Numerical approximation of multi-phase Penrose-Fife systems

Please always quote using this URN:urn:nbn:de:0296-matheon-13722
  • 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.

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Author:Carsten Gräser, Max Kahnt, Ralf Kornhuber
Referee:Alexander Mielke
Date of first Publication:2016/02/14
Institute:Freie Universität Berlin
Project:C Energy and Materials (Production) / C-SE12 Fast solvers for heterogeneous saddle point problems
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K86 Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities [See also 35R35, 49J40]
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Axx Thermodynamics and heat transfer / 80A22 Stefan problems, phase changes, etc. [See also 74Nxx]
Preprint Number:1103
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