First FEM Simulation

Last changes: Documentation changelog

This page runs the finite-element counterpart of the FDM onboarding example. The same film relaxes from a uniform magnetization, but the domain is an unstructured tetrahedral mesh and the magnetostatic field is solved with a Poisson airbox formulation instead of an FFT convolution.

What the example computes

A universe of \(160 \times 160 \times 24\ \mathrm{nm}\) surrounds a \(80 \times 120 \times 8\ \mathrm{nm}\) ferromagnetic film. The film is resolved with \(4\ \mathrm{nm}\) elements while the surrounding air region is coarsened, so the airbox supports the magnetostatic Poisson solve without paying four-nanometer resolution far from the magnet. The demagnetization linear system is solved with a conjugate-gradient method and an algebraic multigrid preconditioner.

Author the study

import fullmag as fm

nm = 1.0e-9
study = fm.study("first_fem_simulation")
study.engine("fem")
study.device("cpu", precision="double")
study.mode("strict")

study.universe(mode="manual", size=(160 * nm, 160 * nm, 24 * nm))
study.universe.mesh(maximum_element_size=40 * nm, maximum_element_growth_rate=1.7)

film = study.geometry(
    fm.Box(size=(80 * nm, 120 * nm, 8 * nm), name="film"),
    name="film",
)
film.Ms = 800.0e3
film.Aex = 13.0e-12
film.alpha = 0.1
film.m = fm.init.UniformMagnetization((1.0, 0.0, 0.0))
film.mesh(maximum_element_size=4 * nm, order=1)

study.demag(realization="poisson_robin")
study.fem_demag_solver(solver="CG", preconditioner="AMG", rtol=1.0e-10, max_iterations=500)
study.build_domain_mesh()

study.stages.add_relax(
    stage_id="relax",
    algorithm="projected_gradient_bb",
    max_steps=2000,
    tolT=5.0e-9,
).tableautosave(
    every_steps=10,
    quantities=["step", "mx", "my", "mz", "e_ex", "e_demag", "e_total", "max_torque_T"],
)

What each part does

  • study.engine("fem") selects the finite-element backend.

  • study.universe.mesh(...) sizes the airbox elements with a growth-rate bound so the magnet is resolved finely while air elements grow away from it.

  • film.mesh(maximum_element_size=4 * nm, order=1) overrides the local element size on the magnetic body.

  • study.demag(realization="poisson_robin") chooses the scalar-potential Poisson demagnetization formulation; the alternative public FEM strategy is the boundary-element method documented on the demagnetization pages.

  • study.fem_demag_solver(...) configures the linear solver for the Poisson system.

  • study.build_domain_mesh() realizes the domain mesh from the universe plus body before lowering.

  • study.stages.add_relax(algorithm="projected_gradient_bb", tolT=5.0e-9, ...) relaxes with the projected Barzilai-Borwein gradient method until the torque magnitude in tesla falls to the requested tolerance or the step budget is spent. This projected-gradient method does not need an LLG timestep, unlike the overdamped stage used on the FDM page.

Run headlessly

Save the block as first_fem_simulation.py. The FEM runtime is built and executed through the repository’s managed runtime recipes:

just ensure-managed-fem-runtime
just fem-managed-headless cpu first_fem_simulation.py

The managed runtime records the resolved backend, device, and precision in the result. To request the FEM GPU lane instead, pass gpu as the execution mode to the same recipe and verify the device identity in the produced provenance.

Reading the result

max_torque_T is the maximum torque magnitude reported in tesla and is the relaxation stop signal, while e_ex, e_demag and e_total are the exchange, demagnetization and total energies. Autosave tables are scalar time series; mesh and field snapshots are separate artifacts.

Limits of this example

Unstructured-mesh relaxation has stricter tolerance and meshing regimes than the small onboarding grid shown here. μMAG Standard Problem 4 and the analytical validation pages provide the qualification evidence for those regimes. FEM GPU execution requires a managed CUDA runtime and is not claimed by this snippet.

Control Room crosswalk

Use the authoring path stated in this guide, normally Model Explorer -> Objects followed by the relevant Geometry, Material, Physics, Mesh, or Stage panel. Any parameter shown in Python but not shown in that path is TODO: frontend support; do not describe it as configurable in the UI. See Control Room capability register.

Python/API crosswalk

The runnable Python example and exact argument contract are authoritative. If this guide is conceptual or does not contain a runnable example, it explicitly defers to the linked {doc}``/python-api/index page rather than duplicating an unverified signature.

Physics, limitations, and bibliography

Use the linked physics or numerical-methods page for governing equations and assumptions. This onboarding page does not add a new physical model. Bibliography: see the linked terminal API or physics page; no additional source is claimed here.

Source-code index

  • No new implementation symbol is introduced by this guide. The exact Python source symbol is owned by the linked terminal API page and the runnable example.