MaterialDerivativeTestKernel

Description

MaterialDerivativeTestKernel is a generic test Kernel that allows checking the correctness of derivative material properties using the built-in Jacobian checks in the MOOSE test harness. Its weak form is given by $var element = document.getElementById("moose-equation-70ff2f85-377b-43ed-9113-0496e5a60ff2");katex.render("(\\psi_i, p)", element, {displayMode:false,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left< I \\right>}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ where p is a material property that depends on the governing variables. MaterialDerivativeTestKernel inherits from DerivativeMaterialInterface which gives it access to functions like getMaterialPropertyDerivative and mapJvarToCvar, explained below:

getMaterialPropertyDerivative takes a material property name (let's call it "p") and a variable name (let's call it "u") and returns a MaterialProperty equal to the derivative of the supplied material property with respect to the supplied variable, e.g. $var element = document.getElementById("moose-equation-288507b6-eb3a-44a0-a549-a5f2fc88af8e");katex.render("\\frac{\\partial p}{\\partial u}", element, {displayMode:false,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left< I \\right>}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$ .
mapJvarToCvar maps the global variable number to the kernel's coupled variable number.

This interface allows for easy and elegant construction of correct Jacobians for physics that depend on materials that are functions of governing variables.

Example Syntax

The Kernel and Material blocks below demonstrate how to utilize the DerivativeMaterialInterface capabilities in an input file.

Kernel block

[Kernels]
  [./test_kernel]
    type = MaterialDerivativeTestKernel
    variable = u
    coupled_variables = 'u v'
    material_property = material_derivative_test_property
  [../]
  # add a dummy kernel for v to prevent singular Jacobian
  [./dummy_kernel]
    type = Diffusion
    variable = v
  [../]
[]

Material block

[Materials]
  [./material_derivative_test_material]
    type = MaterialDerivativeTestMaterial
    var1 = u
    var2 = v
  [../]
[]

MaterialDerivativeTestMaterial takes two variables, var1 and var2 as input parameters. It declares a material property with the name material_derivative_test_property. It also declares two material property derivatives that are the derivatives of material_derivative_test_property with respect to var1 and var2. In our test input file above, we assign var1 = u and var2 = v. Then as long as we pass u and v as coupled variables in the args parameter of MaterialDerivativeTestKernel, we will automatically access the correct material property derivatives in our kernel.

This kernel puts a selected scalar (Real type) material property (material_property) in the residual vector and assembles the Jacobian using the derivatives of the material property as provided by the DerivativeMaterialInterface.

Input Parameters

coupled_variablesList of variables the material property depends on
C++ Type:std::vector<VariableName>
Controllable:No
Description:List of variables the material property depends on
material_propertyName of material property for which derivatives are to be tested.
C++ Type:MaterialPropertyName
Controllable:No
Description:Name of material property for which derivatives are to be tested.
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Controllable:No
Description:The name of the variable that this residual object operates on

Required 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
derivativeSelect derivative to test derivatives of (leave empty for checking derivatives of the original material property)
C++ Type:std::vector<std::string>
Controllable:No
Description:Select derivative to test derivatives of (leave empty for checking derivatives of the original material property)
displacementsThe displacements
C++ Type:std::vector<VariableName>
Controllable:No
Description:The displacements
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
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.

Optional Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging 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.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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

(moose/test/tests/kernels/material_derivatives/material_derivatives_test.i)

###########################################################
# This is a test of the material derivatives test kernel.
###########################################################

[Mesh]
  type = GeneratedMesh
  dim = 1
[]

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

[Functions]
  [./u_IC_fn]
    type = ParsedFunction
    expression = 'x'
  [../]
  [./v_IC_fn]
    type = ParsedFunction
    expression = 'sin(x)'
  [../]
[]

[ICs]
  [./u_IC]
    type = FunctionIC
    variable = u
    function = u_IC_fn
  [../]
  [./v_IC]
    type = FunctionIC
    variable = v
    function = v_IC_fn
  [../]
[]

[Kernels]
  [./test_kernel]
    type = MaterialDerivativeTestKernel
    variable = u
    coupled_variables = 'u v'
    material_property = material_derivative_test_property
  [../]
  # add a dummy kernel for v to prevent singular Jacobian
  [./dummy_kernel]
    type = Diffusion
    variable = v
  [../]
[]

[Materials]
  [./material_derivative_test_material]
    type = MaterialDerivativeTestMaterial
    var1 = u
    var2 = v
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
    solve_type = newton
    petsc_options_iname = '-snes_type -snes_test_err'
    petsc_options_value = 'test       1e-10'
  [../]
[]

[Executioner]
  type = Steady
[]

(moose/test/tests/kernels/material_derivatives/material_derivatives_test.i)

###########################################################
# This is a test of the material derivatives test kernel.
###########################################################

[Mesh]
  type = GeneratedMesh
  dim = 1
[]

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

[Functions]
  [./u_IC_fn]
    type = ParsedFunction
    expression = 'x'
  [../]
  [./v_IC_fn]
    type = ParsedFunction
    expression = 'sin(x)'
  [../]
[]

[ICs]
  [./u_IC]
    type = FunctionIC
    variable = u
    function = u_IC_fn
  [../]
  [./v_IC]
    type = FunctionIC
    variable = v
    function = v_IC_fn
  [../]
[]

[Kernels]
  [./test_kernel]
    type = MaterialDerivativeTestKernel
    variable = u
    coupled_variables = 'u v'
    material_property = material_derivative_test_property
  [../]
  # add a dummy kernel for v to prevent singular Jacobian
  [./dummy_kernel]
    type = Diffusion
    variable = v
  [../]
[]

[Materials]
  [./material_derivative_test_material]
    type = MaterialDerivativeTestMaterial
    var1 = u
    var2 = v
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
    solve_type = newton
    petsc_options_iname = '-snes_type -snes_test_err'
    petsc_options_value = 'test       1e-10'
  [../]
[]

[Executioner]
  type = Steady
[]