Demagnetization¶

Physical problem¶

This page is the public physical and authoring contract for the interaction. It separates authored semantics, planner resolution, executable backend lanes, and scientific qualification.

Governing equations¶

In the magnetostatic approximation,

Introducing a scalar potential \(u\),

in the distributional sense, including volume and surface magnetic charge. The open-boundary solution satisfies \(u(\mathbf x)\to0\) as \(|\mathbf x|\to\infty\). The energy is

The two forms are a valuable implementation cross-check when evaluated consistently.

Symbols and SI units¶

Numerical families¶

• FDM open convolution uses a cell-integrated demagnetization tensor and FFT acceleration.

• FDM periodic/truncated images changes the Green function and requires an explicit zero-mode convention.

• FEM airbox truncates the exterior domain and imposes a documented outer boundary condition.

• FEM–BEM / Fredkin–Koehler represents the open exterior through boundary operators.

• FMM is accepted vocabulary only where the planner/runtime actually materializes it.

No model name may be promoted from “accepted by Python” to “executable” without planner and runtime evidence.

Backend capability matrix¶

Python API and stage-first example¶

# %% Study, execution lane, and magnetic body
import fullmag as fm

nm = 1.0e-9
study = fm.study("demag_reference")
study.engine("fdm")
study.device("cpu", precision="double")
study.mode("strict")
study.objects.mesh.defaults(cell_size=(2 * nm, 2 * nm, 2 * nm))
body = study.geometry(fm.Box(40 * nm, 20 * nm, 4 * nm), name="film")
body.Ms = 8.0e5
body.Aex = 13.0e-12
body.alpha = 0.02
body.m = fm.texture.uniform(1.0, 0.0, 0.0)

study.stages.add_run(stage_id="sample", until=1.0e-12)

Exchange and demagnetization are active by default. Call study.demag(realization=...) only to select a non-default realization. Call study.disable_demag() only when the authored physics intentionally excludes demagnetization. A FEM request should state its realization and solver policy explicitly, for example study.demag(realization="poisson_robin"), together with the airbox and mesh controls.

Public constructor boundary¶

Demag(model=..., variant=..., realization=...) is backend-neutral. model and legacy realization are mutually exclusive. Airbox variants are meaningful only for the airbox family. FDM grid, multilayer topology, periodicity, boundary correction, and FEM linear-solver settings belong to discretization policy, not to the continuum energy.

ProblemIR¶

The default term lowers as

{"kind": "demag", "realization": "auto"}

The planner must retain both requested and resolved realization. It must also record grid/mesh, periodicity, airbox, solver, tolerance, preconditioner, precision, and actual execution device.

Validation and failure semantics¶

Constructor acceptance of bem, fredkin_koehler, or fmm is not proof that a selected solver/device lane executes it. Invalid model/variant combinations, unsupported periodic policies, missing shared-domain meshes, incompatible GPU solver policies, and unavailable observables must fail closed. Algebraic residual tolerance does not bound airbox truncation, mesh, or boundary-quadrature error.

Required numerical validation¶

• analytic uniformly magnetized ellipsoids;

• Newell tensor values and symmetry identities for FDM;

• zero net field for appropriate periodic uniform modes under the documented \(k=0\) policy;

• convergence with cell size, FEM mesh, airbox padding, and boundary discretization;

• equivalence of the two energy expressions where numerically available;

• μMAG standard problems with declared mesh and stopping criteria;

• CPU/GPU comparisons at identical geometry, material, precision, and reduction convention;

• multilayer translation, self/cross-layer symmetry, and common-grid convergence.

Recommended documentation split¶

Keep this root as the physical and capability owner. Detailed pages should separately own: FDM convolution, multilayer convolution, periodic demag, FEM airbox, FEM–BEM/Fredkin–Koehler, boundary conditions, and validation. Avoid duplicating complete parameter tables and enormous ProblemIR documents across all children.

Scientific bibliography¶

1. W. F. Brown, Micromagnetics, Wiley, 1963.

2. A. J. Newell, W. Williams, and D. J. Dunlop, Journal of Geophysical Research 98, 9551–9555 (1993), DOI: 10.1029/93JB00694.

3. D. R. Fredkin and T. R. Koehler, IEEE Transactions on Magnetics 26, 415–417 (1990).

4. NIST μMAG Standard Problems, current benchmark definitions.

Control Room crosswalk¶

This is a navigation page; the selected interaction or foundation is configured by its linked Python API and object/stage editor. The category itself has no standalone control. frontend support is not implemented applies to physical parameters without a matching control. See {doc}/frontend/capability-register; do not infer UI support from backend or Python availability.

Python/API crosswalk¶

The linked Python API page is authoritative for exact functions, arguments, units, and failure semantics. If this page is a foundation or category overview, runnable Python is ot applicable here and must be taken from the terminal API page.

Bibliography and source scope¶

Use the scientific bibliography and source-code index on the linked terminal page. This block adds no new equation or unverified implementation claim.

Round-trip and failure semantics¶

Requested intent preserves the authored model, coefficients, orientations, targets, and execution request. Resolved execution records the selected solver, device, precision, discretization, and capability decision. Validation errors reject malformed or contradictory data before runtime. Unsupported combinations fail closed and are not silently omitted or converted to another interaction.

Assumptions and validity¶

The authored model is valid only within the continuum, discretization, boundary, and capability limits stated on this page.

Implementation mapping¶

Python owns authoring and serialization, ProblemIR owns canonical intent, planners own legality and realization selection, and backend kernels own numerical evaluation.

Limitations¶

Capabilities not listed as executable must fail closed. Source presence alone is not runtime or scientific qualification.

Source-code index¶