Nonlocal operator method for the Cahn-Hilliard phase field model

[1]  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.

[2]  S. Bankoff,et al.  Long-scale evolution of thin liquid films , 1997 .

[3]  Timon Rabczuk,et al.  Dual‐horizon peridynamics , 2015, 1506.05146.

[4]  Cheng Wang,et al.  A Second-Order Energy Stable BDF Numerical Scheme for the Cahn-Hilliard Equation , 2018 .

[5]  Xiaofeng Yang,et al.  Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method , 2017 .

[6]  Sergey Zelik,et al.  The Cahn-Hilliard Equation with Logarithmic Potentials , 2011 .

[7]  I. Pawlow,et al.  On a class of sixth order viscous Cahn-Hilliard type equations , 2012 .

[8]  Timon Rabczuk,et al.  Isogeometric analysis for phase-field models of geometric PDEs and high-order PDEs on stationary and evolving surfaces , 2019, Computer Methods in Applied Mechanics and Engineering.

[9]  Maya Neytcheva,et al.  Efficient numerical solution of discrete multi-component Cahn-Hilliard systems , 2014, Comput. Math. Appl..

[10]  Some properties of solutions for a sixth-order Cahn–Hilliard type equation with inertial term , 2018 .

[11]  P. Voorhees,et al.  Faceting of a growing crystal surface by surface diffusion. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Xiaoping Qian,et al.  Triangulation-based isogeometric analysis of the Cahn–Hilliard phase-field model , 2019 .

[13]  Seunggyu Lee,et al.  Basic Principles and Practical Applications of the Cahn–Hilliard Equation , 2016 .

[14]  Junseok Kim,et al.  A second-order accurate non-linear difference scheme for the N -component Cahn–Hilliard system , 2008 .

[15]  Timon Rabczuk,et al.  A staggered approach for the coupling of Cahn–Hilliard type diffusion and finite strain elasticity , 2016 .

[16]  Franck Boyer,et al.  Numerical schemes for a three component Cahn-Hilliard model , 2011 .

[17]  Charles M. Elliott,et al.  Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy , 1992 .

[18]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[19]  Olga Wodo,et al.  Computationally efficient solution to the Cahn-Hilliard equation: Adaptive implicit time schemes, mesh sensitivity analysis and the 3D isoperimetric problem , 2011, J. Comput. Phys..

[20]  Shiwei Zhou,et al.  Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition , 2006 .

[21]  Amanda E. Diegel,et al.  Stability and Convergence of a Second Order Mixed Finite Element Method for the Cahn-Hilliard Equation , 2014, 1411.5248.

[22]  Alain Miranville,et al.  On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions , 2009 .

[23]  T. Rabczuk,et al.  A nonlocal operator method for solving PDEs , 2018 .

[24]  Zhi-zhong Sun,et al.  A second-order accurate linearized difference scheme for the two-dimensional Cahn-Hilliard equation , 1995 .

[25]  Markus Kästner,et al.  Isogeometric analysis of the Cahn-Hilliard equation - a convergence study , 2016, J. Comput. Phys..

[26]  Jia Zhao,et al.  Efficient linear schemes for the nonlocal Cahn-Hilliard equation of phase field models , 2019, Comput. Phys. Commun..

[27]  Suchuan Dong,et al.  A family of second-order energy-stable schemes for Cahn-Hilliard type equations , 2019, J. Comput. Phys..

[28]  John E. Hilliard,et al.  Free Energy of a Nonuniform System. III. Nucleation in a Two‐Component Incompressible Fluid , 1959 .

[29]  Daisuke Furihata,et al.  A stable and conservative finite difference scheme for the Cahn-Hilliard equation , 2001, Numerische Mathematik.

[30]  T. Rabczuk,et al.  A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem , 2019, Computers, Materials & Continua.

[31]  Xiao Li,et al.  Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation , 2018, J. Comput. Phys..

[32]  Mehdi Dehghan,et al.  Simulation of the phase field Cahn–Hilliard and tumor growth models via a numerical scheme: Element-free Galerkin method , 2019, Computer Methods in Applied Mechanics and Engineering.

[33]  Krishna Garikipati,et al.  A discontinuous Galerkin method for the Cahn-Hilliard equation , 2006, J. Comput. Phys..

[34]  Alain Miranville,et al.  Sixth‐order Cahn–Hilliard systems with dynamic boundary conditions , 2015 .

[35]  Andreas Prohl,et al.  Analysis of a fully discrete finite element method for the phase field model and approximation of its sharp interface limits , 2003, Math. Comput..

[36]  G. Hulbert,et al.  A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method , 2000 .

[37]  T. Hughes,et al.  Isogeometric analysis of the Cahn–Hilliard phase-field model , 2008 .

[38]  T. Rabczuk,et al.  On the use of local maximum entropy approximants for Cahn–Hilliard phase-field models in 2D domains and on surfaces , 2019, Computer Methods in Applied Mechanics and Engineering.

[39]  H. Gómez,et al.  Computational Phase‐Field Modeling , 2017 .

[40]  T. Rabczuk,et al.  Nonlocal operator method with numerical integration for gradient solid , 2020 .

[41]  R. Lehoucq,et al.  Peridynamic Theory of Solid Mechanics , 2010 .

[42]  Yinnian He,et al.  On large time-stepping methods for the Cahn--Hilliard equation , 2007 .

[43]  Timon Rabczuk,et al.  Dual-horizon peridynamics: A stable solution to varying horizons , 2017, 1703.05910.

[44]  L. Segel,et al.  Nonlinear aspects of the Cahn-Hilliard equation , 1984 .

[45]  Global attractor of the Cahn–Hilliard equation in Hk spaces , 2009 .

[46]  R. Hoppe,et al.  High order approximations in space and time of a sixth order Cahn–Hilliard equation , 2015 .

[47]  I. Klapper,et al.  Role of cohesion in the material description of biofilms. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Irena Pawłow,et al.  A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures , 2011 .

[49]  Jie Shen,et al.  Coarsening kinetics from a variable-mobility Cahn-Hilliard equation: application of a semi-implicit Fourier spectral method. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[50]  Desheng Li,et al.  Global Attractor for the Cahn–Hilliard System with Fast Growing Nonlinearity , 1998 .

[51]  Qiang Du,et al.  Computational studies of coarsening rates for the Cahn-Hilliard equation with phase-dependent diffusion mobility , 2016, J. Comput. Phys..

[52]  S. Silling.  Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces , 2000 .

[53]  Timon Rabczuk,et al.  Strong multipatch C1-coupling for isogeometric analysis on 2D and 3D domains , 2019 .

[54]  Alain Miranville,et al.  Sixth-order Cahn–Hilliard equations with singular nonlinear terms , 2015 .

[55]  Charles M. Elliott,et al.  A second order splitting method for the Cahn-Hilliard equation , 1989 .

[56]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[57]  Piotr Rybka,et al.  Global Weak Solutions to a Sixth Order Cahn-Hilliard Type Equation , 2012, SIAM J. Math. Anal..