Implicit Geometry Material¶

Introduction¶

The implicit geometry material defines the material distribution of the Time-Domain Magnetic Model through a level-set function \(\varphi(\mathbf{x})\) instead of through the mesh topology. The material combines two media, air and iron. The sign of the level-set function selects the medium at each point: air where \(\varphi < 0\), and iron with relative permeability \(\mu_r\) where \(\varphi > 0\).

Because the material interface is given implicitly by \(\varphi = 0\), the geometry can be changed — moved, scaled, or reshaped — without re-meshing. This makes the material well suited for shape and topology optimization of magnetic devices and for parametric studies of geometric features. Use it with adaptive mesh refinement along the interface (see refine_along_interface).

Material¶

from mufem.electromagnetics.module.implicit_geometry import (
    TimeDomainMagneticImplicitGeometryMaterial,
)

TimeDomainMagneticImplicitGeometryMaterial(
    name: str,
    marker: Marker,
    phi: CffScalarVariableTrait,
    relative_permeability_iron: float,
)

Args:

• name: Name of the material
• marker: Marker of the support volume on which the material is defined
• phi: The level-set function \(\varphi\), given as a scalar coefficient; air is assumed where \(\varphi < 0\), iron where \(\varphi > 0\)
• relative_permeability_iron: Relative magnetic permeability \(\mu_r\) of the iron phase (default 1.0)

Example¶

import mufem
from mufem import Vol
from mufem.electromagnetics.module.implicit_geometry import (
    TimeDomainMagneticImplicitGeometryMaterial,
)

# Level set of a cylinder of radius 0.05 m centered at the origin:
cff_phi = mufem.CffExpressionScalar("0.05^2 - (x^2 + y^2)")

material = TimeDomainMagneticImplicitGeometryMaterial(
    "Cylinder", Vol.Everywhere, phi=cff_phi, relative_permeability_iron=1000.0
)

magnetic_model.add_materials([material])