Exploiting symmetries in skyrmionic micromagnetic simulations: Cylindrical and radial meshes

Micromagnetic simulations are an essential tool in the theoretical study of magnetic skyrmions. When confined into nanometric samples, these structures can serve as bits of information among other possible applications. Accurate simulations are one of the major sources of theoretical results. In the case of confined skyrmions, it is known that the boundaries play a critical role in their stabilization. However, most of the micromagnetic simulations are done using a finite-difference method with quadrilateral meshes, that do not exactly fit the boundaries. The use of this mesh can introduce a significant numerical error that can completely change the results of the simulations. We present here two different finite-difference meshes to study skyrmions in confined disks, taking advantage of the symmetry of that geometry. A two-dimensional cylindrical mesh for non-symmetric scenarios but geometrically symmetric (boundary conditions) that reduces the propagation of the numerical error, and the particular case of a one dimensional mesh for axisymmetric scenarios where the computation time is hugely reduced.