Numerical Approximation of Multi-Phase Penrose–Fife Systems

Abstract

Abstract. We consider a non-isothermal multi-phase field model. We subsequently discretize implicitly in time and with linear finite elements. The arising algebraic problem is formulated in two variables where one is the multi-phase field, and the other contains the inverse temperature field. We solve this saddle point problem numerically by a non-smooth Schur-Newton approach using truncated non-smooth Newton multigrid methods. An application in grain growth as occurring in liquid phase crystallization of silicon is considered.

Chinese–German Computational and Applied Mathematics

“…In particular, the results clarify previous speculations on the behavior of the constant. Gräser, Kahnt and Kornhuber consider a multi-phase extension of the classical Penrose-Fife system derived from a general entropy functional and an associated thin-film approximation variant in [11]. The entropy functional combines a Ginzburg-Landau energy with the thermodynamic entropy and the unknowns of the resulting problem are the phase field and the inverse temperature.…”