FEM airbox mesh¶

Scope and purpose¶

The airbox is a physical/numerical domain, not background decoration. Use the child pages in order: define geometry, define grading, verify the outer-boundary marker and closure, then consider periodic pairing only when the solver lane explicitly advertises it.

Scientific and numerical model¶

For open-boundary magnetostatics, Fullmag’s FEM route introduces a scalar potential \(u\) on a finite computational domain \(\Omega=\Omega_m\cup\Omega_a\), where \(\Omega_m\) is magnetic material and \(\Omega_a\) is the exterior airbox. In current-free regions,

The infinite exterior is replaced by a finite outer boundary \(\Gamma_{out}\) plus a separately selected boundary closure. The mesh and boundary condition are distinct: making the airbox larger does not itself impose an open boundary, and a Robin condition does not eliminate discretization error near the magnet.

The exterior mesh should be fine enough at magnetic interfaces to represent surface-charge-driven field variation and may grow toward \(\Gamma_{out}\). If \(h_0\) is the near-interface size and \(r>1\) a geometric grading ratio, a conceptual layer sequence is

The outer-boundary distance and exterior mesh size require independent convergence studies.

Selection guide¶

Parameters¶

Python API¶

Complete Python example

import fullmag as fm

nm = 1.0e-9
study = fm.study("fem_airbox_reference")
study.engine("fem")
study.device("cpu", precision="double")
study.mode("strict")
study.universe(
    mode="manual",
    size=(600 * nm, 400 * nm, 240 * nm),
    center=(0.0, 0.0, 0.0),
    padding=(0.0, 0.0, 0.0),
)
study.universe.mesh(
    minimum_element_size=12 * nm,
    maximum_element_size=80 * nm,
    maximum_element_growth_rate=1.5,
    grading="geometric",
)

magnet = study.geometry(
    fm.Box(size=(200 * nm, 100 * nm, 10 * nm), name="film"),
    name="film",
)
magnet.mesh(
    mesh_strategy="free_tetrahedral",
    minimum_element_size=3 * nm,
    maximum_element_size=7 * nm,
    interface_maximum_element_size=5 * nm,
    interface_thickness=12 * nm,
    transition_distance="airbox_boundary",
    transition_growth=1.4,
    order=1,
    compute_quality=True,
)
magnet.Ms = 800.0e3
magnet.Aex = 13.0e-12
magnet.alpha = 0.02
magnet.m = fm.texture.uniform(1.0, 0.0, 0.0)

study.exchange()
study.demag(realization="poisson_robin")
study.build_domain_mesh()
study.stages.add_relax(
    stage_id="equilibrium",
    algorithm="llg_overdamped",
    tolA=1.0e-4,
    max_steps=20_000,
)

Control Room workflow¶

1. In Explorer, select Universe / Airbox Mesh.

2. Choose Domain mode and enter either explicit Size X/Y/Z and Center X/Y/Z, or automatic Padding X/Y/Z.

3. For FEM, set Maximum element size, Minimum element size, Maximum element growth rate, Element grading, Curvature factor and Narrow-region resolution as needed.

4. Select Apply Airbox Policy to store the universe-owned exterior-domain intent. This makes any older shared-domain realization stale.

5. Select Apply & Build Shared-Domain Mesh to dispatch mesh.build-shared-domain.

6. Inspect the effective configuration, shared-domain manifest, outer-boundary marker, interface conformity and mesh-quality scopes. The effective configuration returned by the backend is the source of truth.

For FDM, the panel filters FEM-only air-mesh controls and exposes structured-domain geometry only.

Verification, quality and provenance¶

After every build, inspect the realized resource rather than assuming that the authored request was applied. The production check is:

• geometry and mesh revisions match the current model;

• requested and realized discretization/topology/order are recorded;

• node, element and boundary-facet counts are nonzero for every required region;

• region and boundary markers cover the complete topology;

• inverted and degenerate element counts are zero;

• interface diagnostics report no orphan, coincident, nonmanifold or unmatched facets;

• local size distributions are consistent with the intended edge/interface/core grading;

• any fallback or degradation has an explicit reason and an actual method;

• a mesh-refinement sequence demonstrates convergence of the scientific observable.

MeshQualityReport exposes signed inverse condition number (SICN), gamma/radius quality, volume statistics and optional per-element arrays. The source constants gamma_min=0.08 and SICN p05=0.1 are implementation gates for named report paths; they are not universal physical acceptance thresholds for every element family or study.

Mesh-convergence protocol¶

A production result should include at least three discretizations. Refine only the parameter under study while holding geometry, material parameters, solver tolerances, initial state and output sampling fixed. Let \(Q_h\) denote the observable for characteristic size \(h\). Report

with a documented scale for observables that can cross zero. For dynamics, compare resonance frequency, linewidth and mode profile; for relaxation, compare total energy and texture; for demag, compare field/energy and verify that moving the outer boundary does not change the result beyond the chosen tolerance.

Diagnostics and failure semantics¶

The shared-domain manifest must identify air volume, magnetic/air interfaces and exactly the intended outer boundary. Missing semantic roles are blocking even when the tetrahedralization succeeds.

Where this is implemented¶

Implementation map reviewed against commit 5db00ccf0113b9756fec2d46feb36ade762b12c2 on 2026-08-24.

References¶

• C. Geuzaine and J.-F. Remacle, “Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities,” International Journal for Numerical Methods in Engineering 79 (2009), 1309–1331, doi:10.1002/nme.2579.

• C. Abert, “Micromagnetics and spintronics: models and numerical methods,” European Physical Journal B 92, 120 (2019), doi:10.1140/epjb/e2019-90599-6.

• Gmsh reference manual, mesh algorithms, size fields, extrusion and physical groups: gmsh.info/doc/texinfo.

Documentation tree¶

Source-code index¶

This is a navigation page and introduces no standalone implementation symbol. The exact source-code index is maintained by the selected terminal page.