Swept-prism ferromagnet mesh¶

Physical problem¶

The strict route extrudes a triangular source face into native prism6 layers. A qualified shared domain can use typed pyramid5 transitions to tet4; it does not split prisms into tetrahedra.

Governing equations¶

Symbols and SI units¶

Assumptions and validity¶

The native body path is an axis-aligned Box, P1, fixed distribution, triangular source, and positive integer layers. Control Room additionally enables authoring only when all layered-prism capabilities are executable and supported counts equal [1,2,3].

Python API¶

# %%
import fullmag as fm

nm = 1e-9
study = fm.study("strict_prism")
study.engine("fem")
study.device("cpu", precision="double")
study.mode("strict")
study.universe(mode="manual", size=(100 * nm, 80 * nm, 65 * nm), center=(0.0, 0.0, 0.0))
study.universe.mesh(maximum_element_size=40 * nm, minimum_element_size=15 * nm, growth_rate=1.3, grading="geometric")

# %%
film = study.geometry(fm.Box(size=(24 * nm, 12 * nm, 1 * nm), name="film"), name="film")
film.mesh.thin_film(
    maximum_element_size=3 * nm,
    minimum_element_size=1 * nm,
    layers=1,
    topology="prismatic",
    exact_layers=True,
    transition="pyramid_to_tetrahedra",
    order=1,
)
film.Ms = 800e3
film.Aex = 13e-12
film.m = fm.texture.uniform(1.0, 1e-4, 0.0)
study.exchange()
study.demag(realization="poisson_robin")
study.build_domain_mesh()
study.stages.add_relax(stage_id="equilibrium", algorithm="llg_overdamped", tolA=1e-4, max_steps=20_000, dt=1e-13)

ProblemIR¶

For topology="prismatic", GeometryMeshHandle.thin_film() lowers to mesh_strategy="swept_prism", through_thickness_elements=layers, through_thickness_distribution="fixed", through_thickness_symmetric=False, sweep_face_meshing="triangular", topology="prismatic", sweep_direction="auto", element_family="prism", transition_policy="pyramid_to_tetrahedra", exact_layer_count=True, and order=1. PerObjectMeshRecipe itself accepts distributions None|fixed|linear|exponential and directions None|auto|x|y|z; thin_film() intentionally selects fixed and auto for strict prismatic authoring. The realization report separately records requested/resolved topology, axis, layers, order, and fallbacks.

All four transition-distance arguments accept the sentinels airbox_boundary, airbox-boundary, and auto_boundary; lowering canonicalizes each to airbox_boundary. Perimeter validation also enforces corner_hmax <= edge_hmax when both are active and, for a Box (including translated boxes), requires edge_thickness and corner_extent to be strictly smaller than half the shorter in-plane dimension.

Round-trip and failure semantics¶

Requested intent is the public thin_film() call and its lowered object policy. Resolved execution must report prism6, exact layers, P1, and no fallback. Validation errors reject zero/non-integer layers, non-P1 order, recipe distributions outside None|fixed|linear|exponential, recipe directions outside None|auto|x|y|z, wrong realized family, and wrong layer count. pyramid_to_tetrahedra is mandatory when topology="prismatic", not for every prism-family policy. Unsupported combinations include swept_hex and non-box geometry for explicit native prism strategy. A tet4 result is failure.

Discrete realization¶

generate_swept_mesh dispatches strict prism generation. Its extractor requires prism6-only volume cells and tri3/quad4 facets, validates orientation, and checks exact layer planes. Shared transitions retain pyramid5 and tet4 types.

| Solver | Device | Status | Reason | | — | — | — | | FEM | CPU | source-backed, capability-gated | No runtime receipt is claimed. | | FEM | GPU | source-backed, capability-gated | No GPU identity or parity result is claimed. | | FDM | CPU | not applicable | FEM meshing. | | FDM | GPU | not applicable | FEM meshing. |

Implementation mapping¶

GeometryMeshHandle.thin_film owns public authoring and lowering; PerObjectMeshRecipe owns policy validation; generate_swept_mesh owns dispatch; resolveObjectMeshTopologyCapabilities implements the exact Control Room gate.

Validation¶

Focused tests assert exact planes, all axes, prism-only realization, strict wrong-family/layer rejection, no prism splitter, and no swept-hex fallback. They do not establish CPU/GPU runtime qualification or mesh convergence.

Limitations¶

This is not a general sweepability, higher-order, arbitrary UI layer-count, nonuniform exact-layer, GPU parity, or observable-convergence claim.

Scientific bibliography¶

• C. Geuzaine and J.-F. Remacle, “Gmsh,” International Journal for Numerical Methods in Engineering 79 (2009), doi:10.1002/nme.2579.

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

Source-code index¶

Scope and purpose¶

This page defines the public contract for swept prismatic 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 source surface, layer count, element size, and topology. 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.