期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 197, 期 49-50, 页码 4333-4352出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2008.05.003
关键词
Phase-field; Cahn-Hilliard; Isogeometric analysis; NURBS; Steady state solutions; Isoperimetric problem
资金
- Ministerio de Educacion y Ciencia
- Xunta de Galicia [PGIDIT05PXIC118002PN, PGDIT06TAM11801PR]
- Ministerio de Educacion y Ciencia [DPI2004-05156, DPI2006-15275, DPI2007-61214]
- FEDER
- Universidad de A Coruna and Fundacion de la Ingenieria Civil de Galicia
- Oden ICES Postdoctoral Fellowship
- Institute for Computational Engineering and Sciences
- Office of Naval Research [N00014-03-0263]
- MURI [18412450-35520-B]
The Cahn-Hilliard equation involves fourth-order spatial derivatives. Finite element solutions are not common because primal variational formulations of fourth-order operators are only well defined and integrable if the finite element basis functions are piecewise smooth and globally C-1-continuous. There are a very limited number of two-dimensional finite elements possessing C-1-continuity applicable to complex geometries but none in three-dimensions. We propose isogeometric analysis as a technology that possesses a unique combination of attributes for complex problems involving higher-order differential operators, namely, higher-order accuracy, robustness, two- and three-dimensional geometric flexibility, compact support, and, most importantly, the possibility of C-1 and higher-order continuity. A NURBS-based variational formulation for the Cahn-Hilliard equation was tested on two- and three-dimensional problems. We present steady state solutions in two-dimensions and, for the first time, in three-dimensions. To achieve these results an adaptive time-stepping method is introduced. We also present a technique for desensitizing calculations to dependence on mesh refinement. This enables the calculation of topologically correct solutions on coarse meshes, opening the way to practical engineering applications of phase-field methodology. (c) 2008 Elsevier B.V. All rights reserved.
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