Analytical Cases¶

Exchange sinusoidal mode¶

A \(180^\circ\)-mode sinusoidal magnetization has a closed-form exchange field, \(\mathbf{H}_{\mathrm{ex}} = \frac{2 A_{\mathrm{ex}}}{\mu_0 M_s} \nabla^2 \mathbf{m}\), and an exchange energy converging to \(A_{\mathrm{ex}} k^2 V\). The acceptance gate is scripted in tests/fem_exchange_validation/sinusoidal_mode.py and requires a MFEM/libCEED runtime for the full refinement sweep.

• Criterion — recovered \(H_{\mathrm{ex}}\) agrees with the analytic Laplacian within 25% on the finest mesh and the energy converges to \(A_{\mathrm{ex}} k^2 V\) under refinement.

• Status — scripted; the representative finest-mesh stage materializes and runs on the managed CPU path, while the full sweep is runtime-open.

Uniformly magnetized sphere¶

A uniformly magnetized sphere produces the demagnetizing field \(\mathbf{H}_{\mathrm{demag}} = -\frac{M_s}{3} \mathbf{m}\) inside the body. The gate is tests/fem_demag_validation/sphere_validation.py.

• Criterion — interior \(H_{\mathrm{demag}} \approx -M_s/3\).

• Status — scripted; requires the MFEM/libCEED/hypre runtime.

Osborn ellipsoid demagnetization factors¶

For an ellipsoid magnetized uniformly along a principal axis, the demagnetization factors follow Osborn’s closed form. The gate is tests/fem_demag_validation/ellipsoid_validation.py.

• Criterion — per-axis demagnetization factors agree with Osborn within 10% and sum to 1 within 0.15 per shape.

• Status — scripted; requires the MFEM/libCEED/hypre runtime.

Macrospin LLG checkpoints¶

Two damping-only macrospin checks constrain the LLG right-hand side:

• the damping-only macrospin energy decreases under relaxation (fem_llg_rhs_contract);

• the directed STT current-perpendicular macrospin torque reproduces the expected precession direction (fem_stt_contract).

Also the contracted Poisson demagnetization sign uses the uniformly magnetized sphere. DMI sign, chirality, boundary-tilt, and thermal variance (Brown scaling with \(1/dt\)) have both local weak residual contract gates and separate MFEM-visible runtime gates.

Evidence boundary¶

Local contract executables (no MFEM host) are valid source/unit/sign regression gates but are not runtime qualification. A row is qualified only when the executable runtime case passes in the matching MFEM/CUDA environment; the individual solver pages record which acceptance commands they cover.

Control Room crosswalk¶

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Python/API crosswalk¶

Validation is not a standalone Python constructor unless the linked case page names one. Reproduce the exact case, inputs, device, precision, and receipt described by the page; use the referenced API pages for callable signatures.

Physics and bibliography scope¶

The page either states the governing benchmark model or delegates it to the linked physics/numerical-methods page. Any missing derivation is a documented boundary, not an implicit equation. Bibliography and source evidence remain the authoritative references listed by the validation case.

Source-code index¶

• No standalone implementation function is introduced by this validation page. Source evidence is the exact API, managed recipe, runtime manifest, and receipt named by the validation case.