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Volumn 181, Issue 2, 2002, Pages 526-544

A moving mesh method for the solution of the one-dimensional phase-field equations

Author keywords

Adaptive method; Equidistribution; Moving meshes; Phase change; Phase field

Indexed keywords

NUMERICAL METHODS;

EID: 0037144945     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2002.7140     Document Type: Article
Times cited : (50)

References (33)
  • 1
    • 0034300742 scopus 로고    scopus 로고
    • Convergence analysis of finite-difference approximations on equidistributed grids to a singularly perturbed boundary value problem
    • G. Beckett and J. A. Mackenzie, Convergence analysis of finite-difference approximations on equidistributed grids to a singularly perturbed boundary value problem, Appl. Numer. Math. 35, 7 (2000).
    • (2000) Appl. Numer. Math , vol.35 , pp. 7
    • Beckett, G.1    Mackenzie, J.A.2
  • 2
    • 0035361441 scopus 로고    scopus 로고
    • On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution
    • G. Beckett and J. A. Mackenzie, On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution, J. Comput. Appl. Math. 131, 381 (2001).
    • (2001) J. Comput. Appl. Math , vol.131 , pp. 381
    • Beckett, G.1    Mackenzie, J.A.2
  • 3
    • 0001689357 scopus 로고    scopus 로고
    • On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution
    • G. Beckett, J. A. Mackenzie, A. Ramage, and D. M. Sloan, On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution, J. Comput. Phys. 167, 372 (2001).
    • (2001) J. Comput. Phys , vol.167 , pp. 372
    • Beckett, G.1    Mackenzie, J.A.2    Ramage, A.3    Sloan, D.M.4
  • 4
    • 0000402730 scopus 로고    scopus 로고
    • A moving mesh finite element method for the solution of two-dimensional Stefan problems
    • G. Beckett, J. A. Mackenzie, and M. L. Robertson, A moving mesh finite element method for the solution of two-dimensional Stefan problems, J. Comput. Phys. 168, 500 (2001).
    • (2001) J. Comput. Phys , vol.168 , pp. 500
    • Beckett, G.1    Mackenzie, J.A.2    Robertson, M.L.3
  • 5
    • 0010924802 scopus 로고    scopus 로고
    • An r-Adaptive Finite Element Method for the Solution of the Two-Dimensional Phase-Field Equations
    • Technical Report 32 (Strathclyde University, Mathematics Department) submitted for publication
    • G. Beckett, J. A. Mackenzie, and M. L. Robertson, An r-Adaptive Finite Element Method for the Solution of the Two-Dimensional Phase-Field Equations, Technical Report 32 (Strathclyde University, Mathematics Department, 2001), submitted for publication.
    • (2001)
    • Beckett, G.1    Mackenzie, J.A.2    Robertson, M.L.3
  • 6
    • 0028443125 scopus 로고
    • A moving-grid interface for systems of one-dimensional time dependent partial differential equations
    • J. G. Blom and P. A. Zegeling, A moving-grid interface for systems of one-dimensional time dependent partial differential equations, ACM Trans. Math. Software 20, 194 (1994).
    • (1994) ACM Trans. Math. Software , vol.20 , pp. 194
    • Blom, J.G.1    Zegeling, P.A.2
  • 7
    • 0000770248 scopus 로고
    • Morphological instability in phase-field models of solidification
    • R. J. Braun, G. B. McFaddenn, and S. R. Coriell, Morphological instability in phase-field models of solidification, Phys. Rev. E 49, 4336 (1994).
    • (1994) Phys. Rev. E , vol.49 , pp. 4336
    • Braun, R.J.1    McFaddenn, G.B.2    Coriell, S.R.3
  • 8
    • 33646973938 scopus 로고
    • Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations
    • G. Caginalp, Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations, Phys. Rev. A 39, 5887 (1989).
    • (1989) Phys. Rev. A , vol.39 , pp. 5887
    • Caginalp, G.1
  • 9
    • 0010785643 scopus 로고
    • The existence of travelling waves for phase field equations and convergence to sharp interface models in the singular limit
    • G. Caginalp and Y. Nishiura, The existence of travelling waves for phase field equations and convergence to sharp interface models in the singular limit, Q. Appl. Math. 49, 147 (1991).
    • (1991) Q. Appl. Math , vol.49 , pp. 147
    • Caginalp, G.1    Nishiura, Y.2
  • 10
    • 0002920401 scopus 로고
    • Computation of sharp phase boundaries by spreading: The planar and spherically symmetric cases
    • G. Caginalp and E. A. Socolovsky, Computation of sharp phase boundaries by spreading: The planar and spherically symmetric cases, J. Comput. Phys. 95, 85 (1991).
    • (1991) J. Comput. Phys , vol.95 , pp. 85
    • Caginalp, G.1    Socolovsky, E.A.2
  • 11
    • 0001512634 scopus 로고
    • Phase field computations of single-needle crystals, crystal growth, and motion by mean curvature
    • G. Caginalp and E. A. Socolovsky, Phase field computations of single-needle crystals, crystal growth, and motion by mean curvature, SIAM J. Sci. Comput. 15, 106 (1994).
    • (1994) SIAM J. Sci. Comput , vol.15 , pp. 106
    • Caginalp, G.1    Socolovsky, E.A.2
  • 12
    • 0000359177 scopus 로고    scopus 로고
    • An r-adaptive finite element method based upon moving mesh PDEs
    • W. Cao, W. Huang, and R. D. Russell, An r-adaptive finite element method based upon moving mesh PDEs, J. Comput. Phys. 149, 221 (1999).
    • (1999) J. Comput. Phys , vol.149 , pp. 221
    • Cao, W.1    Huang, W.2    Russell, R.D.3
  • 13
    • 0004207845 scopus 로고
    • Principles of Solidification
    • (Krieger, New York)
    • B. Chalmers, Principles of Solidification (Krieger, New York, 1977).
    • (1977)
    • Chalmers, B.1
  • 14
    • 0003432643 scopus 로고
    • Free and Moving Boundary Value Problems
    • (Oxford Science, Oxford, UK)
    • J. Crank, Free and Moving Boundary Value Problems (Oxford Science, Oxford, UK, 1984).
    • (1984)
    • Crank, J.1
  • 15
    • 0002791812 scopus 로고
    • Good approximation by splines with variables knots II
    • Lecture Notes in Mathematics (Springer-Verlag, Berlin/New York)
    • C. de Boor, Good approximation by splines with variables knots II, in Lecture Notes in Mathematics (Springer-Verlag, Berlin/New York, 1974). Vol. 363, pp. 12-20.
    • (1974) , vol.363 , pp. 12-20
    • de Boor, C.1
  • 16
    • 0001121137 scopus 로고
    • Simple adaptive grids for 1-D initial value problems
    • E. A. Dorfi and L. O'c. Drury, Simple adaptive grids for 1-D initial value problems, J. Comput. Phys. 69, 175 (1987).
    • (1987) J. Comput. Phys , vol.69 , pp. 175
    • Dorfi, E.A.1    O'c. Drury, L.2
  • 18
    • 0031568153 scopus 로고    scopus 로고
    • The phase-field method in the sharp-interface limit: A comparison between model potentials
    • M. Fabbri and V. R. Voller, The phase-field method in the sharp-interface limit: A comparison between model potentials, J. Comput. Phys. 130, 256 (1997).
    • (1997) J. Comput. Phys , vol.130 , pp. 256
    • Fabbri, M.1    Voller, V.R.2
  • 19
    • 0031626249 scopus 로고    scopus 로고
    • An explicit, adaptive grid algorithm for one-dimensional initial value problems
    • K. Farrell and L. Drury, An explicit, adaptive grid algorithm for one-dimensional initial value problems, Appl. Numer. Math. 26, 3 (1997).
    • (1997) Appl. Numer. Math , vol.26 , pp. 3
    • Farrell, K.1    Drury, L.2
  • 20
    • 0028446372 scopus 로고
    • Moving mesh PDEs based on the equidistribution principle
    • W. Huang, Y. Ren, and R. D. Russel, Moving mesh PDEs based on the equidistribution principle, SIAM J. Numer. Anal. 31, 709 (1994).
    • (1994) SIAM J. Numer. Anal , vol.31 , pp. 709
    • Huang, W.1    Ren, Y.2    Russel, R.D.3
  • 21
    • 0000448909 scopus 로고    scopus 로고
    • Analysis of moving mesh partial differential equations with spatial smoothing
    • W. Huang and R. D. Russell, Analysis of moving mesh partial differential equations with spatial smoothing, SIAM J. Numer. Anal. 34, 1106 (1997).
    • (1997) SIAM J. Numer. Anal , vol.34 , pp. 1106
    • Huang, W.1    Russell, R.D.2
  • 22
    • 0031644105 scopus 로고    scopus 로고
    • A high dimensional moving mesh strategy
    • W. Huang and R. D. Russell, A high dimensional moving mesh strategy, Appl. Numer. Math. 26, 63 (1997).
    • (1997) Appl. Numer. Math , vol.26 , pp. 63
    • Huang, W.1    Russell, R.D.2
  • 23
    • 4243457001 scopus 로고    scopus 로고
    • Quantitative phase-field modeling of dendritic growth in two and three dimensions
    • A. Karma and W.-J. Rappel, Quantitative phase-field modeling of dendritic growth in two and three dimensions, Phys. Rev. E 57, 4323 (1998).
    • (1998) Phys. Rev. E , vol.57 , pp. 4323
    • Karma, A.1    Rappel, W.-J.2
  • 24
    • 34249817369 scopus 로고
    • Modeling and numerical simulations of dendritic growth
    • R. Kobayashi, Modeling and numerical simulations of dendritic growth, Physica D 63, 410 (1993).
    • (1993) Physica D , vol.63 , pp. 410
    • Kobayashi, R.1
  • 25
    • 0001617135 scopus 로고    scopus 로고
    • The numerical solution of one-dimensional phase change problems using an adaptive moving mesh method
    • J. A. Mackenzie and M. L. Robertson, The numerical solution of one-dimensional phase change problems using an adaptive moving mesh method, J. Comput. Phys. 161, 537 (2000).
    • (2000) J. Comput. Phys , vol.161 , pp. 537
    • Mackenzie, J.A.1    Robertson, M.L.2
  • 26
    • 0032215961 scopus 로고    scopus 로고
    • One-dimensional phase field models with adaptive grids
    • J. F. McCarthy, One-dimensional phase field models with adaptive grids, Trans. ASME 120, 956 (1998).
    • (1998) Trans. ASME , vol.120 , pp. 956
    • McCarthy, J.F.1
  • 27
    • 0003602606 scopus 로고
    • Iterative Solution of Nonlinear Equations in Several Variables
    • (Academic Press, San Diego)
    • J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, San Diego 1970).
    • (1970)
    • Ortega, J.M.1    Rheinboldt, W.C.2
  • 28
    • 0000358571 scopus 로고
    • On the relation between the standard phase-field model and a thermodynamically consistent phase-field model
    • O. Penrose and P. C. Fife, On the relation between the standard phase-field model and a thermodynamically consistent phase-field model, Physica D 69, 107 (1993).
    • (1993) Physica D , vol.69 , pp. 107
    • Penrose, O.1    Fife, P.C.2
  • 29
    • 1842576356 scopus 로고    scopus 로고
    • Efficient computation of dendritic microstructures using adaptive mesh refinement
    • N. Provatas, N. Goldenfeld, and J. Dantzig, Efficient computation of dendritic microstructures using adaptive mesh refinement, Phys. Rev. Lett. 80(15), 3308 (1998).
    • (1998) Phys. Rev. Lett , vol.80 , Issue.15 , pp. 3308
    • Provatas, N.1    Goldenfeld, N.2    Dantzig, J.3
  • 30
    • 0001480945 scopus 로고
    • On the convergence of iterated remeshing
    • J. D. Pryce, On the convergence of iterated remeshing, IMA J. Numer. Anal. 9, 315 (1989).
    • (1989) IMA J. Numer. Anal , vol.9 , pp. 315
    • Pryce, J.D.1
  • 31
    • 0030137571 scopus 로고    scopus 로고
    • Computation of three dimensional dendrites with finite elements
    • A. Schmidt, Computation of three dimensional dendrites with finite elements, J. Comput. Phys. 125, 293 (1996).
    • (1996) J. Comput. Phys , vol.125 , pp. 293
    • Schmidt, A.1
  • 33
    • 25744454700 scopus 로고
    • Computation of dendrites using a phase field model
    • A. A. Wheeler, B. T. Murray, and R. J. Schaefer, Computation of dendrites using a phase field model, Physica D 66, 243 (1993).
    • (1993) Physica D , vol.66 , pp. 243
    • Wheeler, A.A.1    Murray, B.T.2    Schaefer, R.J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.