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Volume 6, Issue 3
Geometric Evolution Laws for Thin Crystalline Films: Modeling and Numerics

Bo Li, John Lowengrub, Andreas Rätz & Axel Voigt

Commun. Comput. Phys., 6 (2009), pp. 433-482.

Published online: 2009-06

[An open-access article; the PDF is free to any online user.]

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  • Abstract

Geometrical evolution laws are widely used in continuum modeling of surface and interface motion in materials science. In this article, we first give a brief review of various kinds of geometrical evolution laws and their variational derivations, with an emphasis on strong anisotropy. We then survey some of the finite element based numerical methods for simulating the motion of interfaces focusing on the field of thin film growth. We discuss the finite element method applied to front-tracking, phase-field and level-set methods. We describe various applications of these geometrical evolution laws to materials science problems, and in particular, the growth and morphologies of thin crystalline films.

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@Article{CiCP-6-433, author = {Bo Li, John Lowengrub, Andreas Rätz and Axel Voigt}, title = {Geometric Evolution Laws for Thin Crystalline Films: Modeling and Numerics}, journal = {Communications in Computational Physics}, year = {2009}, volume = {6}, number = {3}, pages = {433--482}, abstract = {

Geometrical evolution laws are widely used in continuum modeling of surface and interface motion in materials science. In this article, we first give a brief review of various kinds of geometrical evolution laws and their variational derivations, with an emphasis on strong anisotropy. We then survey some of the finite element based numerical methods for simulating the motion of interfaces focusing on the field of thin film growth. We discuss the finite element method applied to front-tracking, phase-field and level-set methods. We describe various applications of these geometrical evolution laws to materials science problems, and in particular, the growth and morphologies of thin crystalline films.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7688.html} }
TY - JOUR T1 - Geometric Evolution Laws for Thin Crystalline Films: Modeling and Numerics AU - Bo Li, John Lowengrub, Andreas Rätz & Axel Voigt JO - Communications in Computational Physics VL - 3 SP - 433 EP - 482 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7688.html KW - AB -

Geometrical evolution laws are widely used in continuum modeling of surface and interface motion in materials science. In this article, we first give a brief review of various kinds of geometrical evolution laws and their variational derivations, with an emphasis on strong anisotropy. We then survey some of the finite element based numerical methods for simulating the motion of interfaces focusing on the field of thin film growth. We discuss the finite element method applied to front-tracking, phase-field and level-set methods. We describe various applications of these geometrical evolution laws to materials science problems, and in particular, the growth and morphologies of thin crystalline films.

Bo Li, John Lowengrub, Andreas Rätz and Axel Voigt. (2009). Geometric Evolution Laws for Thin Crystalline Films: Modeling and Numerics. Communications in Computational Physics. 6 (3). 433-482. doi:
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