FDM → FEM state transfer¶

Scope and purpose¶

This page specifies the source-backed continuation from a Cartesian FDM state to a target FEM state, including interpolation, normalization, provenance and explicit failure reporting.

Scientific and numerical model¶

The transfer samples the source grid at target FEM points and does not transfer solver operators or derived fields between discretizations.

Physical and numerical problem¶

FDM→FEM continuation transfers a Cartesian cell-centred magnetization to a new FEM mesh when a continuation changes backend or FEM mesh. The runtime uses the target element locator and interpolates the source grid field; it does not reinterpret FDM cell values as FEM nodal values without geometry.

Governing equations¶

For a target FEM point \(\mathbf x\), trilinear interpolation over the source cell with weights \(w_{abc}\) is

The target FEM field is then sampled on its target topology and normalized using the same unit-vector policy as the continuation contract.

Symbols and SI units¶

Assumptions and validity¶

• The FDM grid origin, cell size and dimensions are resolved metadata; omitting them makes the transfer non-reproducible.

• Target FEM points outside the source grid require an explicit fallback/error policy. Extrapolation is not equivalent to interpolation.

• This operation transfers magnetization state, not FEM potentials, stiffness matrices or energy fields. Those quantities must be recomputed on the target backend.

Python API¶

There is no separate public transfer constructor. The runtime selects this operation when a FDM continuation state is consumed by a FEM stage; the user continues to author the target study through the stage-first API:

# %% Stage-first target FEM continuation
import fullmag as fm

nm = 1.0e-9
study = fm.study("fem_continuation_target")
study.engine("fem")
study.device("cpu", precision="double")
study.mode("strict")
study.universe(mode="manual", size=(700 * nm, 250 * nm, 250 * nm))
film = study.geometry(fm.Box(size=(500 * nm, 125 * nm, 3 * nm), name="film"), name="film")
film.Ms = 8.0e5
film.Aex = 1.3e-11
film.m = fm.init.UniformMagnetization((1.0, 0.0, 0.0))
study.stages.add_relax(stage_id="continue", algorithm="nonlinear_cg", tolT=1.0e-6, max_steps=100)

Parameters¶

The resolved parameters are the source-grid metadata, target FEM topology, coverage policy and normalization policy recorded by the continuation operation; there is no separate public transfer constructor.

ProblemIR and provenance¶

Record source FDM grid metadata, target FEM mesh digest, target-point coverage, fallback/error policy, normalization, transfer counters and source/target backend identity. The transferred state is not a new physical interaction and must not alter the requested energy terms.

Diagnostics and failure semantics¶

Diagnostics must distinguish interpolated points, outside-domain points, fallback or error decisions, normalization changes and source/target artifact mismatches. Missing grid metadata or target topology is a validation failure, not an implicit default.

Round-trip and failure semantics¶

Requested intent and resolved execution are recorded separately. Validation errors include missing grid metadata, target topology mismatch and outside-domain failure. Unsupported combinations are explicitly reported; no invisible nearest-neighbour or extrapolation fallback is permitted.

Discrete realization by lane¶

Implementation mapping¶

Validation¶

Validate affine/vector fields, grid coverage, target mesh coverage, unit-vector norms and first-stage energy/torque continuity. Report outside/fallback counts and the source/target artifact digests.

Limitations¶

State interpolation does not transfer FDM convolution kernels, FEM potentials or discretization operators. After transfer the target backend must rebuild all derived fields.

Scientific bibliography¶

• Standard trilinear interpolation reference for Cartesian grids.

• Canonical continuation implementation is listed below.

Control Room workflow¶

Author the target FEM stage in Control Room and inspect the resolved continuation resource before execution. Only controls surfaced by the current stage draft are authorable; transfer counters and artifact provenance remain runtime evidence.

Control Room crosswalk¶

Use Model Explorer -> Stages -> Add stage -> <stage kind> for stage-level controls when the terminal page identifies a matching field. The current editor is partial: only fields surfaced by the stage draft are authorable. Numerical parameters without a matching control are not implemented in the frontend. Do not infer frontend support from Python or backend availability. See {doc}/frontend/capability-register for the current register and exact source owner.

Where this is implemented¶

The source-code index below records the stable routing and interpolation declarations used by this page and its sidecar map.

Source-code index¶