Numerical approximation of multi-phase Penrose-Fife systems

TL;DR

This paper develops a numerical method for simulating multi-phase Penrose-Fife systems, combining implicit time discretization, finite element spatial discretization, and a non-smooth Schur-Newton solver, applied to grain growth in silicon crystallization.

Contribution

It introduces a novel numerical approach for multi-phase Penrose-Fife models using a saddle point formulation and non-smooth Newton methods, enabling efficient simulations.

Findings

Effective numerical scheme for multi-phase systems

Successful application to silicon grain growth

Demonstrates stability and accuracy of the method

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.