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Title: Computational methods for a phase-field model of grain growth kinetics
Keywords: Phase-Field Model, Grain Growth, Allen-Cahn Equation, Operator Splitting Method, Exact Solution, Active Parameter Tracking
Issue Date: 29-Dec-2006
Citation: BIPIN KUMAR (2006-12-29). Computational methods for a phase-field model of grain growth kinetics. ScholarBank@NUS Repository.
Abstract: An apriori understanding of micro structures and its linkage to material properties is possible through the use of workable models. In this thesis, we explore a variety of computational algorithms for solving partial differential equations that govern the kinetics of grain growth. To start with, we employ the emerging phase-field approach to model the micro structural evolutions. In the model we have to design the appropriate energy functional. Then, solve the Allen-Cahn equations or the Complex Ginzhburg Landau equations (CGLE).Following computational schemes are devised for the phase-field equations: (i) Solve the equations by Finite difference method with a simple explicit time marching scheme. (ii) Solve the Allen-Cahn equations using operator splitting method, where the equation is divided into a Poisson part and a cubic equation. (iii) A simple observation that only the interfaces have more than one active phase-field variables at every grid point was successfully exploited by devising AIA-PT approach.
Appears in Collections:Master's Theses (Open)

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