THE HYSTERETIC EVENT IN THE COMPUTATION OF MAGNETIZATION

Simulations of magnetic and magnetostrictive behavior based on microma gnetic theory exhibit hysteresis. These systems have a highly nonlinea r character involving both short range anisotropy and elastic fields a nd dispersive demagnetization fields. Hysteresis occurs even in the ab sence of an imposed dynamical mechanism, for example, a Landau-Lifshit z-Gilbert dissipative equation for the magnetic moment, and is symptom atic of the way the system navigates a path through local minima of it s energy space. It is not sensitive to the particular method: We imple ment continuation based on the conjugate gradient method, although the same results were obtained by, for example, a Newton's method. The ph enomenon is robust: Computational experiments confirm that the shape o f the loop is invariant over several decades of mesh refinement. Our e xperience has led us to hold that optimization procedures have the pro pensity to become marooned at local extrema when applied to nonconvex situations and that this presents a fundamental challenge to analysis. Understanding and controlling such phenomena present the opportunity to develop predictive tools and diagnostics. For example, since the en ergy picture is mesh-independent, computing on a fairly coarse grid su ffices to establish its character.