Thin-film tetrahedral ferromagnet mesh¶

Problem statement¶

The public object.mesh.thin_film(...) contract for thickness-aware tetrahedral meshing and its explicit strict-prism branch.

Governing equations¶

Symbols and SI units¶

Assumptions and validity¶

The body needs a meaningful thin direction. layers is a nominal tetrahedral spacing request unless the prismatic branch produces and certifies exact layers. Thickness and in-plane refinement both require convergence checks.

Python API¶

The table is exhaustive for this public family entry point. Alias rows are alternatives, not extra simultaneous requirements.

# %% imports
import fullmag as fm

# %% explicit tetrahedral thin-film route
study = fm.study("thin_film_tetrahedral_reference")
study.engine("fem")
film = study.geometry(fm.Box(size=(100e-9, 50e-9, 6e-9)), name="film")
film.Ms = 800.0e3
film.Aex = 13.0e-12
film.m = fm.texture.uniform(1.0, 0.0, 0.0)
film.mesh.thin_film(
    maximum_element_size=5e-9,
    minimum_element_size=2e-9,
    layers=3,
    topology="tetrahedral",
    surface_maximum_element_size=3e-9,
    surface_thickness=3e-9,
    surface_transition_distance=12e-9,
    edge_maximum_element_size=2e-9,
    edge_thickness=3e-9,
    edge_transition_distance=8e-9,
    corner_maximum_element_size=1.5e-9,
    corner_extent=2e-9,
    corner_transition_distance=6e-9,
    order=1,
)
study.stages.add_relax(stage_id="equilibrium", dt=5.0e-13, max_steps=1)

ProblemIR¶

For topology=None or "tetrahedral", thin_film sets mesh_strategy="thin_film_tetrahedral", fixed through-thickness distribution, triangular face meshing, and through_thickness_elements=layers; it also resolves inferred body/surface/edge/corner sizes listed below. For topology="prismatic", it sets mesh_strategy="swept_prism", topology="prismatic", element_family="prism", sweep_direction="auto", exact_layer_count=True when exact_layers is omitted, and transition_policy="pyramid_to_tetrahedra" by default. Every serialized value is under the matching mesh_workflow.per_geometry[] entry.

Round-trip and failure semantics¶

Requested intent is the exact thin_film call. Resolved execution includes the actual method, inferred thickness, realized layer count, topology certificate, and any degradation. Validation errors reject layers < 1, unknown topology, non-boolean exact_layers, prismatic order other than 1, exact_layers=False in strict mode, or a transition other than pyramid_to_tetrahedra. Numeric interface/surface transition distance may be zero; numeric edge/corner transition distances must be strictly positive. Unsupported combinations fail closed; a tetrahedral request is never reported as exact prism layers, and a failed strict-prism certificate has no silent tetrahedral fallback.

Discrete realization¶

The tetrahedral branch explicitly lowers to mesh_strategy="thin_film_tetrahedral" and uses ordinary Gmsh tetrahedral extraction plus thickness-aware fields. The prismatic branch classifies sweepability and invokes the swept generator. _build_thin_film_diagnostics and the shared-domain report separate requested layers/topology from actual method and certificate.

Implementation mapping¶

The source index maps public authoring, lowering, realization, reporting, and backend consumption. Source-backed FEM CPU support does not imply that every requested topology is supported; FEM GPU remains capability-gated by the realized mesh and active runtime.

Validation¶

Confirm source identity, requested and actual methods, typed cell families, complete region/boundary markers, zero inverted or degenerate cells, and the relevant quality distributions. Then refine the controlling size or layer count while holding geometry, materials, solver tolerances, and outputs fixed, and require convergence of a physical observable.

Limitations¶

layers does not certify exact tetrahedral planes. Strict prismatic P1 is a distinct branch: order 1, exact layers, triangular sweep faces, prism family, and pyramid_to_tetrahedra transition. Use the realized certificate before claiming prism/pyramid/tet mixed topology.

Scientific bibliography¶

• 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.

Source-code index¶

Scope and purpose¶

This page defines the public contract for thin-film tetrahedral FEM meshes. It is an authoring and implementation reference: the Python example, the serialized ProblemIR description, the implementation mapping, and the adjacent source map are the source-backed contract. A capability marked partial or not evaluated is not presented as a production guarantee.

Scientific and numerical model¶

The mesh or grid is a discrete approximation of the continuous domain. For a Cartesian partition, each spacing satisfies Delta_i = L_i / N_i; for a geometry-dependent FEM mesh, the requested local target is bounded by the active bulk, interface, boundary, and topology constraints. In compact form, h_target(x) = min(h_bulk(x), h_interface(x), h_boundary(x)). Length quantities use SI metres (m); counts, orders, and topology labels are dimensionless.

The equations and assumptions in the earlier physical-problem and governing-equations sections state the model-specific specialization. This section does not introduce a conversion from FEM to FDM, a hidden topology conversion, or a silent CPU fallback.

Parameters¶

The exact callable and argument names are the ones shown in the ## Python API section above. For this page the parameter family is film thickness, element size, FEM order, and topology policy. Use the documented defaults, validation rules, and ProblemIR lowering exactly as shown; do not replace a canonical argument with an unlisted alias. Numerical lengths must be supplied in metres, and invalid positive-length, count, order, periodicity, or topology constraints must fail closed rather than being silently repaired.

Control Room workflow¶

In Control Room, select the engine and mesh workflow, enter the same values as the Python authoring example, inspect the planned mesh or grid report, and only then submit the run. The UI is a projection of the public contract: a missing control is not evidence that the backend accepts the option, and a visible control is not evidence that a production lane is enabled. When the page or capability register marks a field partial or not evaluated, keep the workflow explicitly bounded to the implemented path.

Diagnostics and failure semantics¶

A valid request must preserve the declared geometry, units, element or cell topology, and backend lane. Reject non-finite or non-positive lengths, invalid counts and orders, incompatible periodic or shared-boundary data, and unsupported topology combinations at the owning validation layer. Reports should retain requested and resolved values, source identity, and any capability gate. No diagnostic may hide a failed mesh realization by substituting another discretization.

Where this is implemented¶

The existing implementation-mapping and source-code-index sections identify the exact public authoring, ProblemIR, planner, realization, and runtime owners for this topic. The adjacent .source-map.json file is the machine-readable source of truth for those paths, symbols, responsibilities, backend matrix, and reviewed revision. Claims in this page must be updated together with that map when an owner moves.