FEM boundary-layer mesh controls¶

Problem statement¶

Targeted Gmsh boundary-layer controls for a ferromagnetic FEM mesh.

Governing equations¶

Symbols and SI units¶

Assumptions and validity¶

At least one explicit surface or curve target is required for realization. Tags are Gmsh entity identifiers and can change after geometry edits; selector mappings are resolved against current geometry. Boundary layers can create high-aspect-ratio cells and require observable-level convergence.

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

# %% stage-first study and a target-bearing mesh recipe
study = fm.study("boundary_layer_reference")
study.engine("fem")
film = study.geometry(
    fm.Box(size=(80e-9, 40e-9, 8e-9), name="film"),
    name="film",
)
film.Ms = 800.0e3
film.Aex = 13.0e-12
film.m = fm.texture.uniform(1.0, 0.0, 0.0)
film.mesh(
    maximum_element_size=6e-9,
    boundary_layer_count=3,
    boundary_layer_thickness=1e-9,
    boundary_layer_stretching=1.25,
    boundary_layer_target_surface_tags=[1],
    compute_quality=True,
)
study.stages.add_relax(stage_id="equilibrium", dt=5.0e-13, max_steps=1)

ProblemIR¶

GeometryMeshHandle.configure normalizes the four target forms and _mesh_spec_to_metadata writes them under the matching mesh_workflow.per_geometry[] entry. _collect_mesh_workflow_metadata uses mesh_workflow.mesh_options only for the default mesh spec, not for this film.mesh(...) request. Tags and selectors are requested intent; selector-resolution records and BoundaryLayerResult are resolved evidence.

Round-trip and failure semantics¶

Requested intent contains count, first spacing, ratio, and at least one target form. Resolved execution contains selector matches and a boundary-layer status: applied, degraded, or ignored, with a reason where applicable. Validation errors include a boundary-layer count whose int(...) conversion fails or whose converted value is below one, nonpositive thickness, invalid tags, and non-mapping selectors. Because conversion precedes range validation, for example 3.9 resolves to 3 and 0.9 resolves to 0 and is rejected. Unsupported combinations do not acquire a hidden fallback: no targets yields ignored; surface-to-curve failure yields ignored; unavailable setAsBoundaryLayer yields degraded.

Discrete realization¶

_add_boundary_layer_field converts selected surfaces to boundary curves, sets CurvesList, hwall_n, thickness, ratio, and NbLayers, then calls setAsBoundaryLayer. This is a Gmsh field request; the extracted cell topology and build report remain authoritative.

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¶

A configured layer without targets is deliberately ignored. The implementation sets both hwall_n and thickness from boundary_layer_thickness; it does not document that value as total geometric-series thickness. Tag-based targeting is not stable across geometry revisions.

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 FEM ferromagnet boundary-layer controls. 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 layer thickness, element size, growth, and FEM order. 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.