Micromagnetic output

Matlab solution struct

The MEX-file returns the solution struct, and optionally the grid information as a second output:

solution = struct();
[solution, GridInfo] = problem.MagTenseLandauLifshitzSolver_mex( struct(problem), solution );

The solution struct contains

Field	Size	Description
`t`	`(nt)`	The times at which the solution was stored.
`M`	`(nt, ntot, nt_Hext, 3)`	The reduced magnetization. The third dimension is the applied-field index, which is 1 for the dynamic solver and the number of field steps for the explicit solver.
`pts`	`(ntot, 3)`	Centre coordinates of the cells, in the same order as the other per-cell arrays.
`H_exc`	`(nt, ntot, nt_Hext, 3)`	Exchange field in A/m. Only filled when `ReturnHall` is set.
`H_ext`	`(nt, ntot, nt_Hext, 3)`	Applied field in A/m. Only filled when `ReturnHall` is set.
`H_dem`	`(nt, ntot, nt_Hext, 3)`	Demagnetization field in A/m. Only filled when `ReturnHall` is set.
`H_ani`	`(nt, ntot, nt_Hext, 3)`	Anisotropy field in A/m. Only filled when `ReturnHall` is set.
`n_Hext_acc`	scalar	Number of accepted applied-field steps. Only meaningful for Adaptive hysteresis.

ReturnHall (Python usereturnhall) is off by default. Turning it on costs four additional (nt, ntot, nt_Hext, 3) arrays, which for a large problem is substantial, so leave it off unless the individual field terms are actually needed.

Note

The four H_* arrays are not the fields the integrator ran on. They are recomputed from the stored solution at the nt output times after the integration has finished, because the integrator’s last right-hand-side evaluation is at an internal step rather than at the requested output state.

The optional GridInfo output carries the analysed mesh - face normals, face areas, cell volumes, cell and face centres, the interpolation index arrays, and the assembled exchange matrix in COO form (ExchMat_r, ExchMat_c, ExchMat_v, ExchMat_nr, ExchMat_nc). It is what cartesianUnstructuredMeshPlot plots.

The Matlab helper computeMagneticMomentGeneralMesh converts a solution into the volume-averaged magnetic moment, and computeMagneticEnergy evaluates the energy terms.

Python result list

run_simulation and run_hysteresis return a list:

Index	Name	Description
0	`t_out`	Output times.
1	`M_out`	Reduced magnetization, `(nt, ntot, nt_h_ext, 3)`.
2	`pts`	Cell centres, `(ntot, 3)`.
3	`H_exc`	Exchange field, same shape as `M_out`.
4	`H_ext`	Applied field.
5	`H_dem`	Demagnetization field.
6	`H_ani`	Anisotropy field.
7	`Exch_mat_ntot`	Number of non-zero entries in the exchange matrix.
8, 9, 10	`Exch_mat_r`, `Exch_mat_c`, `Exch_mat_v`	The exchange matrix in COO form, already sliced to `Exch_mat_ntot` entries.
11, 12	`Exch_mat_nr`, `Exch_mat_nc`	Number of rows and columns of the exchange matrix.

run_hysteresis_adaptive returns the same twelve entries followed by one extra element, the number of accepted field steps, and the arrays with an applied-field dimension are already sliced to that number.

A typical unpacking is

t_out, M_out = problem.run_simulation(
    t_end=1e-9, nt=200, fct_h_ext=h_ext_fct, nt_h_ext=2000
)[:2]

# Volume-averaged reduced magnetization as a function of time
M_avg = M_out[:, :, 0, :].mean(axis=1)

The helper magtense.utils.plot_M_thin_film plots the magnetization of a thin-film problem, and magtense.utils.create_plot handles the magnetostatic tile plots.

Dry runs

Setting dummy_run = 1 builds the problem, the mesh, the exchange operator and the demagnetization tensor, but skips the time integration. This is useful for timing the setup phase, for checking the memory footprint of a large problem, and for extracting the exchange matrix or the demagnetization tensor without paying for a solve. The returned magnetization arrays are zeroed in that case.