Micromagnetic examples and validation

The examples below ship with MagTense and are the recommended starting point. The Matlab and the Python versions of each test are written to mirror each other, so the same physics is checked from both interfaces. The standard problems take the same options in both languages, with the same defaults:

Matlab option	Python argument	Meaning
use_CUDA	cuda	Use CUDA for the calculations (default true)
use_CVODE	cvode	Use CVODE for the time integration (default false)
ShowTheResult	plotting, figpath	Show the result, or in Python save it to figpath
use_minimizer	use_minimizer	Relax with the Energy minimizer instead of the time integration
use_adaptive	use_adaptive	Problem 2: adaptive field stepping instead of the fixed table
mesh_type	mesh_type	'uniform', 'unstructuredPrisms' or, in problem 3, 'tetrahedron'
mesh_file	mesh_file	The text file with the unstructured Cartesian mesh
mesh_res_param	mesh_res_param	Problem 3: tetrahedra per edge length
use_AvgN	use_avgn	Problem 4: the averaged prism tensor for the demag field
cart_dir, TwoDsim, TwoDsize	cart_dir, two_d_sim, two_d_size	Problem 6: the axis of the sample and the 2D strip

The unstructured Cartesian meshes are text files, one prism per row with its centre and its side lengths, and both languages read the same files from documentation/examples_mumag_validation.

muMag standard problems

Problem	Matlab	Python
Standard problem 2	Standard_problem_2.m	std_problem_2.py
Standard problem 3	Standard_problem_3.m	std_problem_3.py
Standard problem 4	Standard_problem_4.m	std_problem_4.py
Standard problem 6	Standard_problem_6.m	std_problem_6.py

What each of these exercises do:

• Standard problem 2 - the quasi-static hysteresis loop of a rectangular bar, computed with the explicit solver and swept over the width of the bar in units of the exchange length. This is the example to copy for a hysteresis calculation.

• Standard problem 3 - the flower/vortex energy crossover of a cube as a function of its size in units of the exchange length. The mesh_type option runs it on a uniform grid ('uniform', the default), on an unstructured Cartesian mesh read from a text file ('unstructuredPrisms') or on a tetrahedral mesh ('tetrahedron'), so it is also the example to copy for either kind of unstructured mesh. The tetrahedral branch is the shortest illustration of a tetrahedral problem: it meshes the cube with CreateTetraMesh (Matlab, PDE Toolbox) or magtense.utils.create_tetra_mesh (Python), hands the mesh over with a single call to setMicroMagGridTetrahedron or the grid_nod and grid_ele arguments of MicromagProblem, and lets MagTense do the rest.

• Standard problem 4 - the switching dynamics of a thin film under a reversed field, compared against the published mean solutions. It is a two-stage calculation: first an s-state is relaxed, then that state is used as the initial condition for the dynamic run. With mesh_type = 'unstructuredPrisms' it runs on an unstructured Cartesian mesh, and the exchange operator MagTense builds in the first stage is handed to the second, so the mesh is analysed only once.

• Standard problem 6 - domain-wall pinning at a phase boundary, which is the test of the spatially varying \(A_0\), \(K_0\) and \(M_s\) and of the modified exchange stencil. cart_dir orients the sample along x, y or z, which must not change the result, and mesh_type runs the same chain of cells as unstructured prisms.

Standard problems 2, 3 and 6 take a use_minimizer switch in both languages (options.use_minimizer in Matlab, the use_minimizer argument in Python). With it set, the equilibrium at each field is found by the Energy minimizer instead of the Landau-Lifshitz time integration, and the scripts print the number of effective-field evaluations spent either way, which is the cost to compare. Problem 3 reads its energies from the E output of the solver in both cases. In problem 6 the switch replaces the time ramp of the applied field by the same field values visited as constant fields, so the depinning field it reports is the static one, which is what the analytical values of the reference paper are; the ramp gives a rate-dependent one. Problem 2 additionally takes use_adaptive, which replaces the fixed table of 40 fields by the Adaptive hysteresis stepping, refining the field step to 0.0005 T across the coercive field.

The Python script minimizer_vs_llg.py runs the single-grain hysteresis loop and standard problem 3 with both the Landau-Lifshitz relaxation and the Energy minimizer, and prints the switching fields, the energies and the number of field evaluations each method needed.

Feature tests

These live in matlab/examples/Micromagnetism/MagTense_tests and in python/examples/micromagnetism/MagTense_tests, and each of them compares against an analytical result rather than against a reference simulation.

Test	What it checks
macrogeometry_PBC_test	Periodic boundaries through the macrogeometry method. Two cubes are repeated along one axis and the critical spacing at which the effective anisotropy vanishes is compared with the analytical prediction. The whole setup is rotated so that the axis of periodicity becomes x, y and z in turn, which validates all three directions. Two further spacings act as controls. See Macrogeometry.
periodic_exchange_test	Periodic exchange coupling, on a uniform grid, on an unstructured mesh and on a grain mesh. Exchange-coupled moments across the periodic boundary must end up identical. See Periodic exchange boundaries.
shape_correction_test	Both the shape anisotropy (shape-dependent demagnetisation) and the magnetocrystalline anisotropy give uniaxial anisotropy energies. The shape correction field rewrites the shape anisotropy so it precisely cancels the magnetocrystalline contribution. Consequently, in a successful test the magnetization stays put. See Sample shape correction.
temperature_test	Thermal fluctuations against the analytical angular diffusion of non-interacting moments. See Thermal fluctuations.

Other examples

• CoFe_nanopillar.m - a nanopillar on an externally generated unstructured prism mesh.

• python/examples/micromagnetism/adaptive_hysteresis/adaptive_hysteresis_minimal.py - the smallest possible adaptive hysteresis run, with no plotting or post-processing. adaptive_hysteresis_demo.py in the same folder adds a comparison against a fixed-step loop.

Running the test suites

Both interfaces ship a runner that executes the examples, turns each of them into a set of pass/fail checks and prints a summary table. The two run the same tests - the magnetostatic field of every tile type against FEM, and the micromagnetic tests and standard problems - under the same names, with the same checks and limits.

In Matlab, from matlab/util:

testMagTenseFunctions

The tests to run can be restricted with the environment variables MAGTENSE_TESTS and MAGTENSE_SKIP, and the CUDA and CVODE variants are selected with MAGTENSE_TEST_CUDA and MAGTENSE_TEST_CVODE. MAGTENSE_INCLUDE_SLOW=1 adds standard problem 3 by time integration, which takes considerably longer than the rest of the suite.

In Python, from python/util:

python testMagTenseFunctions.py

python testMagTenseFunctions.py --list

python testMagTenseFunctions.py --tests temperature_test,std_problem_4

python testMagTenseFunctions.py --skip std_problem_6

--include-slow adds standard problem 3 by time integration. Each example lives in its own directory and is run from there, so the figures and timer logs it produces land beside it, and the overview figure of the suite is written to python/util/results, as the Matlab suite writes to matlab/util/results. There are in addition pytest suites in python/examples/magnetostatics and python/examples/micromagnetism/MagTense_tests.