EffectiveEField

Supplies the source term of the time derivative calculation of the effective electric field for ions.

Overview

EffectiveEField supplies the source term of the time derivative calculation of an effective electric field for ions.

This object supplies the right hand term of the following equation: $var element = document.getElementById("moose-equation-55624409-36dd-4f59-adf5-01b1d82f860f");katex.render("\\frac{\\vec{E}_{\\text{Eff.}}}{\\partial t} = \\nu_{i} \\left( \\vec{E} - \\vec{E}_{\\text{Eff.}} \\right)", element, {displayMode:true,throwOnError:false});$

where

$var element = document.getElementById("moose-equation-ba1d711a-fa42-450b-8cac-2216bc5979b3");katex.render("\\vec{E}_{\\text{Eff.}}", element, {displayMode:false,throwOnError:false});$ is the effective electric field acting on the ions,
$var element = document.getElementById("moose-equation-30a860e1-0334-4858-a311-57fba08bc968");katex.render("\\vec{E}", element, {displayMode:false,throwOnError:false});$ is the electric field, and
$var element = document.getElementById("moose-equation-8d65f2e8-f27f-4012-9899-c994fb078a36");katex.render("\\nu_{i}", element, {displayMode:false,throwOnError:false});$ is the ion-collision frequency.

Example Input File Syntax

[Kernels<<<{"href": "../../syntax/Kernels/index.html"}>>>]
  [EffEfield_X_ForceBody]
    type = EffectiveEField<<<{"description": "Supplies the source term of the time derivative calculation of the effective electric field for ions.", "href": "EffectiveEField.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = Ex
    nu<<<{"description": "The momentum-transfer frequency of the ion."}>>> = 5.0
    component<<<{"description": "The Efield component that this is applied to."}>>> = 0
    position_units<<<{"description": "Units of position."}>>> = 1.0
  []
[]

Input Parameters

componentThe Efield component that this is applied to.
C++ Type:unsigned int
Controllable:No
Description:The Efield component that this is applied to.
nuThe momentum-transfer frequency of the ion.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The momentum-transfer frequency of the ion.
position_unitsUnits of position.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Units of position.
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
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
displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
field_property_namefield_solver_interface_propertyName of the solver interface material property.
Default:field_solver_interface_property
C++ Type:std::string
Controllable:No
Description:Name of the solver interface material property.

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

Contribution To Tagged Field Data 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>
Unit:(no unit assumed)
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>
Unit:(no unit assumed)
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

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

Input Files

(test/tests/mms/continuity_equations/2D_Coupling_Electons_Potential_Ions_MeanEnergy_Einstein_Relation_EffEfield.i)

(test/tests/mms/continuity_equations/2D_Coupling_Electons_Potential_Ions_MeanEnergy_Einstein_Relation_EffEfield.i)

[Mesh]
  [geo]
    type = FileMeshGenerator
    file = '2D_Coupling_Electons_Potential_Ions_MeanEnergy_Einstein_Relation_EffEfield_IC_out.e'
    use_for_exodus_restart = true
  []
[]

[Problem]
  type = FEProblem
[]

[Variables]
  [em]
    initial_from_file_var = em
  []
  [potential]
    initial_from_file_var = potential
  []
  [ion]
    initial_from_file_var = ion
  []
  [mean_en]
    initial_from_file_var = mean_en
  []

  [Ex]
    initial_from_file_var = Ex
  []
  [Ey]
    initial_from_file_var = Ey
  []
[]

[Kernels]
#Electron Equations
  [em_time_derivative]
    type = TimeDerivativeLog
    variable = em
  []
  [em_diffusion]
    type = CoeffDiffusion
    variable = em
    position_units = 1.0
  []
  [em_advection]
    type = EFieldAdvection
    variable = em
    position_units = 1.0
  []
  [em_source]
    type = BodyForce
    variable = em
    function = 'em_source'
  []

#Ion Equations
  [ion_time_derivative]
    type = TimeDerivativeLog
    variable = ion
  []
  [ion_diffusion]
    type = CoeffDiffusion
    variable = ion
    position_units = 1.0
  []
  [ion_advection]
    type = EffectiveEFieldAdvection
    variable = ion
    u = Ex
    v = Ey
    position_units = 1.0
  []
  [ion_source]
    type = BodyForce
    variable = ion
    function = 'ion_source'
  []

#Potential Equations
  [potential_diffusion]
    type = CoeffDiffusionLin
    variable = potential
    position_units = 1.0
  []
  [ion_charge_source]
    type = ChargeSourceMoles_KV
    variable = potential
    charged = ion
    potential_units = V
  []
  [em_charge_source]
    type = ChargeSourceMoles_KV
    variable = potential
    charged = em
    potential_units = V
  []

#Eff. Efield
  [EffEfield_X_time_deriv]
    type = TimeDerivative
    variable = Ex
  []
  [EffEfield_X_ForceBody]
    type = EffectiveEField
    variable = Ex
    nu = 5.0
    component = 0
    position_units = 1.0
  []
  [EffEfield_Y_time_deriv]
    type = TimeDerivative
    variable = Ey
  []
  [EffEfield_Y_ForceBody]
    type = EffectiveEField
    variable = Ey
    nu = 5.0
    component = 1
    position_units = 1.0
  []

#Electron Energy Equations
  [mean_en_time_deriv]
    type = TimeDerivativeLog
    variable = mean_en
  []
  [mean_en_advection]
    type = EFieldAdvection
    variable = mean_en
    position_units = 1.0
  []
  [mean_en_diffusion]
    type = CoeffDiffusion
    variable = mean_en
    position_units = 1.0
  []
  [mean_en_diffusion_correction]
    type = ThermalConductivityDiffusion
    variable = mean_en
    em = em
    position_units = 1.0
  []
  [mean_en_joule_heating]
    type = JouleHeating
    variable = mean_en
    em = em
    position_units = 1.0
    potential_units = V
  []
  [mean_en_source]
    type = BodyForce
    variable = mean_en
    function = 'energy_source'
  []
[]

[AuxVariables]
  [potential_sol]
  []

  [mean_en_sol]
  []

  [em_sol]
  []

  [ion_sol]
  []

  [Ex_sol]
  []
  [Ey_sol]
  []
[]

[AuxKernels]
  [potential_sol]
    type = FunctionAux
    variable = potential_sol
    function = potential_fun
  []

  [mean_en_sol]
    type = FunctionAux
    variable = mean_en_sol
    function = mean_en_fun
  []

  [em_sol]
    type = FunctionAux
    variable = em_sol
    function = em_fun
  []

  [ion_sol]
    type = FunctionAux
    variable = ion_sol
    function = ion_fun
  []

  [Ex_sol]
    type = FunctionAux
    variable = Ex_sol
    function = Ex_fun
  []
  [Ey_sol]
    type = FunctionAux
    variable = Ey_sol
    function = Ey_fun
  []
[]

[Functions]
#Material Variables
  #Electron diffusion coeff.
  [diffem_coeff]
    type = ConstantFunction
    value = 0.05
  []
  #Electron mobility coeff.
  [muem_coeff]
    type = ConstantFunction
    value = 0.01
  []
  #Electron energy diffusion coeff.
  [diffmean_en_coeff]
    type = ParsedFunction
    vars = 'diffem_coeff'
    vals = 'diffem_coeff'
    value = '5.0 / 3.0 * diffem_coeff'
  []
  #Electron energy mobility coeff.
  [mumean_en_coeff]
    type = ParsedFunction
    vars = 'muem_coeff'
    vals = 'muem_coeff'
    value = '5.0 / 3.0 * muem_coeff'
  []
  #Ion diffusion coeff.
  [diffion]
    type = ConstantFunction
    value = 0.1
  []
  #Ion mobility coeff.
  [muion]
    type = ConstantFunction
    value = 0.025
  []
  [N_A]
    type = ConstantFunction
    value = 1.0
  []
  [ee]
    type = ConstantFunction
    value = 1.0
  []
  [diffpotential]
    type = ConstantFunction
    value = 0.01
  []


#Manufactured Solutions
  #The manufactured electron density solution
  [em_fun]
    type = ParsedFunction
    vars = 'N_A'
    vals = 'N_A'
    value = 'log((sin(pi*y) + 0.2*sin(2*pi*t)*cos(pi*y) + 1.0 + cos(pi/2*x)) / N_A)'
  []
  #The manufactured ion density solution
  [ion_fun]
    type = ParsedFunction
    vars = 'N_A'
    vals = 'N_A'
    value = 'log((sin(pi*y) + 1.0 + 0.9*cos(pi/2*x)) / N_A)'
  []
  #The manufactured electron density solution
  [potential_fun]
    type = ParsedFunction
    vars = 'ee diffpotential'
    vals = 'ee diffpotential'
    value = '-(ee*(2*cos((pi*x)/2) + cos(pi*y)*sin(2*pi*t)))/(5*diffpotential*pi^2)'
  []
  #The manufactured electron energy solution
  [energy_fun]
    type = ParsedFunction
    vars = 'N_A'
    vals = 'N_A'
    value = 'sin(pi*y) + sin(2*pi*t)*cos(pi*y)*sin(pi*y) + 0.75 + cos(pi/2*x)'
  []
  [mean_en_fun]
    type = ParsedFunction
    vars = 'energy_fun em_fun'
    vals = 'energy_fun em_fun'
    value = 'log(energy_fun) + em_fun'
  []
  #The manufactured eff. Efield solution
  [Ex_fun]
    type = ParsedFunction
    vars = 'ee diffpotential'
    vals = 'ee diffpotential'
    value = '-(ee*exp(-5*t)*sin((pi*x)/2)*(exp(5*t) - 1))/(5*diffpotential*pi)'
  []
  [Ey_fun]
    type = ParsedFunction
    vars = 'ee diffpotential'
    vals = 'ee diffpotential'
    value = '-(2*ee*exp(-5*t)*sin(pi*y))/(4*diffpotential*pi^2 + 25*diffpotential) -
             (ee*sin(pi*y)*(5*sin(2*pi*t) - 2*pi*cos(2*pi*t)))/(diffpotential*pi*(4*pi^2 + 25))'
  []

  #Electron diffusion coeff.
  [diffem]
    type = ParsedFunction
    vars = 'diffem_coeff energy_fun'
    vals = 'diffem_coeff energy_fun'
    value = 'diffem_coeff * energy_fun'
  []
  #Electron mobility coeff.
  [muem]
    type = ParsedFunction
    vars = 'muem_coeff energy_fun'
    vals = 'muem_coeff energy_fun'
    value = 'muem_coeff * energy_fun'
  []
  #Electron energy diffusion coeff.
  [diffmean_en]
    type = ParsedFunction
    vars = 'diffmean_en_coeff energy_fun'
    vals = 'diffmean_en_coeff energy_fun'
    value = 'diffmean_en_coeff * energy_fun'
  []
  #Electron energy mobility coeff.
  [mumean_en]
    type = ParsedFunction
    vars = 'mumean_en_coeff energy_fun'
    vals = 'mumean_en_coeff energy_fun'
    value = 'mumean_en_coeff * energy_fun'
  []

#Source Terms in moles
  #The electron source term.
  [em_source]
    type = ParsedFunction
    vars = 'ee diffpotential diffem_coeff muem_coeff N_A'
    vals = 'ee diffpotential diffem_coeff muem_coeff N_A'
    value = '((2*pi*cos(2*pi*t)*cos(pi*y))/5 - (diffem_coeff*pi^2*sin((pi*x)/2)^2)/4 -
              diffem_coeff*pi*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos(pi*y) -
              sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t)) + (diffem_coeff*pi^2*cos((pi*x)/2)*(cos((pi*x)/2) +
              sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 + (diffem_coeff*pi^2*(5*sin(pi*y) +
              cos(pi*y)*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/5 -
              (ee*muem_coeff*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) +
              cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(10*diffpotential) -
              (ee*muem_coeff*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/(10*diffpotential) +
              (ee*muem_coeff*cos((pi*x)/2)*(cos((pi*x)/2) + sin(pi*y) +
              (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(10*diffpotential) +
              (ee*muem_coeff*cos(pi*y)*sin(2*pi*t)*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) +
              sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential) + (ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(cos(pi*y) -
              sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/(5*diffpotential) +
              (ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos((pi*x)/2) + sin(pi*y) +
              cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential*pi)) / N_A'
  []
  #The ion source term.
  [ion_source]
    type = ParsedFunction
    vars = 'ee diffpotential diffion muion N_A'
    vals = 'ee diffpotential diffion muion N_A'
    value = '((diffion*pi^2*(9*cos((pi*x)/2) + 40*sin(pi*y)))/40 +
              (9*ee*muion*exp(-5*t)*sin((pi*x)/2)^2*(exp(5*t) - 1))/(100*diffpotential) -
              (ee*muion*exp(-5*t)*cos((pi*x)/2)*(exp(5*t) - 1)*((9*cos((pi*x)/2))/10 + sin(pi*y) + 1))/(10*diffpotential) -
              (ee*muion*exp(-5*t)*cos(pi*y)*(2*pi + 5*exp(5*t)*sin(2*pi*t) -
              2*pi*exp(5*t)*cos(2*pi*t))*((9*cos((pi*x)/2))/10 + sin(pi*y) + 1))/(diffpotential*(4*pi^2 + 25)) -
              (ee*muion*exp(-5*t)*cos(pi*y)*sin(pi*y)*(2*pi + 5*exp(5*t)*sin(2*pi*t) -
              2*pi*exp(5*t)*cos(2*pi*t)))/(diffpotential*(4*pi^2 + 25))) / N_A'
  []
  [energy_source]
    type = ParsedFunction
    vars = 'ee diffpotential diffem_coeff muem_coeff N_A'
    vals = 'ee diffpotential diffem_coeff muem_coeff N_A'
    value = '(((4*cos((pi*x)/2) + 4*sin(pi*y) + 4*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3)*(172*ee*muem_coeff*cos(2*pi*t)^2 -
              282*ee*muem_coeff + 180*ee*muem_coeff*cos((pi*x)/2)^2 + 160*ee*muem_coeff*cos((pi*x)/2)^3 +
              664*ee*muem_coeff*cos(pi*y)^2 - 480*ee*muem_coeff*cos(pi*y)^4 -
              66*ee*muem_coeff*cos((pi*x)/2) - 296*ee*muem_coeff*sin(pi*y) +
              200*diffem_coeff*diffpotential*pi^2 - 664*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^2 +
              480*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^4 + 364*ee*muem_coeff*cos(pi*y)*sin(2*pi*t) -
              90*ee*muem_coeff*cos((pi*x)/2)*sin(pi*y) + 75*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2) +
              140*diffem_coeff*diffpotential*pi^2*sin(pi*y) + 16*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2) -
              8*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^2 + 176*ee*muem_coeff*cos(2*pi*t)^2*sin(pi*y) -
              320*ee*muem_coeff*cos(pi*y)^3*sin(2*pi*t) + 200*ee*muem_coeff*cos((pi*x)/2)^2*sin(pi*y) +
              464*ee*muem_coeff*cos(pi*y)^2*sin(pi*y) + 300*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)^2 -
              1200*diffem_coeff*diffpotential*pi^2*cos(pi*y)^2 + 160*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*sin(pi*y) +
              104*ee*muem_coeff*cos((pi*x)/2)^2*cos(pi*y)*sin(2*pi*t) - 40*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^3*sin(2*pi*t) +
              408*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^2*sin(pi*y) + 96*ee*muem_coeff*cos(pi*y)^3*sin(2*pi*t)*sin(pi*y) +
              160*diffem_coeff*diffpotential*pi^2*cos(2*pi*t)^2*sin(pi*y) -
              2000*diffem_coeff*diffpotential*pi^2*cos(pi*y)^3*sin(2*pi*t) + 400*diffem_coeff*diffpotential*pi^2*cos(pi*y)^2*sin(pi*y) -
              32*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*cos(pi*y)^2 - 464*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^2*sin(pi*y) +
              186*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t) + 272*ee*muem_coeff*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
              1260*diffem_coeff*diffpotential*pi^2*cos(pi*y)*sin(2*pi*t) + 500*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*sin(pi*y) -
              408*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*cos(pi*y)^2*sin(pi*y) -
              96*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^3*sin(2*pi*t)*sin(pi*y) -
              400*diffem_coeff*diffpotential*pi^2*cos(2*pi*t)^2*cos(pi*y)^2*sin(pi*y) +
              448*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
              80*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t) +
              240*diffem_coeff*diffpotential*pi^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
              48*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 80*ee*muem_coeff*cos((pi*x)/2)^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
              100*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t)*sin(pi*y)))/(960*diffpotential) +
              (pi*cos(2*pi*t)*cos(pi*y)*(4*cos((pi*x)/2) + 24*sin(pi*y) + 20*cos((pi*x)/2)*sin(pi*y) + 20*sin(pi*y)^2 +
              8*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3))/10 - (diffem_coeff*pi^2*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) +
              cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 - (diffem_coeff*pi^2*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) +
              (cos(pi*y)*sin(2*pi*t))/5 + 1))/4 - diffem_coeff*pi^2*(cos(pi*y) - sin(2*pi*t) +
              2*cos(pi*y)^2*sin(2*pi*t))^2*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1) +
              (diffem_coeff*pi^2*cos((pi*x)/2)*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) +
              cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 - diffem_coeff*pi*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos(pi*y) -
              sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) +
              (ee*sin(2*pi*t)*sin(pi*y)*(diffem_coeff*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos((pi*x)/2) +
              sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) - (ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(cos((pi*x)/2) +
              sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) +
              cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential*pi)))/(5*diffpotential*pi) +
              diffem_coeff*pi^2*sin(pi*y)*(4*cos(pi*y)*sin(2*pi*t) + 1)*(cos((pi*x)/2) + sin(pi*y) +
              (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) -
              (ee*sin((pi*x)/2)^2*(4*cos((pi*x)/2) + 4*sin(pi*y) +
              4*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3)*(10*ee*muem_coeff + 10*ee*muem_coeff*cos((pi*x)/2) +
              10*ee*muem_coeff*sin(pi*y) + 25*diffem_coeff*diffpotential*pi^2 +
              2*ee*muem_coeff*cos(pi*y)*sin(2*pi*t)))/(1000*diffpotential^2*pi^2)) / N_A'
  []

  [em_ICs]
    type = ParsedFunction
    vars = 'N_A'
    vals = 'N_A'
    value = 'log((3.0 + cos(pi/2*x)) / N_A)'
  []
  [ion_ICs]
    type = ParsedFunction
    vars = 'N_A'
    vals = 'N_A'
    value = 'log((3.0 + 0.9*cos(pi/2*x)) / N_A)'
  []
  [mean_en_ICs]
    type = ParsedFunction
    vars = 'em_ICs'
    vals = 'em_ICs'
    value = 'log(32. + cos(pi/2*x)) + em_ICs'
  []
[]

[BCs]
  [potential_BC]
    type = FunctionDirichletBC
    variable = potential
    function = 'potential_fun'
    boundary = '0 1 2 3'
    preset = true
  []

  [em_BC]
    type = FunctionDirichletBC
    variable = em
    function = 'em_fun'
    boundary = '0 1 2 3'
    preset = true
  []

  [ion_BC]
    type = FunctionDirichletBC
    variable = ion
    function = 'ion_fun'
    boundary = '0 1 2 3'
    preset = true
  []

  [energy_BC]
    type = FunctionDirichletBC
    variable = mean_en
    function = 'mean_en_fun'
    boundary = '0 1 2 3'
    preset = true
  []

  [Ex_BC]
    type = FunctionDirichletBC
    variable = Ex
    function = 'Ex_fun'
    boundary = '0 1 2 3'
    preset = true
  []

  [Ey_BC]
    type = FunctionDirichletBC
    variable = Ey
    function = 'Ey_fun'
    boundary = '0 1 2 3'
    preset = true
  []
[]

[Materials]
  [field_solver]
    type = FieldSolverMaterial
    potential = potential
  []
  [Material_Coeff]
    type = GenericFunctionMaterial
    prop_names =  'e N_A'
    prop_values = 'ee N_A'
  []
  [ADMaterial_Coeff_Set1]
    type = ADGenericFunctionMaterial
    prop_names =  'diffpotential diffion muion'
    prop_values = 'diffpotential diffion muion'
  []
  [Material_Coeff_Set2]
    type = ADMMSEEDFRates
    electrons = em
    mean_energy = mean_en
    prop_names =              'diffem        muem        diffmean_en        mumean_en'
    prop_values =             'diffem        muem        diffmean_en        mumean_en'
    d_prop_d_actual_mean_en = 'diffem_coeff  muem_coeff  diffmean_en_coeff  mumean_en_coeff'
  []
  [Charge_Signs]
    type = GenericConstantMaterial
    prop_names =  'sgnem  sgnion  sgnmean_en'
    prop_values = '-1.0   1.0     -1.0'
  []
[]

[Postprocessors]
  [em_l2Error]
    type = ElementL2Error
    variable = em
    function = em_fun
  []
  [ion_l2Error]
    type = ElementL2Error
    variable = ion
    function = ion_fun
  []
  [potential_l2Error]
    type = ElementL2Error
    variable = potential
    function = potential_fun
  []
  [mean_en_l2Error]
    type = ElementL2Error
    variable = mean_en
    function = mean_en_fun
  []

  [Ex_l2Error]
    type = ElementL2Error
    variable = Ex
    function = Ex_fun
  []
  [Ey_l2Error]
    type = ElementL2Error
    variable = Ey
    function = Ey_fun
  []

  [h]
    type = AverageElementSize
  []
[]

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

  [fdp]
    type = FDP
    full = true
  []
[]

[Executioner]
  type = Transient
  start_time = 50
  end_time = 51

  # dt = 0.008
  dt = 0.02

  automatic_scaling = true
  compute_scaling_once = false
  petsc_options = '-snes_converged_reason -snes_linesearch_monitor'
  solve_type = NEWTON
  line_search = none
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu NONZERO 1.e-10'

  scheme = bdf2

  nl_abs_tol = 1e-13
[]

[Outputs]
  perf_graph = true
  [out]
    type = Exodus
    interval = 10
  []
[]

(test/tests/mms/continuity_equations/2D_Coupling_Electons_Potential_Ions_MeanEnergy_Einstein_Relation_EffEfield.i)

[Mesh]
  [geo]
    type = FileMeshGenerator
    file = '2D_Coupling_Electons_Potential_Ions_MeanEnergy_Einstein_Relation_EffEfield_IC_out.e'
    use_for_exodus_restart = true
  []
[]

[Problem]
  type = FEProblem
[]

[Variables]
  [em]
    initial_from_file_var = em
  []
  [potential]
    initial_from_file_var = potential
  []
  [ion]
    initial_from_file_var = ion
  []
  [mean_en]
    initial_from_file_var = mean_en
  []

  [Ex]
    initial_from_file_var = Ex
  []
  [Ey]
    initial_from_file_var = Ey
  []
[]

[Kernels]
#Electron Equations
  [em_time_derivative]
    type = TimeDerivativeLog
    variable = em
  []
  [em_diffusion]
    type = CoeffDiffusion
    variable = em
    position_units = 1.0
  []
  [em_advection]
    type = EFieldAdvection
    variable = em
    position_units = 1.0
  []
  [em_source]
    type = BodyForce
    variable = em
    function = 'em_source'
  []

#Ion Equations
  [ion_time_derivative]
    type = TimeDerivativeLog
    variable = ion
  []
  [ion_diffusion]
    type = CoeffDiffusion
    variable = ion
    position_units = 1.0
  []
  [ion_advection]
    type = EffectiveEFieldAdvection
    variable = ion
    u = Ex
    v = Ey
    position_units = 1.0
  []
  [ion_source]
    type = BodyForce
    variable = ion
    function = 'ion_source'
  []

#Potential Equations
  [potential_diffusion]
    type = CoeffDiffusionLin
    variable = potential
    position_units = 1.0
  []
  [ion_charge_source]
    type = ChargeSourceMoles_KV
    variable = potential
    charged = ion
    potential_units = V
  []
  [em_charge_source]
    type = ChargeSourceMoles_KV
    variable = potential
    charged = em
    potential_units = V
  []

#Eff. Efield
  [EffEfield_X_time_deriv]
    type = TimeDerivative
    variable = Ex
  []
  [EffEfield_X_ForceBody]
    type = EffectiveEField
    variable = Ex
    nu = 5.0
    component = 0
    position_units = 1.0
  []
  [EffEfield_Y_time_deriv]
    type = TimeDerivative
    variable = Ey
  []
  [EffEfield_Y_ForceBody]
    type = EffectiveEField
    variable = Ey
    nu = 5.0
    component = 1
    position_units = 1.0
  []

#Electron Energy Equations
  [mean_en_time_deriv]
    type = TimeDerivativeLog
    variable = mean_en
  []
  [mean_en_advection]
    type = EFieldAdvection
    variable = mean_en
    position_units = 1.0
  []
  [mean_en_diffusion]
    type = CoeffDiffusion
    variable = mean_en
    position_units = 1.0
  []
  [mean_en_diffusion_correction]
    type = ThermalConductivityDiffusion
    variable = mean_en
    em = em
    position_units = 1.0
  []
  [mean_en_joule_heating]
    type = JouleHeating
    variable = mean_en
    em = em
    position_units = 1.0
    potential_units = V
  []
  [mean_en_source]
    type = BodyForce
    variable = mean_en
    function = 'energy_source'
  []
[]

[AuxVariables]
  [potential_sol]
  []

  [mean_en_sol]
  []

  [em_sol]
  []

  [ion_sol]
  []

  [Ex_sol]
  []
  [Ey_sol]
  []
[]

[AuxKernels]
  [potential_sol]
    type = FunctionAux
    variable = potential_sol
    function = potential_fun
  []

  [mean_en_sol]
    type = FunctionAux
    variable = mean_en_sol
    function = mean_en_fun
  []

  [em_sol]
    type = FunctionAux
    variable = em_sol
    function = em_fun
  []

  [ion_sol]
    type = FunctionAux
    variable = ion_sol
    function = ion_fun
  []

  [Ex_sol]
    type = FunctionAux
    variable = Ex_sol
    function = Ex_fun
  []
  [Ey_sol]
    type = FunctionAux
    variable = Ey_sol
    function = Ey_fun
  []
[]

[Functions]
#Material Variables
  #Electron diffusion coeff.
  [diffem_coeff]
    type = ConstantFunction
    value = 0.05
  []
  #Electron mobility coeff.
  [muem_coeff]
    type = ConstantFunction
    value = 0.01
  []
  #Electron energy diffusion coeff.
  [diffmean_en_coeff]
    type = ParsedFunction
    vars = 'diffem_coeff'
    vals = 'diffem_coeff'
    value = '5.0 / 3.0 * diffem_coeff'
  []
  #Electron energy mobility coeff.
  [mumean_en_coeff]
    type = ParsedFunction
    vars = 'muem_coeff'
    vals = 'muem_coeff'
    value = '5.0 / 3.0 * muem_coeff'
  []
  #Ion diffusion coeff.
  [diffion]
    type = ConstantFunction
    value = 0.1
  []
  #Ion mobility coeff.
  [muion]
    type = ConstantFunction
    value = 0.025
  []
  [N_A]
    type = ConstantFunction
    value = 1.0
  []
  [ee]
    type = ConstantFunction
    value = 1.0
  []
  [diffpotential]
    type = ConstantFunction
    value = 0.01
  []


#Manufactured Solutions
  #The manufactured electron density solution
  [em_fun]
    type = ParsedFunction
    vars = 'N_A'
    vals = 'N_A'
    value = 'log((sin(pi*y) + 0.2*sin(2*pi*t)*cos(pi*y) + 1.0 + cos(pi/2*x)) / N_A)'
  []
  #The manufactured ion density solution
  [ion_fun]
    type = ParsedFunction
    vars = 'N_A'
    vals = 'N_A'
    value = 'log((sin(pi*y) + 1.0 + 0.9*cos(pi/2*x)) / N_A)'
  []
  #The manufactured electron density solution
  [potential_fun]
    type = ParsedFunction
    vars = 'ee diffpotential'
    vals = 'ee diffpotential'
    value = '-(ee*(2*cos((pi*x)/2) + cos(pi*y)*sin(2*pi*t)))/(5*diffpotential*pi^2)'
  []
  #The manufactured electron energy solution
  [energy_fun]
    type = ParsedFunction
    vars = 'N_A'
    vals = 'N_A'
    value = 'sin(pi*y) + sin(2*pi*t)*cos(pi*y)*sin(pi*y) + 0.75 + cos(pi/2*x)'
  []
  [mean_en_fun]
    type = ParsedFunction
    vars = 'energy_fun em_fun'
    vals = 'energy_fun em_fun'
    value = 'log(energy_fun) + em_fun'
  []
  #The manufactured eff. Efield solution
  [Ex_fun]
    type = ParsedFunction
    vars = 'ee diffpotential'
    vals = 'ee diffpotential'
    value = '-(ee*exp(-5*t)*sin((pi*x)/2)*(exp(5*t) - 1))/(5*diffpotential*pi)'
  []
  [Ey_fun]
    type = ParsedFunction
    vars = 'ee diffpotential'
    vals = 'ee diffpotential'
    value = '-(2*ee*exp(-5*t)*sin(pi*y))/(4*diffpotential*pi^2 + 25*diffpotential) -
             (ee*sin(pi*y)*(5*sin(2*pi*t) - 2*pi*cos(2*pi*t)))/(diffpotential*pi*(4*pi^2 + 25))'
  []

  #Electron diffusion coeff.
  [diffem]
    type = ParsedFunction
    vars = 'diffem_coeff energy_fun'
    vals = 'diffem_coeff energy_fun'
    value = 'diffem_coeff * energy_fun'
  []
  #Electron mobility coeff.
  [muem]
    type = ParsedFunction
    vars = 'muem_coeff energy_fun'
    vals = 'muem_coeff energy_fun'
    value = 'muem_coeff * energy_fun'
  []
  #Electron energy diffusion coeff.
  [diffmean_en]
    type = ParsedFunction
    vars = 'diffmean_en_coeff energy_fun'
    vals = 'diffmean_en_coeff energy_fun'
    value = 'diffmean_en_coeff * energy_fun'
  []
  #Electron energy mobility coeff.
  [mumean_en]
    type = ParsedFunction
    vars = 'mumean_en_coeff energy_fun'
    vals = 'mumean_en_coeff energy_fun'
    value = 'mumean_en_coeff * energy_fun'
  []

#Source Terms in moles
  #The electron source term.
  [em_source]
    type = ParsedFunction
    vars = 'ee diffpotential diffem_coeff muem_coeff N_A'
    vals = 'ee diffpotential diffem_coeff muem_coeff N_A'
    value = '((2*pi*cos(2*pi*t)*cos(pi*y))/5 - (diffem_coeff*pi^2*sin((pi*x)/2)^2)/4 -
              diffem_coeff*pi*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos(pi*y) -
              sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t)) + (diffem_coeff*pi^2*cos((pi*x)/2)*(cos((pi*x)/2) +
              sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 + (diffem_coeff*pi^2*(5*sin(pi*y) +
              cos(pi*y)*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/5 -
              (ee*muem_coeff*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) +
              cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(10*diffpotential) -
              (ee*muem_coeff*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/(10*diffpotential) +
              (ee*muem_coeff*cos((pi*x)/2)*(cos((pi*x)/2) + sin(pi*y) +
              (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(10*diffpotential) +
              (ee*muem_coeff*cos(pi*y)*sin(2*pi*t)*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) +
              sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential) + (ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(cos(pi*y) -
              sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1))/(5*diffpotential) +
              (ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos((pi*x)/2) + sin(pi*y) +
              cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential*pi)) / N_A'
  []
  #The ion source term.
  [ion_source]
    type = ParsedFunction
    vars = 'ee diffpotential diffion muion N_A'
    vals = 'ee diffpotential diffion muion N_A'
    value = '((diffion*pi^2*(9*cos((pi*x)/2) + 40*sin(pi*y)))/40 +
              (9*ee*muion*exp(-5*t)*sin((pi*x)/2)^2*(exp(5*t) - 1))/(100*diffpotential) -
              (ee*muion*exp(-5*t)*cos((pi*x)/2)*(exp(5*t) - 1)*((9*cos((pi*x)/2))/10 + sin(pi*y) + 1))/(10*diffpotential) -
              (ee*muion*exp(-5*t)*cos(pi*y)*(2*pi + 5*exp(5*t)*sin(2*pi*t) -
              2*pi*exp(5*t)*cos(2*pi*t))*((9*cos((pi*x)/2))/10 + sin(pi*y) + 1))/(diffpotential*(4*pi^2 + 25)) -
              (ee*muion*exp(-5*t)*cos(pi*y)*sin(pi*y)*(2*pi + 5*exp(5*t)*sin(2*pi*t) -
              2*pi*exp(5*t)*cos(2*pi*t)))/(diffpotential*(4*pi^2 + 25))) / N_A'
  []
  [energy_source]
    type = ParsedFunction
    vars = 'ee diffpotential diffem_coeff muem_coeff N_A'
    vals = 'ee diffpotential diffem_coeff muem_coeff N_A'
    value = '(((4*cos((pi*x)/2) + 4*sin(pi*y) + 4*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3)*(172*ee*muem_coeff*cos(2*pi*t)^2 -
              282*ee*muem_coeff + 180*ee*muem_coeff*cos((pi*x)/2)^2 + 160*ee*muem_coeff*cos((pi*x)/2)^3 +
              664*ee*muem_coeff*cos(pi*y)^2 - 480*ee*muem_coeff*cos(pi*y)^4 -
              66*ee*muem_coeff*cos((pi*x)/2) - 296*ee*muem_coeff*sin(pi*y) +
              200*diffem_coeff*diffpotential*pi^2 - 664*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^2 +
              480*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^4 + 364*ee*muem_coeff*cos(pi*y)*sin(2*pi*t) -
              90*ee*muem_coeff*cos((pi*x)/2)*sin(pi*y) + 75*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2) +
              140*diffem_coeff*diffpotential*pi^2*sin(pi*y) + 16*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2) -
              8*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^2 + 176*ee*muem_coeff*cos(2*pi*t)^2*sin(pi*y) -
              320*ee*muem_coeff*cos(pi*y)^3*sin(2*pi*t) + 200*ee*muem_coeff*cos((pi*x)/2)^2*sin(pi*y) +
              464*ee*muem_coeff*cos(pi*y)^2*sin(pi*y) + 300*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)^2 -
              1200*diffem_coeff*diffpotential*pi^2*cos(pi*y)^2 + 160*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*sin(pi*y) +
              104*ee*muem_coeff*cos((pi*x)/2)^2*cos(pi*y)*sin(2*pi*t) - 40*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^3*sin(2*pi*t) +
              408*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)^2*sin(pi*y) + 96*ee*muem_coeff*cos(pi*y)^3*sin(2*pi*t)*sin(pi*y) +
              160*diffem_coeff*diffpotential*pi^2*cos(2*pi*t)^2*sin(pi*y) -
              2000*diffem_coeff*diffpotential*pi^2*cos(pi*y)^3*sin(2*pi*t) + 400*diffem_coeff*diffpotential*pi^2*cos(pi*y)^2*sin(pi*y) -
              32*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*cos(pi*y)^2 - 464*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^2*sin(pi*y) +
              186*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t) + 272*ee*muem_coeff*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
              1260*diffem_coeff*diffpotential*pi^2*cos(pi*y)*sin(2*pi*t) + 500*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*sin(pi*y) -
              408*ee*muem_coeff*cos(2*pi*t)^2*cos((pi*x)/2)*cos(pi*y)^2*sin(pi*y) -
              96*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)^3*sin(2*pi*t)*sin(pi*y) -
              400*diffem_coeff*diffpotential*pi^2*cos(2*pi*t)^2*cos(pi*y)^2*sin(pi*y) +
              448*ee*muem_coeff*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
              80*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t) +
              240*diffem_coeff*diffpotential*pi^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
              48*ee*muem_coeff*cos(2*pi*t)^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 80*ee*muem_coeff*cos((pi*x)/2)^2*cos(pi*y)*sin(2*pi*t)*sin(pi*y) +
              100*diffem_coeff*diffpotential*pi^2*cos((pi*x)/2)*cos(pi*y)*sin(2*pi*t)*sin(pi*y)))/(960*diffpotential) +
              (pi*cos(2*pi*t)*cos(pi*y)*(4*cos((pi*x)/2) + 24*sin(pi*y) + 20*cos((pi*x)/2)*sin(pi*y) + 20*sin(pi*y)^2 +
              8*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3))/10 - (diffem_coeff*pi^2*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) +
              cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 - (diffem_coeff*pi^2*sin((pi*x)/2)^2*(cos((pi*x)/2) + sin(pi*y) +
              (cos(pi*y)*sin(2*pi*t))/5 + 1))/4 - diffem_coeff*pi^2*(cos(pi*y) - sin(2*pi*t) +
              2*cos(pi*y)^2*sin(2*pi*t))^2*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1) +
              (diffem_coeff*pi^2*cos((pi*x)/2)*(cos((pi*x)/2) + sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) +
              cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/4 - diffem_coeff*pi*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos(pi*y) -
              sin(2*pi*t) + 2*cos(pi*y)^2*sin(2*pi*t))*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) +
              (ee*sin(2*pi*t)*sin(pi*y)*(diffem_coeff*(pi*cos(pi*y) - (pi*sin(2*pi*t)*sin(pi*y))/5)*(cos((pi*x)/2) +
              sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) - (ee*muem_coeff*sin(2*pi*t)*sin(pi*y)*(cos((pi*x)/2) +
              sin(pi*y) + (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) +
              cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4))/(5*diffpotential*pi)))/(5*diffpotential*pi) +
              diffem_coeff*pi^2*sin(pi*y)*(4*cos(pi*y)*sin(2*pi*t) + 1)*(cos((pi*x)/2) + sin(pi*y) +
              (cos(pi*y)*sin(2*pi*t))/5 + 1)*(cos((pi*x)/2) + sin(pi*y) + cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3/4) -
              (ee*sin((pi*x)/2)^2*(4*cos((pi*x)/2) + 4*sin(pi*y) +
              4*cos(pi*y)*sin(2*pi*t)*sin(pi*y) + 3)*(10*ee*muem_coeff + 10*ee*muem_coeff*cos((pi*x)/2) +
              10*ee*muem_coeff*sin(pi*y) + 25*diffem_coeff*diffpotential*pi^2 +
              2*ee*muem_coeff*cos(pi*y)*sin(2*pi*t)))/(1000*diffpotential^2*pi^2)) / N_A'
  []

  [em_ICs]
    type = ParsedFunction
    vars = 'N_A'
    vals = 'N_A'
    value = 'log((3.0 + cos(pi/2*x)) / N_A)'
  []
  [ion_ICs]
    type = ParsedFunction
    vars = 'N_A'
    vals = 'N_A'
    value = 'log((3.0 + 0.9*cos(pi/2*x)) / N_A)'
  []
  [mean_en_ICs]
    type = ParsedFunction
    vars = 'em_ICs'
    vals = 'em_ICs'
    value = 'log(32. + cos(pi/2*x)) + em_ICs'
  []
[]

[BCs]
  [potential_BC]
    type = FunctionDirichletBC
    variable = potential
    function = 'potential_fun'
    boundary = '0 1 2 3'
    preset = true
  []

  [em_BC]
    type = FunctionDirichletBC
    variable = em
    function = 'em_fun'
    boundary = '0 1 2 3'
    preset = true
  []

  [ion_BC]
    type = FunctionDirichletBC
    variable = ion
    function = 'ion_fun'
    boundary = '0 1 2 3'
    preset = true
  []

  [energy_BC]
    type = FunctionDirichletBC
    variable = mean_en
    function = 'mean_en_fun'
    boundary = '0 1 2 3'
    preset = true
  []

  [Ex_BC]
    type = FunctionDirichletBC
    variable = Ex
    function = 'Ex_fun'
    boundary = '0 1 2 3'
    preset = true
  []

  [Ey_BC]
    type = FunctionDirichletBC
    variable = Ey
    function = 'Ey_fun'
    boundary = '0 1 2 3'
    preset = true
  []
[]

[Materials]
  [field_solver]
    type = FieldSolverMaterial
    potential = potential
  []
  [Material_Coeff]
    type = GenericFunctionMaterial
    prop_names =  'e N_A'
    prop_values = 'ee N_A'
  []
  [ADMaterial_Coeff_Set1]
    type = ADGenericFunctionMaterial
    prop_names =  'diffpotential diffion muion'
    prop_values = 'diffpotential diffion muion'
  []
  [Material_Coeff_Set2]
    type = ADMMSEEDFRates
    electrons = em
    mean_energy = mean_en
    prop_names =              'diffem        muem        diffmean_en        mumean_en'
    prop_values =             'diffem        muem        diffmean_en        mumean_en'
    d_prop_d_actual_mean_en = 'diffem_coeff  muem_coeff  diffmean_en_coeff  mumean_en_coeff'
  []
  [Charge_Signs]
    type = GenericConstantMaterial
    prop_names =  'sgnem  sgnion  sgnmean_en'
    prop_values = '-1.0   1.0     -1.0'
  []
[]

[Postprocessors]
  [em_l2Error]
    type = ElementL2Error
    variable = em
    function = em_fun
  []
  [ion_l2Error]
    type = ElementL2Error
    variable = ion
    function = ion_fun
  []
  [potential_l2Error]
    type = ElementL2Error
    variable = potential
    function = potential_fun
  []
  [mean_en_l2Error]
    type = ElementL2Error
    variable = mean_en
    function = mean_en_fun
  []

  [Ex_l2Error]
    type = ElementL2Error
    variable = Ex
    function = Ex_fun
  []
  [Ey_l2Error]
    type = ElementL2Error
    variable = Ey
    function = Ey_fun
  []

  [h]
    type = AverageElementSize
  []
[]

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

  [fdp]
    type = FDP
    full = true
  []
[]

[Executioner]
  type = Transient
  start_time = 50
  end_time = 51

  # dt = 0.008
  dt = 0.02

  automatic_scaling = true
  compute_scaling_once = false
  petsc_options = '-snes_converged_reason -snes_linesearch_monitor'
  solve_type = NEWTON
  line_search = none
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu NONZERO 1.e-10'

  scheme = bdf2

  nl_abs_tol = 1e-13
[]

[Outputs]
  perf_graph = true
  [out]
    type = Exodus
    interval = 10
  []
[]

Overview
Example Input File Syntax
Input Parameters
Input Files