FDM¶

Last changes: 05:44 31.08.2026Documentation changelog

Contract¶

This page records the current public Python authoring contract and canonical lowering; it does not redefine solver physics.

Governing equations¶

This API page introduces no independent governing equation. Physical equations belong to interaction and solver-lane pages.

Symbols and SI units¶

Every owned input has its SI unit below; \(1\) denotes dimensionless data.

Assumptions and validity¶

Constructor checks run immediately. Lowering and planning additionally check mesh cardinality, capability, and backend legality.

Python API¶

Python	Type	Default	SI unit	Validation	Meaning	Backend support	ProblemIR
`FDM.cell`	`three positive floats or` None``	`None`	\(\mathrm{m}\)	Canonical uniform cell size; it also becomes `default_cell` when supplied.	Canonical uniform cell size; it also becomes `default_cell` when supplied.	FEM/FDM CPU/GPU; planner checks combinations	`backend_policy.discretization_hints.fdm.cell`
`FDM.default_cell`	`three positive floats or` None``	`None`	\(\mathrm{m}\)	Default cell size when per-magnet grids are present.	Default cell size when per-magnet grids are present.	FEM/FDM CPU/GPU; planner checks combinations	`backend_policy.discretization_hints.fdm.default_cell`
`FDM.per_magnet`	`mapping or` None``	`None`	\(1\)	Optional explicit per-magnet FDM grids.	Optional explicit per-magnet FDM grids.	FEM/FDM CPU/GPU; planner checks combinations	`backend_policy.discretization_hints.fdm.per_magnet`
`FDM.demag`	`FDMDemag \| None`	`None`	\(1\)	Demagnetization hint.	Demagnetization hint.	FEM/FDM CPU/GPU; planner checks combinations	`backend_policy.discretization_hints.fdm.demag`
`FDM.boundary_correction`	`str \| None`	`None`	\(1\)	Optional `T0`/`T1`-family sub-cell policy. Support differs by precision and device.	Optional `T0`/`T1`-family sub-cell policy. Support differs by precision and device.	FEM/FDM CPU/GPU; planner checks combinations	`backend_policy.discretization_hints.fdm.boundary_correction`
`FDM.boundary_phi_floor`	`float \| None`	`None`	\(1\)	Optional lower bound \(\varphi_{\mathrm{floor}}\) with strict domain \(0<\varphi_{\mathrm{floor}}<1\).	Optional lower bound \(\varphi_{\mathrm{floor}}\) with strict domain \(0<\varphi_{\mathrm{floor}}<1\).	FEM/FDM CPU/GPU; planner checks combinations	`backend_policy.discretization_hints.fdm.boundary_phi_floor`
`FDM.boundary_delta_min`	`float \| None`	`None`	\(\mathrm{m}\)	Optional T1 distance floor \(\delta_{\min}\geq0\); zero is accepted.	Optional T1 distance floor \(\delta_{\min}\geq0\); zero is accepted.	FEM/FDM CPU/GPU; planner checks combinations	`backend_policy.discretization_hints.fdm.boundary_delta_min`

Complete FDM stage scenario¶

The FDM grid is selected on the study before the physical stages are declared.

# %% FDM discretization in the public stage workflow
import fullmag as fm

nm = 1.0e-9
study = fm.study("fdm_api_example")
study.engine("fdm")
study.device("cpu", precision="double")
study.mode("strict")
study.objects.mesh.defaults(cell_size=(2 * nm, 2 * nm, 5 * nm))
study.exchange()
film = study.geometry(fm.Box(100 * nm, 20 * nm, 5 * nm), name="film")
film.Ms = 800.0e3
film.Aex = 13.0e-12
film.alpha = 0.02
film.m = fm.init.UniformMagnetization((1.0, 0.0, 0.0))
study.solver(integrator="rk45", fix_dt=1.0e-15, gamma=2.211e5)
study.stages.add_run(stage_id="run", until=1.0e-9)

ProblemIR¶

The final column gives the serialized destination owned by the current lowering implementation.

Round-trip and failure semantics¶

Requested intent is preserved in Python and IR. Resolved execution is selected by the planner. Validation errors reject malformed values; unsupported combinations fail capability checks without silent fallback.

Discrete realization¶

This page owns authoring and lowering only; numerical realization belongs to solver-lane documentation.

Implementation mapping¶

The adjacent map anchors claims to packages/fullmag-py/src/fullmag/model/discretization.py and class FDM.

Validation¶

Tests compare this inventory with live signatures and validate its source map.

Limitations¶

Representability does not prove every backend combination executable; planner capabilities are authoritative.

Scientific bibliography¶

No physical model is introduced. Primary references belong to consuming interaction pages.

Control Room crosswalk¶

Status: Advertised global/object mesh controls are partial; compatibility-only frontend fields remain not implemented.

Python/API surface	Control Room path	Status	Transaction
Parameters documented on this page	`Model Explorer -> Study or Objects -> <object> -> Mesh`	`partial`	Apply mesh policy or Build Mesh; mesh resources become stale
Parameters without a named UI field	`Model Explorer -> Study or Objects -> <object> -> Mesh`	`not implemented`	Python-only until implemented

Frontend support is not implemented for discretization parameters not represented by the mesh panels. See Control Room capability register for the support matrix and explicit not-implemented status. Frontend source owner: apps/control-room/src/modules/inspector/panels/ObjectMeshPolicyPanel.tsx (ObjectMeshPolicyPanel).

Source-code index¶

Claim	Path	Stable symbol	Responsibility	Evidence
Constructor, validation, lowering	`packages/fullmag-py/src/fullmag/model/discretization.py`	`class FDM`	Canonical Python API behavior	Ownership test and source-map validator