FEM Meshing API¶

Problem statement¶

FEM(...) supplies study-level finite-element defaults. Universe, ferromagnet, region, and build facades add their own policy before the backend creates one conforming shared-domain mesh.

Governing equations¶

This API introduces no independent interaction equation. It selects the finite-element space and mesh asset used by weak-form operators, scalar-potential domains, eigenproblems, and response solves.

Symbols and SI units¶

Element sizes, airbox geometry, layer thicknesses, interface distances, and transition distances are SI metres. Orders, counts, algorithms, ratios, and quality controls are dimensionless.

Assumptions and validity¶

Order is at least one. A positive maximum element size is required. hmax is an alias and must agree with maximum_element_size when both are present. Imported mesh references are nonempty and remain subject to native validation. Element-family/device support is capability-gated.

Python API¶

# %% Complete stage-first FEM mesh scenario
import fullmag as fm

nm = 1.0e-9
study = fm.study("fem_meshing_api")
study.engine("fem")
study.device("cpu", precision="double")
study.mode("strict")

study.universe(mode="manual", size=(800 * nm, 400 * nm, 300 * nm))
study.universe.mesh(
    minimum_element_size=8 * nm,
    maximum_element_size=80 * nm,
    maximum_element_growth_rate=1.5,
    grading="geometric",
)

film = study.geometry(fm.Box(300 * nm, 100 * nm, 5 * nm), name="film")
film.mesh(
    minimum_element_size=2.5 * nm,
    maximum_element_size=5 * nm,
    order=1,
    compute_quality=True,
)
film.Ms = 800.0e3
film.Aex = 13.0e-12
film.alpha = 0.02
film.m = fm.texture.uniform(1.0, 0.0, 0.0)

study.exchange()
study.demag(model="airbox", variant="robin")
study.build_domain_mesh()
study.stages.add_relax(stage_id="equilibrium", tolT=1.0e-6)

ProblemIR¶

The table covers constructor-owned request fields. Object/universe/region policies are separate canonical resources. Resolved execution adds effective targets, element/facet families, markers, selectors, fallbacks, quality statistics, versions, and the final mesh digest.

Round-trip and failure semantics¶

Requested intent and resolved execution remain separate. Validation errors reject malformed sizes, orders, and contradictory topology fields. Unsupported combinations fail capability checks. Strict mode forbids silent replacement of requested prism, airbox shape, periodic, selector, or GPU semantics.

Discrete realization¶

Meshing itself is normally a host/Gmsh operation even when the simulation executes on GPU.

Implementation mapping¶

FEM owns study defaults. PerObjectMeshRecipe, MeshOperation, and SweptMeshControls own ferromagnet topology. Universe and region facades add airbox and local-region policy. Backend reports are authoritative for what ran.

Validation¶

Validate geometry/volume, conformity, markers, selectors, Jacobians, quality tails, topology certificates, mesh and layer convergence, airbox convergence, and CPU/GPU identity using one mesh digest.

Limitations¶

hmax is a target, exact layered support is intentionally bounded, swept hex is not production enabled in the reviewed UI gate, and general multi-object or airbox-plus-swept support is scenario-dependent.

Scientific bibliography¶

1. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, SIAM, 2002.

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

3. R. Anderson et al., “MFEM,” Comput. Math. Appl. 81, 42–74 (2021).

Control Room crosswalk¶

Status: Frontend support is not implemented unless a named source-backed panel is added.

frontend support is not implemented for this API surface and its parameters. See Control Room capability register for the support matrix and not implemented policy. Frontend source owner: apps/control-room/src/modules/inspector/inspectorRouteCatalog.tsx (inspectorRouteCatalog).

Source-code index¶