MagneticSymmetryValue

MagneticSymmetryValue[pred,vars,pars]

represents a magnetic symmetry boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.

MagneticSymmetryValue[pred,vars,pars,lkey]

represents a magnetic symmetry boundary condition with local parameters specified in pars[lkey].

Details

MagneticSymmetryValue specifies a symmetry boundary condition for MagnetostaticPDEComponent.
MagneticSymmetryValue specifies a boundary condition for MagnetostaticPDEComponent and is used as part of the modeling equation:

MagneticSymmetryValue is typically used to model a boundary with mirror symmetry along an axis.

MagneticSymmetryValue models a boundary with mirror symmetry with dependent variable and independent variables .
Stationary variables vars are vars={V_m[x₁,…,x_n],{x₁,…,x_n}}.
The linear form of MagnetostaticPDEComponent with vacuum permeability in units of [] and relative permeability is given by:

MagneticSymmetryValue with boundary unit normal and a magnetic flux density vector models:

Model parameters pars as specified as for MagnetostaticPDEComponent.
MagneticSymmetryValue is effectively the same as MagneticFluxDensityValue with a magnetic flux of 0.
The boundary predicate pred can be specified as in NeumannValue.
If the MagneticSymmetryValue depends on parameters that are specified in the association pars as …,keyp_i…,p_iv_i,…], the parameters are replaced with .

Examples

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Basic Examples (1)

Set up a magnetic symmetry boundary condition:

Scope (1)

Set up a magnetic symmetry boundary condition in 3D:

Applications (1)

Model an iron cube embedded in air and emerged in a homogeneous magnetic field of [] directed along the axis. The domain is composed of an iron cube of length []. Due to symmetry, only 1/8 of the whole domain is simulated. The air boundary surrounding the iron cube is modeled as a second cube of length [].

In the reduced geometry, at the surfaces parallel to the planes - and - a symmetry boundary condition needs to be applied.

Define the mesh:

The mesh has internal boundaries that represent the inner iron cube. Define the iron cube:

Visualize a wireframe of the mesh:

Define variables:

Define parameters the permeability of vacuum and iron :

To specify the homogeneous magnetic field across the domain, an outward magnetic flux density normal to the boundary at is specified.

Set up the magnetic flux density condition:

Set up the magnetic symmetry condition:

Since the magnetic symmetry condition is a Neumann zero boundary condition, which is the default boundary condition if nothing is specified on a boundary, it could also be omitted.

Solve the magnetostatic PDE model:

Compute the magnetic field intensity:

To visualize another 1/8 of the field, at , the symmetric behavior of the field must be considered. At positive values, the field is and at negative values, the field is .