Multigrid hysteretic heat diffusion

Abstract

In this paper a transient non-linear heat diffusion problem is studied. Considering hysteretic type temperature-dependence of thermal diffusion, the numerical solution is very resource- and time-consuming. Utilizing the advantages of the multigrid technique a coarse level iterating algorithm is introduced. Applying a hierarchical algorithm the solution time could be reduced. The proposed method has been verified by comparing to other numerical schemes. The thermal heating-cooling asymmetry resulted by the hysteresis and the memory character of diffusivity are proved by numerical simulations.