2. Numerical methods: towards multiscale description

``It is difficult to make predictions, especially about the future''
Yogi Berra, baseball coach

In this chapter we present numerical methods for magnetic material modeling. Some of these methods can be considered in our days as standard for micromagnetic modeling. Special attention is paid to the methods which were developed by the author of the thesis (Sections 2.2.4, 2.3.6 and 2.3.7). Several of them were taken from the modeling in other branches of physics and firstly applied to magnetic properties, as for example, the A.Voter method for dynamics acceleration. Other methods, as for example, the Lagrangian multiplier technique was previously applied in magnetism to small nanoparticles only. The development of methods has been done in collaboration with Seagate Technology with the aim to find ways to predict correctly long-time thermal stability.