseq' # since w = A*(c-cseq)
    derivative_order = 2
  [../]
  [./cl]
    type = DerivativeParsedMaterial
    coupled_variables = 'w'
    property_name = cl
    material_property_names = 'A cleq'
    expression = 'w/A + cleq' # since w = A*(c-cleq)
    derivative_order = 2
  [../]
  [./total_GrandPotential]
    type = DerivativeTwoPhaseMaterial
    coupled_variables = 'w'
    eta = eta
    fa_name = f1
    fb_name = f2
    derivative_order = 2
    W = 1.0
  [../]
  [./coupled_eta_function]
    type = DerivativeParsedMaterial
    expression = '(cs - cl) * dh'
    coupled_variables = 'eta w'
    property_name = ft
    material_property_names = 'cs cl dh:=D[h,eta]'
    derivative_order = 1
    outputs = exodus
  [../]

  [./concentration]
    type = ParsedMaterial
    property_name = c
    material_property_names = 'dF:=D[F,w]'
    expression = '-dF'
    outputs = exodus
  [../]
[]

[Postprocessors]
  [./C]
    type = ElementIntegralMaterialProperty
    mat_prop = c
    execute_on = 'initial timestep_end'
  [../]
[]

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

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = NEWTON

  l_max_its = 15
  l_tol = 1e-3
  nl_max_its = 15
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8

  num_steps = 5
  dt = 10.0
[]

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

Input Parameters