- Hext_xThe fixed x-component of the magnetic field variable
C++ Type:std::vector<VariableName>
Controllable:No
Description:The fixed x-component of the magnetic field variable
- Hext_yThe fixed y-component of the magnetic field variable
C++ Type:std::vector<VariableName>
Controllable:No
Description:The fixed y-component of the magnetic field variable
- Hext_zThe fixed z-component of the magnetic field variable
C++ Type:std::vector<VariableName>
Controllable:No
Description:The fixed z-component of the magnetic field variable
- componentAn integer corresponding to the direction in order parameter space this kernel acts in (e.g. for unrotated functionals 0 for q_x, 1 for q_y, 2 for q_z).
C++ Type:unsigned int
Controllable:No
Description:An integer corresponding to the direction in order parameter space this kernel acts in (e.g. for unrotated functionals 0 for q_x, 1 for q_y, 2 for q_z).
- mag_xThe x component of the constrained magnetic vector
C++ Type:std::vector<VariableName>
Controllable:No
Description:The x component of the constrained magnetic vector
- mag_yThe y component of the constrained magnetic vector
C++ Type:std::vector<VariableName>
Controllable:No
Description:The y component of the constrained magnetic vector
- mag_zThe z component of the constrained magnetic vector
C++ Type:std::vector<VariableName>
Controllable:No
Description:The z component of the constrained magnetic vector
- potential_H_intThe internal magnetic potential variable
C++ Type:std::vector<VariableName>
Controllable:No
Description:The internal magnetic potential variable
- 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
MasterInteractionCartLLGHConst
Calculates a residual contribution - MH in the total energy, assuming H = - div * potential.
Overview
We consider the residual and jacobian contributions due to a magnetic field (can be an externally applied field or user-defined). The free energy density due to the Zeeman interaction is,
This yields an effective field of
The LLG equation for the normalized magnetization is,
(1)
with the gyromagnetic ratio. Multiplying by a test function , moving over the RHS, neglecting the time derivative, and integrating over the volume, we have,
This equation in index notation is,
with the Levi-Civita symbol. Inserting the expression for the effective field due to the exchange stiffness, we have
Therefore the residual for can be written as,
The on-diagonal and off-diagonal jacobian expression is,
where is the shape function of the finite element method. Note that if depends on any variables, we would need to also compute the derivatives of those variables (i.e. ). However, using the preconditioned Jacobian-free Newton-Krylov (PFJNK) method in the Executioner
can help with convergence (exact jacobian components are not needed) The advantage of using this Kernel
in a simulation is that we do not solve the Poisson equation.
Example Input File Syntax
Input Parameters
- Hscale1scaling factor for effective fields
Default:1
C++ Type:double
Controllable:No
Description:scaling factor for effective fields
- 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>
Controllable:No
Description:The displacements
- g01electron gyromagnetic factor
Default:1
C++ Type:double
Controllable:No
Description:electron gyromagnetic factor
- potential_H_extThe external magnetic potential variable
C++ Type:std::vector<VariableName>
Controllable:No
Description:The external magnetic potential variable
- 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.
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
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
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.