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Volumn 33, Issue 4, 2009, Pages 522-528

A numerical method based on the boundary integral equation and dual reciprocity methods for one-dimensional Cahn-Hilliard equation

Author keywords

Boundary integral equation; Cahn Hilliard equation; Dual reciprocity method; Energy dissipation; Mass conservation

Indexed keywords

BOUNDARY INTEGRAL EQUATIONS; CONTROL NONLINEARITIES; CONTROL THEORY; ELECTRON ENERGY LOSS SPECTROSCOPY; ENERGY DISSIPATION; ENERGY DISSIPATORS; INTEGRAL EQUATIONS; NUMBER THEORY; NUMERICAL METHODS; ULTRASONIC MEASUREMENT;

EID: 59649101812     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2008.08.008     Document Type: Article
Times cited : (36)

References (61)
  • 1
    • 43449102981 scopus 로고
    • On spinodal decomposition
    • Cahn J.W. On spinodal decomposition. Acta Metall 9 (1961) 795-801
    • (1961) Acta Metall , vol.9 , pp. 795-801
    • Cahn, J.W.1
  • 2
    • 33746012315 scopus 로고
    • Free energy of a nonuniform system I, interfacial free energy
    • Cahn J.W., and Hilliard J.E. Free energy of a nonuniform system I, interfacial free energy. J Chem Phys 28 2 (1958) 258-267
    • (1958) J Chem Phys , vol.28 , Issue.2 , pp. 258-267
    • Cahn, J.W.1    Hilliard, J.E.2
  • 3
    • 0001158204 scopus 로고    scopus 로고
    • Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance
    • Gurtin M. Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance. Physica D 92 (1996) 178-192
    • (1996) Physica D , vol.92 , pp. 178-192
    • Gurtin, M.1
  • 5
    • 0027554074 scopus 로고
    • Interdiffusion in bilinear polymer mixtures
    • Wang S.Q., and Shi Q. Interdiffusion in bilinear polymer mixtures. Macromolecules 26 (1993) 1091-1096
    • (1993) Macromolecules , vol.26 , pp. 1091-1096
    • Wang, S.Q.1    Shi, Q.2
  • 6
    • 0029252992 scopus 로고
    • A model for interdiffusion at interfaces of polymers with dissimilar physical properties
    • Jabbari E., and Peppas N.A. A model for interdiffusion at interfaces of polymers with dissimilar physical properties. Polymer 36 (1995) 575-586
    • (1995) Polymer , vol.36 , pp. 575-586
    • Jabbari, E.1    Peppas, N.A.2
  • 7
    • 0001302262 scopus 로고
    • Phenomenological theory for the formation of interfaces via the interdiffusion of layem
    • Puri S., and Binder K. Phenomenological theory for the formation of interfaces via the interdiffusion of layem. Phys Rev B 44 (1991) 9735-9738
    • (1991) Phys Rev B , vol.44 , pp. 9735-9738
    • Puri, S.1    Binder, K.2
  • 9
    • 21144473934 scopus 로고
    • Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy
    • Copetti M.I.M., and Elliott C.M. Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy. Numer Math 63 (1992) 39-65
    • (1992) Numer Math , vol.63 , pp. 39-65
    • Copetti, M.I.M.1    Elliott, C.M.2
  • 10
    • 21844484383 scopus 로고
    • An error bound for the finite element approximation of the Cahn-Hilliard equation with logarithmic free energy
    • Barrett J.W., and Blowery J.F. An error bound for the finite element approximation of the Cahn-Hilliard equation with logarithmic free energy. Numer Math 72 (1995) 1-20
    • (1995) Numer Math , vol.72 , pp. 1-20
    • Barrett, J.W.1    Blowery, J.F.2
  • 12
    • 0004794523 scopus 로고
    • On the existence of nonnegative continuous solutions of the Cahn-Hilliard equation
    • Yin J. On the existence of nonnegative continuous solutions of the Cahn-Hilliard equation. J Diff Eqs 97 (1992) 319-327
    • (1992) J Diff Eqs , vol.97 , pp. 319-327
    • Yin, J.1
  • 13
    • 44949275928 scopus 로고
    • Slow motion for the Cahn-Hilliard equation in one space dimension
    • Alikakos N., Bates P.W., and Fusco G. Slow motion for the Cahn-Hilliard equation in one space dimension. J Diff Eqs 90 (1991) 81-135
    • (1991) J Diff Eqs , vol.90 , pp. 81-135
    • Alikakos, N.1    Bates, P.W.2    Fusco, G.3
  • 14
    • 34547595689 scopus 로고    scopus 로고
    • Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy
    • Abels H., and Wilke M. Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy. Nonlinear Anal 67 (2007) 3176-3193
    • (2007) Nonlinear Anal , vol.67 , pp. 3176-3193
    • Abels, H.1    Wilke, M.2
  • 15
    • 0000358405 scopus 로고
    • Structured phase transitions on a finite interval
    • Carr J., Gurtin M.E., and Slemrod M. Structured phase transitions on a finite interval. Arch Rat Mech Anal 86 (1984) 317-351
    • (1984) Arch Rat Mech Anal , vol.86 , pp. 317-351
    • Carr, J.1    Gurtin, M.E.2    Slemrod, M.3
  • 16
    • 0001386608 scopus 로고
    • Nonlinear aspects of the Cahn-Hilliard equation
    • Novick-Cohen A., and Segel L.A. Nonlinear aspects of the Cahn-Hilliard equation. Physica D 10 (1984) 277-298
    • (1984) Physica D , vol.10 , pp. 277-298
    • Novick-Cohen, A.1    Segel, L.A.2
  • 17
    • 0042403841 scopus 로고
    • Energy method for the Cahn-Hilliard equation
    • Novick-Cohen A. Energy method for the Cahn-Hilliard equation. Quart Appl Math XLVI (1988) 681-690
    • (1988) Quart Appl Math , vol.XLVI , pp. 681-690
    • Novick-Cohen, A.1
  • 18
    • 0001617217 scopus 로고
    • Numerical studies of the Cahn-Hilliard equation for phase separation
    • Elliott C.M., and French D.A. Numerical studies of the Cahn-Hilliard equation for phase separation. IMA J Appl Math 38 (1987) 97-128
    • (1987) IMA J Appl Math , vol.38 , pp. 97-128
    • Elliott, C.M.1    French, D.A.2
  • 19
    • 0000662072 scopus 로고
    • A nonconforming finite element method for the two dimensional Cahn-Hilliard equation
    • Elliott C.M., and French D.A. A nonconforming finite element method for the two dimensional Cahn-Hilliard equation. SIAM J Numer Anal 26 (1989) 884-903
    • (1989) SIAM J Numer Anal , vol.26 , pp. 884-903
    • Elliott, C.M.1    French, D.A.2
  • 20
    • 84968516048 scopus 로고
    • Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation
    • Elliott C.M., and Larsson S. Error estimates with smooth and nonsmooth data for a finite element method for the Cahn-Hilliard equation. Math Comput 58 (1992) 603-630
    • (1992) Math Comput , vol.58 , pp. 603-630
    • Elliott, C.M.1    Larsson, S.2
  • 21
    • 0001475208 scopus 로고
    • A second order splitting method of the Cahn-Hilliard equation
    • Elliott C.M., French D.A., and Milner F.A. A second order splitting method of the Cahn-Hilliard equation. Numer Math 54 (1989) 575-590
    • (1989) Numer Math , vol.54 , pp. 575-590
    • Elliott, C.M.1    French, D.A.2    Milner, F.A.3
  • 22
    • 0242420138 scopus 로고
    • Long-time behaviour of arbitrary order continuous time Galerkin schemes for some one-dimensional phase transition problems
    • French D.A., and Jensen S. Long-time behaviour of arbitrary order continuous time Galerkin schemes for some one-dimensional phase transition problems. IMA J Numer Anal 14 (1994) 421-442
    • (1994) IMA J Numer Anal , vol.14 , pp. 421-442
    • French, D.A.1    Jensen, S.2
  • 23
    • 0040374434 scopus 로고    scopus 로고
    • An approximate factorization least squares solution method for a mixed finite element approximation of the Cahn-Hilliard equation
    • Dean E.J., Glowinski R., and Trevas D.A. An approximate factorization least squares solution method for a mixed finite element approximation of the Cahn-Hilliard equation. Jpn J Ind Appl Math 13 (1996) 495-517
    • (1996) Jpn J Ind Appl Math , vol.13 , pp. 495-517
    • Dean, E.J.1    Glowinski, R.2    Trevas, D.A.3
  • 24
    • 44449107046 scopus 로고    scopus 로고
    • Baňas L, Nürnberg R. Adaptive finite element methods for Cahn-Hilliard equations. J Comput Appl Math, 2008;218(1):2-11.
    • Baňas L, Nürnberg R. Adaptive finite element methods for Cahn-Hilliard equations. J Comput Appl Math, 2008;218(1):2-11.
  • 25
    • 29144470271 scopus 로고    scopus 로고
    • A multigrid finite element solver for the Cahn-Hilliard equation
    • Kay D., and Welford R. A multigrid finite element solver for the Cahn-Hilliard equation. J Comput Phys 212 (2006) 288-304
    • (2006) J Comput Phys , vol.212 , pp. 288-304
    • Kay, D.1    Welford, R.2
  • 26
    • 19944391320 scopus 로고    scopus 로고
    • A discontinuous Galerkin method for the Cahn-Hilliard equation
    • Choo S.M., and Lee Y.J. A discontinuous Galerkin method for the Cahn-Hilliard equation. J Appl Math Comput 18 (2005) 113-126
    • (2005) J Appl Math Comput , vol.18 , pp. 113-126
    • Choo, S.M.1    Lee, Y.J.2
  • 27
    • 33748907906 scopus 로고    scopus 로고
    • A discontinuous Galerkin method for the Cahn-Hilliard equation
    • Wells G.N., Kuhl E., and Garikipati K. A discontinuous Galerkin method for the Cahn-Hilliard equation. J Comput Phys 218 (2006) 860-877
    • (2006) J Comput Phys , vol.218 , pp. 860-877
    • Wells, G.N.1    Kuhl, E.2    Garikipati, K.3
  • 28
    • 85189849942 scopus 로고    scopus 로고
    • Xia Y, Xu Y, Shu CW. Local discontinuous Galerkin methods for the Cahn-Hilliard type equations. J Comput Phys 2007;227(1):472-91.
    • Xia Y, Xu Y, Shu CW. Local discontinuous Galerkin methods for the Cahn-Hilliard type equations. J Comput Phys 2007;227(1):472-91.
  • 29
    • 0041401496 scopus 로고
    • A finite difference scheme for the Cahn-Hilliard equation based on a Lyapunov functional
    • Furihata D., Onda T., and Mori M. A finite difference scheme for the Cahn-Hilliard equation based on a Lyapunov functional. GAKUTO Int Ser Math Sci Appl 2 (1993) 347-358
    • (1993) GAKUTO Int Ser Math Sci Appl , vol.2 , pp. 347-358
    • Furihata, D.1    Onda, T.2    Mori, M.3
  • 30
    • 0001193685 scopus 로고    scopus 로고
    • α δ G / δ u that inherit energy conservation or dissipation property
    • α δ G / δ u that inherit energy conservation or dissipation property. J Comput Phys 156 (1999) 181-205
    • (1999) J Comput Phys , vol.156 , pp. 181-205
    • Furihata, D.1
  • 31
    • 0041079077 scopus 로고    scopus 로고
    • A stable and conservative finite difference scheme for the Cahn-Hilliard equation
    • Furihata D. A stable and conservative finite difference scheme for the Cahn-Hilliard equation. Numer Math 87 (2001) 675-699
    • (2001) Numer Math , vol.87 , pp. 675-699
    • Furihata, D.1
  • 32
    • 0032186765 scopus 로고    scopus 로고
    • Conservative nonlinear difference scheme for the Cahn-Hilliard equation
    • Choo S.M., and Chung S.K. Conservative nonlinear difference scheme for the Cahn-Hilliard equation. Comput Math Appl 36 7 (1998) 31-39
    • (1998) Comput Math Appl , vol.36 , Issue.7 , pp. 31-39
    • Choo, S.M.1    Chung, S.K.2
  • 33
    • 0039929677 scopus 로고    scopus 로고
    • Conservative nonlinear difference scheme for the Cahn-Hilliard equation-II
    • Choo S.M., Chung S.K., and Kim K.I. Conservative nonlinear difference scheme for the Cahn-Hilliard equation-II. Comput Math Appl 39 (2000) 229-243
    • (2000) Comput Math Appl , vol.39 , pp. 229-243
    • Choo, S.M.1    Chung, S.K.2    Kim, K.I.3
  • 35
    • 34249662156 scopus 로고    scopus 로고
    • A numerical method for the Cahn-Hilliard equation with a variable mobility
    • Kim J. A numerical method for the Cahn-Hilliard equation with a variable mobility. Commun Nonlinear Sci Numer Simul 12 (2007) 1560-1571
    • (2007) Commun Nonlinear Sci Numer Simul , vol.12 , pp. 1560-1571
    • Kim, J.1
  • 36
    • 10844251567 scopus 로고    scopus 로고
    • Numerical study of the Cahn-Hilliard equation in one, two and three dimensions
    • de Mello E.V.L., and Filho O.T.d.S. Numerical study of the Cahn-Hilliard equation in one, two and three dimensions. Physica A 347 (2005) 429-443
    • (2005) Physica A , vol.347 , pp. 429-443
    • de Mello, E.V.L.1    Filho, O.T.d.S.2
  • 37
    • 28444475844 scopus 로고    scopus 로고
    • The Fourier spectral method for the Cahn-Hilliard equation
    • Ye X., and Cheng X. The Fourier spectral method for the Cahn-Hilliard equation. Appl Math Comput 171 (2005) 345-357
    • (2005) Appl Math Comput , vol.171 , pp. 345-357
    • Ye, X.1    Cheng, X.2
  • 38
    • 34147135231 scopus 로고    scopus 로고
    • On large time-stepping methods for the Cahn-Hilliard equation
    • He Y., Liu Y., and Tang T. On large time-stepping methods for the Cahn-Hilliard equation. Appl Numer Math 57 (2007) 616-628
    • (2007) Appl Numer Math , vol.57 , pp. 616-628
    • He, Y.1    Liu, Y.2    Tang, T.3
  • 39
    • 0036630249 scopus 로고    scopus 로고
    • The Fourier collocation method for the Cahn-Hilliard equation
    • Ye X. The Fourier collocation method for the Cahn-Hilliard equation. Comput Math Appl 44 (2002) 213-229
    • (2002) Comput Math Appl , vol.44 , pp. 213-229
    • Ye, X.1
  • 40
    • 0037211421 scopus 로고    scopus 로고
    • The Legendre collocation method for the Cahn-Hilliard equation
    • Ye X. The Legendre collocation method for the Cahn-Hilliard equation. J Comput Appl Math 150 (2003) 87-108
    • (2003) J Comput Appl Math , vol.150 , pp. 87-108
    • Ye, X.1
  • 41
    • 33751539409 scopus 로고    scopus 로고
    • Orthogonal cubic spline collocation method for the Cahn-Hilliard equation
    • Danumjaya P., and Nandakumaran A.K. Orthogonal cubic spline collocation method for the Cahn-Hilliard equation. Appl Math Comput 182 (2006) 1316-1329
    • (2006) Appl Math Comput , vol.182 , pp. 1316-1329
    • Danumjaya, P.1    Nandakumaran, A.K.2
  • 42
    • 85120589861 scopus 로고    scopus 로고
    • Momani Sh, Erturk VS. A numerical scheme for the solution of viscous Cahn-Hilliard equation. Numer Methods Partial Differential Equations 2008;24(2):663-69.
    • Momani Sh, Erturk VS. A numerical scheme for the solution of viscous Cahn-Hilliard equation. Numer Methods Partial Differential Equations 2008;24(2):663-69.
  • 43
    • 33746801650 scopus 로고    scopus 로고
    • On the μ-transform: applications to the Cahn-Hilliard equation
    • Mitlin V. On the μ-transform: applications to the Cahn-Hilliard equation. Phys Lett A 358 (2006) 142-148
    • (2006) Phys Lett A , vol.358 , pp. 142-148
    • Mitlin, V.1
  • 44
    • 0142259489 scopus 로고    scopus 로고
    • Instability of traveling waves of the convective-diffusive Cahn-Hilliard equation
    • Hongjun G., and Changchun L. Instability of traveling waves of the convective-diffusive Cahn-Hilliard equation. Chaos, Solitons and Fractals 20 (2004) 253-258
    • (2004) Chaos, Solitons and Fractals , vol.20 , pp. 253-258
    • Hongjun, G.1    Changchun, L.2
  • 45
    • 0001578881 scopus 로고
    • Dynamic analysis in solid mechanics by an alternative boundary element procedure
    • Brebbia C.A., and Nardini D. Dynamic analysis in solid mechanics by an alternative boundary element procedure. Int J Soil Dyn Earthquake Eng 2 (1983) 228-233
    • (1983) Int J Soil Dyn Earthquake Eng , vol.2 , pp. 228-233
    • Brebbia, C.A.1    Nardini, D.2
  • 46
    • 0003048395 scopus 로고
    • The dual reciprocity boundary element method for the Helmholtz equation
    • Brebbia C.A., and Choudouet-Miranda A. (Eds), Computational Mechanics Publications, Springer, Berlin
    • Partridge P.W., and Brebbia C.A. The dual reciprocity boundary element method for the Helmholtz equation. In: Brebbia C.A., and Choudouet-Miranda A. (Eds). Proceedings of the International Boundary Elements Symposium (1990), Computational Mechanics Publications, Springer, Berlin 543-555
    • (1990) Proceedings of the International Boundary Elements Symposium , pp. 543-555
    • Partridge, P.W.1    Brebbia, C.A.2
  • 47
    • 0002847155 scopus 로고
    • Radial basis function approximation in dual reciprocity method
    • Karur S.R., and Ramachandran P.A. Radial basis function approximation in dual reciprocity method. Math Comput Modelling 20 7 (1994) 59-70
    • (1994) Math Comput Modelling , vol.20 , Issue.7 , pp. 59-70
    • Karur, S.R.1    Ramachandran, P.A.2
  • 48
    • 0022757495 scopus 로고
    • Free vibration analysis by BEM using particular integrals
    • Ahmad S., and Banerjee P.K. Free vibration analysis by BEM using particular integrals. J Eng Mech Div ASCE 112 (1986) 682-695
    • (1986) J Eng Mech Div ASCE , vol.112 , pp. 682-695
    • Ahmad, S.1    Banerjee, P.K.2
  • 49
    • 0036471601 scopus 로고    scopus 로고
    • 2D and 3D transient heat conduction analysis by BEM via particular integrals
    • Yang M.T., Park K.H., and Banerjee P.K. 2D and 3D transient heat conduction analysis by BEM via particular integrals. Comput Methods Appl Mech Eng 191 (2002) 1701-1722
    • (2002) Comput Methods Appl Mech Eng , vol.191 , pp. 1701-1722
    • Yang, M.T.1    Park, K.H.2    Banerjee, P.K.3
  • 50
    • 0032042502 scopus 로고    scopus 로고
    • Dual reciprocity boundary element analysis of time-independent Burger's equation
    • Chino E., and Tosaka N. Dual reciprocity boundary element analysis of time-independent Burger's equation. Eng Anal Bound Elem 21 (1998) 261-270
    • (1998) Eng Anal Bound Elem , vol.21 , pp. 261-270
    • Chino, E.1    Tosaka, N.2
  • 51
    • 33744510547 scopus 로고    scopus 로고
    • A numerical method for the wave equation subject to a non-local conservation condition
    • Ang W.T. A numerical method for the wave equation subject to a non-local conservation condition. Appl Numer Math 56 (2006) 1054-1060
    • (2006) Appl Numer Math , vol.56 , pp. 1054-1060
    • Ang, W.T.1
  • 52
    • 59649095602 scopus 로고    scopus 로고
    • Dehghan M, Mirzaei D. The boundary integral equation approach for numerical solution of the one-dimensional Sine-Gordon equation. Numer Methods Partial Differential Equations, in press.
    • Dehghan M, Mirzaei D. The boundary integral equation approach for numerical solution of the one-dimensional Sine-Gordon equation. Numer Methods Partial Differential Equations, in press.
  • 53
    • 0031176257 scopus 로고    scopus 로고
    • Analytical derivations for one-dimensional eigenproblems using dual boundary element method and multiple reciprocity method
    • Chen J.T., and Wong F.C. Analytical derivations for one-dimensional eigenproblems using dual boundary element method and multiple reciprocity method. Eng Anal Bound Elem 20 (1997) 25-33
    • (1997) Eng Anal Bound Elem , vol.20 , pp. 25-33
    • Chen, J.T.1    Wong, F.C.2
  • 54
    • 59649087279 scopus 로고    scopus 로고
    • Chen JT, Lee JW. On the spurious eigensolutions for the real-part boundary element method. Eng Anal Bound Elem, accepted for publication.
    • Chen JT, Lee JW. On the spurious eigensolutions for the real-part boundary element method. Eng Anal Bound Elem, accepted for publication.
  • 55
    • 32644435892 scopus 로고    scopus 로고
    • Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
    • Dehghan M. Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices. Math Comput Simul 71 (2006) 16-30
    • (2006) Math Comput Simul , vol.71 , pp. 16-30
    • Dehghan, M.1
  • 56
    • 19744375661 scopus 로고    scopus 로고
    • Parameter determination in a partial differential equation from the overspecified data
    • Dehghan M. Parameter determination in a partial differential equation from the overspecified data. Math Comput Modell 41 (2005) 196-213
    • (2005) Math Comput Modell , vol.41 , pp. 196-213
    • Dehghan, M.1
  • 57
    • 18744412104 scopus 로고    scopus 로고
    • Identification of a time-dependent coefficient in a partial differential equation subject to an extra measurement
    • Dehghan M. Identification of a time-dependent coefficient in a partial differential equation subject to an extra measurement. Numer Methods Partial Differ Equations 21 (2005) 611-622
    • (2005) Numer Methods Partial Differ Equations , vol.21 , pp. 611-622
    • Dehghan, M.1
  • 58
    • 33748938323 scopus 로고    scopus 로고
    • Implicit collocation technique for heat equation with non-classic initial condition
    • Dehghan M. Implicit collocation technique for heat equation with non-classic initial condition. Int J Non-Linear Sci Numer Simul 7 (2007) 447-450
    • (2007) Int J Non-Linear Sci Numer Simul , vol.7 , pp. 447-450
    • Dehghan, M.1
  • 59
    • 33749559910 scopus 로고    scopus 로고
    • The one-dimensional heat equation subject to a boundary integral specification
    • Dehghan M. The one-dimensional heat equation subject to a boundary integral specification. Chaos Solitons Fractals 32 (2007) 661-757
    • (2007) Chaos Solitons Fractals , vol.32 , pp. 661-757
    • Dehghan, M.1
  • 60
    • 35448960877 scopus 로고    scopus 로고
    • Numerical solution of the Klein-Gordon equation via He's variational iteration method
    • Shakeri F., and Dehghan M. Numerical solution of the Klein-Gordon equation via He's variational iteration method. Nonlinear Dyn 51 (2008) 89-97
    • (2008) Nonlinear Dyn , vol.51 , pp. 89-97
    • Shakeri, F.1    Dehghan, M.2
  • 61
    • 33645276878 scopus 로고    scopus 로고
    • A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications
    • Dehghan M. A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications. Numer Methods Partial Differ Equations 22 (2006) 220-257
    • (2006) Numer Methods Partial Differ Equations , vol.22 , pp. 220-257
    • Dehghan, M.1


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