A magnetic strip with rectangular cross section and infinite extension
in the third, easy direction is used as a vehicle to explore numerica
l micromagnetic algorithms. The manifold of (meta-)stable domain wall
solutions is calculated as a function of the thickness of the strip an
d of the relative strength of the magnetic anisotropy. With improved a
lgorithms it became possible to calculate the complete phase diagram o
f domain walls including all first- and second-order phase transitions
between the walls. We took care to make sure that the obtained result
s were independent of the chosen discretization.