Programming Phase-Field Modeling

This textbook provides a fast-track pathway to numerical implementation of phase-field modeling--a relatively new paradigm that has become the method of choice for modeling and simulation of microstructure evolution in materials. It serves as a cookbook for the phase-field method by presenting a collection of codes that act as foundations and templates for developing other models with more complexity. Programming Phase-Field Modeling uses the Matlab/Octave programming package, simpler and more compact than other high-level programming languages, providing ease of use to the widest audience. Particular attention is devoted to the computational efficiency and clarity during development of the codes, which allows the reader to easily make the connection between the mathematical formulism and the numerical implementation of phase-field models. The background materials provided in each case study also provide a forum for undergraduate level modeling-simulations courses as part of their curriculum. Emphasizes the numerical aspects of phase-field modeling; Explains both the underlying physics and formulism of phase-field modeling; Reinforces reader understanding with a collection of algorithms; Adopts a cross-disciplinary approach to PFM relevant to students of engineering, physics, biology, and other disciplines concerned with microstructure evolution and solutions to interfacial problems; Includes all necessary source code, downloadable from the publisher Front Matter....Pages i-xvi An Overview of the Phase-Field Method and Its Formalisms....Pages 1-7 Introduction to Numerical Solution of Partial Differential Equations....Pages 9-11 Preliminaries About the Codes....Pages 13-15 Solving Phase-Field Models with Finite Difference Algorithms....Pages 17-97 Solving Phase-Field Models with Fourier Spectral Methods....Pages 99-168 Solving Phase-Field Equations with Finite Elements....Pages 169-336 Phase-Field Crystal Modeling of Material Behavior....Pages 337-368 Concluding Remarks....Pages 369-369 Back Matter....Pages 371-400