Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method
暂无分享,去创建一个
[1] Conyers Herring,et al. Some Theorems on the Free Energies of Crystal Surfaces , 1951 .
[2] Axel Voigt,et al. A numerical scheme for regularized anisotropic curve shortening flow , 2006, Appl. Math. Lett..
[3] Q. Du,et al. A phase field approach in the numerical study of the elastic bending energy for vesicle membranes , 2004 .
[4] Harald Garcke,et al. Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid , 2005, Math. Comput..
[5] Martin Burger,et al. A level set approach to anisotropic flows with curvature regularization , 2007, J. Comput. Phys..
[6] John Lowengrub,et al. Microstructural Evolution in Inhomogeneous Elastic Media , 1997 .
[7] John W. Barrett,et al. Finite Element Approximation of a Phase Field Model for Void Electromigration , 2004, SIAM J. Numer. Anal..
[8] Axel Voigt,et al. Facet formation and coarsening modeled by a geometric evolution law for epitaxial growth , 2005 .
[9] Peter W. Voorhees,et al. Ordered growth of nanocrystals via a morphological instability , 2002 .
[10] J. Lowengrub,et al. Conservative multigrid methods for Cahn-Hilliard fluids , 2004 .
[11] Martin Burger,et al. Numerical simulation of anisotropic surface diffusion with curvature-dependent energy , 2005 .
[12] J. Lowengrub,et al. Quasi–incompressible Cahn–Hilliard fluids and topological transitions , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[13] Héctor D. Ceniceros,et al. Computation of multiphase systems with phase field models , 2002 .
[14] Isidore Rigoutsos,et al. An algorithm for point clustering and grid generation , 1991, IEEE Trans. Syst. Man Cybern..
[15] D. J. Eyre. Unconditionally Gradient Stable Time Marching the Cahn-Hilliard Equation , 1998 .
[16] J. E. Hilliard,et al. Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .
[17] D. Brandt,et al. Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .
[18] W. K. Burton,et al. The growth of crystals and the equilibrium structure of their surfaces , 1951, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.
[19] M. Berger,et al. Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .
[20] P. Colella,et al. Local adaptive mesh refinement for shock hydrodynamics , 1989 .
[21] P. Voorhees,et al. Faceting of a growing crystal surface by surface diffusion. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.
[22] John W. Cahn,et al. Diffuse interfaces with sharp corners and facets: phase field models with strongly anisotropic surfaces , 1998 .
[23] Richard Welford,et al. A multigrid finite element solver for the Cahn-Hilliard equation , 2006, J. Comput. Phys..
[24] W. W. Mullins,et al. Proof that the Two‐Dimensional Shape of Minimum Surface Free Energy is Convex , 1962 .
[25] E. Wagner. International Series of Numerical Mathematics , 1963 .
[26] Morton E. Gurtin,et al. A regularized equation for anisotropic motion-by-curvature , 1992 .
[27] Daisuke Furihata,et al. A stable and conservative finite difference scheme for the Cahn-Hilliard equation , 2001, Numerische Mathematik.
[28] Shenyang Y. Hu,et al. A phase-field model for evolving microstructures with strong elastic inhomogeneity , 2001 .
[29] Charles M. Elliott,et al. The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature , 1996, European Journal of Applied Mathematics.
[30] D. M. Anderson,et al. DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS , 1997 .
[31] Lisa L. Lowe,et al. Multigrid elliptic equation solver with adaptive mesh refinement , 2005 .
[32] Daniel F. Martin,et al. A Cell-Centered Adaptive Projection Method for the Incompressible Euler Equations , 2000 .
[33] Qiang Du,et al. Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions , 2006, J. Comput. Phys..
[34] Axel Voigt,et al. A discrete scheme for regularized anisotropic surface diffusion: a 6th order geometric evolution equation , 2005 .
[35] Alexander A. Nepomnyashchy,et al. Model for faceting in a kinetically controlled crystal growth , 1999 .
[36] Stephen J. Watson,et al. Crystal Growth, Coarsening and the Convective Cahn—Hilliard Equation , 2003 .
[37] Long-Qing Chen. Phase-Field Models for Microstructure Evolution , 2002 .
[38] Alexander A. Nepomnyashchy,et al. A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth , 1998 .
[39] Peter W Voorhees,et al. A phase-field model for highly anisotropic interfacial energy , 2001 .
[40] Wei Lu,et al. Ordering of nanovoids in an anisotropic solid driven by surface misfit , 2005 .
[41] M. Miksis,et al. Evolution of material voids for highly anisotropic surface energy , 2004 .
[42] A. A. Wheeler,et al. Phase-field theory of edges in an anisotropic crystal , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[43] Axel Voigt,et al. Surface evolution of elastically stressed films under deposition by a diffuse interface model , 2006, J. Comput. Phys..
[44] R. Kobayashi. Modeling and numerical simulations of dendritic crystal growth , 1993 .
[45] H. Frieboes,et al. Computer simulation of glioma growth and morphology , 2007, NeuroImage.
[46] Qiang Du,et al. A phase field formulation of the Willmore problem , 2005 .
[47] D. Moldovan,et al. Interfacial coarsening dynamics in epitaxial growth with slope selection , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[48] R. Howie,et al. Crystal growth , 1982, Nature.
[49] Brian J Spencer,et al. Asymptotic solutions for the equilibrium crystal shape with small corner energy regularization. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.
[50] Steven M. Wise,et al. Quantum dot formation on a strain-patterned epitaxial thin film , 2005 .
[51] Morton E. Gurtin,et al. Interface Evolution in Three Dimensions¶with Curvature-Dependent Energy¶and Surface Diffusion:¶Interface-Controlled Evolution, Phase Transitions, Epitaxial Growth of Elastic Films , 2002 .
[52] Martin Siegert,et al. COARSENING DYNAMICS OF CRYSTALLINE THIN FILMS , 1998 .
[53] Scott A Norris,et al. Scaling theory and morphometrics for a coarsening multiscale surface, via a principle of maximal dissipation. , 2006, Physical review letters.
[54] Harald Garcke,et al. The Cahn-Hilliard equation with elasticity-finite element approximation and qualitative studies , 2001 .
[55] A. A. Wheeler. Cahn–Hoffman ξ-Vector and Its Relation to Diffuse Interface Models of Phase Transitions , 1999 .
[56] Robert F. Sekerka,et al. Analytical criteria for missing orientations on three-dimensional equilibrium shapes , 2005 .
[57] Harald Garcke,et al. Numerical approximation of the Cahn-Larché equation , 2005, Numerische Mathematik.
[58] Yoshikazu Giga,et al. Equations with Singular Diffusivity , 1998 .
[59] Felix Otto,et al. Coarsening dynamics of the convective Cahn-Hilliard equation , 2003 .
[60] Jeffrey W. Bullard,et al. Computational and mathematical models of microstructural evolution , 1998 .
[61] E. Favvas,et al. What is spinodal decomposition , 2008 .
[62] F. Campelo,et al. Dynamic model and stationary shapes of fluid vesicles , 2006, The European physical journal. E, Soft matter.