  We demonstrate a fast numerical method of theoretical studies of skyrmion
lattice or spiral order in magnetic materials with Dzyaloshinsky-Moriya
interaction. The method is based on the Fourier expansion of the magnetization
combined with a minimization of the free energy functional of the magnetic
material in Fourier space, yielding the optimal configuration of the system for
any given set of parameters. We employ a Lagrange multiplier technique in order
to satisfy micromagnetic constraints. We apply this method to a system that
exhibits, depending on the parameter choice, ferromagnetic, skyrmion lattice,
or spiral (helical) order. Known critical fields corresponding to the
helical-skyrmion as well as the skyrmion-ferromagnet phase transitions are
reproduced with high precision. Using this numerical method we predict new
types of excited (metastable) states of the skyrmion lattice, which may be
stabilized by coupling the skyrmion lattice with a superconducting vortex
lattice. The method can be readily adapted to other micromagnetic systems.
