FEM Airbox Mesh API¶

1. What it is and when to use it¶

The airbox (universe) is the surrounding air volume around the magnetic objects, required to solve magnetostatics (stray field, demagnetization). Airbox authoring belongs to the universe, not to a ferromagnet:

• exterior geometry: study.universe(...),

• air sizing: study.universe.mesh(...),

• magnetostatic realization (Poisson/Robin/PBC): separately via study.demag(...).

When to use it: in every FEM scenario with an airbox demag model. Impact on the simulation: a too-small airbox corrupts boundary conditions of the stray field; a too-fine one costs unacceptably. Grading (section 2) gives resolution near objects and cheap elements far away.

2. Physical and mathematical explanation¶

The airbox is the solution domain of the magnetostatic equation for the scalar potential outside magnetic bodies:

where \(\phi\) — scalar potential (\(\mathrm{A}\)), \(\mu\) — permeability (\(\mathrm{H\,m^{-1}}\)). The air element size should grow with distance from the bodies (geometric grading), and the airbox extent must be large enough that the boundary condition (Dirichlet/Robin) does not distort the near field.

3. Example — complete Python script¶

# %% Airbox geometry and grading
import fullmag as fm

nm = 1.0e-9

study = fm.study("airbox_mesh_api_example")
study.engine("fem")
study.device("cpu", precision="double")
study.mode("strict")

# Exterior geometry of the universe / airbox:
study.universe(mode="manual", size=(800 * nm, 400 * nm, 300 * nm))

# Air sizing with geometric grading away from magnetic bodies:
study.universe.mesh(
    minimum_element_size=8 * nm,
    maximum_element_size=100 * nm,
    maximum_element_growth_rate=1.3,
    grading="geometric",
)

film = study.geometry(fm.Box(300 * nm, 100 * nm, 5 * nm), name="film")
film.Ms = 800.0e3
film.Aex = 13.0e-12
film.alpha = 0.02
film.m = fm.texture.uniform(1.0, 0.0, 0.0)
film.mesh(minimum_element_size=2.5 * nm, maximum_element_size=5 * nm)

# Magnetostatic realization is selected separately from mesh sizing:
study.exchange()
study.demag(model="airbox", variant="robin")
study.build_domain_mesh()
study.stages.add_relax(stage_id="equilibrium", tolT=1.0e-6)

4. Exact API¶

study.universe.mesh(**kwargs) (StudyUniverseMeshHandle, world.py):

Advanced policy (universe resource advanced policy) additionally covers curvature and narrow-region resolution.

Failure behavior: cell_size (FDM) cannot be combined with FEM controls and vice versa → ValueError; non-positive sizes → ValueError. Values are targets, not guaranteed realized extrema.

ProblemIR mapping: universe policy lands in mesh workflow metadata (airbox hmin/hmax/growth/grading); realization and any fallbacks are recorded in the build report.

5. How to set it in Control Room¶

Model Explorer
└── Universe / Airbox      → selection kinds: airbox.* 

The Airbox Mesh Parameters inspector edits air sizing; exterior geometry (size/padding/center) lives in the universe geometry panels; the magnetostatic realization choice (study.demag) is made in the Physics/Demag panel. Full description: FEM Airbox Mesh Panel.

6. Backend support¶

7. Limitations and known pitfalls¶

• Airbox extent and boundary policy (study.demag) are two different decisions; changing one does not fix the other.

• Size extrema are targets — check realized values in the build report.

8. Scientific bibliography¶

1. J. D. Jackson, Classical Electrodynamics, 3rd ed., Wiley, 1999.

2. C. Geuzaine and J.-F. Remacle, “Gmsh,” Int. J. Numer. Methods Eng. 79, 1309–1331 (2009).

9. Source-code index¶

Source-code index¶

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