메뉴 건너뛰기




Volumn 229, Issue 9, 2010, Pages 3171-3188

Parametric FEM for geometric biomembranes

Author keywords

Bending energy; Biomembrane; Geometric flow; Gradient flow; Helfrich; Isoparametric elements; Moving finite elements; Red blood cell; Shape differential calculus; Willmore

Indexed keywords

BLOOD; CELLS; GEOMETRY;

EID: 77949325543     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.12.036     Document Type: Article
Times cited : (81)

References (43)
  • 1
    • 0014709498 scopus 로고
    • The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell
    • Canham P. The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J. Theor. Biol. 1970, 26(1):61-81.
    • (1970) J. Theor. Biol. , vol.26 , Issue.1 , pp. 61-81
    • Canham, P.1
  • 3
    • 0037534552 scopus 로고
    • The equations of mechanical equilibrium of a model membrane
    • Jenkins J. The equations of mechanical equilibrium of a model membrane. SIAM J. Appl. Math. 1977, 32(4):755-764.
    • (1977) SIAM J. Appl. Math. , vol.32 , Issue.4 , pp. 755-764
    • Jenkins, J.1
  • 4
    • 0033267258 scopus 로고    scopus 로고
    • Fluid films with curvature elasticity
    • Steigmann D. Fluid films with curvature elasticity. Arch. Ration. Mech. Anal. 1999, 150(2):127-152.
    • (1999) Arch. Ration. Mech. Anal. , vol.150 , Issue.2 , pp. 127-152
    • Steigmann, D.1
  • 5
    • 34247639492 scopus 로고    scopus 로고
    • Continuum theory of a moving membrane
    • Hu D., Zhang P., E W. Continuum theory of a moving membrane. Phys. Rev. E 2007, 375(4):41605-41611.
    • (2007) Phys. Rev. E , vol.375 , Issue.4 , pp. 41605-41611
    • Hu, D.1    Zhang, P.2    E, W.3
  • 6
    • 85189840622 scopus 로고    scopus 로고
    • Curves and surfaces, Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, (Translated and updated from the 1998 Spanish edition by the authors).
    • S. Montiel, A. Ros, Curves and surfaces, Graduate Studies in Mathematics, vol. 69. American Mathematical Society, Providence, RI, 2005 (Translated and updated from the 1998 Spanish edition by the authors).
    • (2005) , vol.69
    • Montiel, S.1    Ros, A.2
  • 7
    • 0004265477 scopus 로고
    • Oxford Science Publications, The Clarendon Press Oxford University Press, New York
    • Willmore T.J. Riemannian Geometry 1993, Oxford Science Publications, The Clarendon Press Oxford University Press, New York.
    • (1993) Riemannian Geometry
    • Willmore, T.J.1
  • 8
    • 0018538681 scopus 로고
    • Mechanics and thermodynamics of biomembranes
    • 2
    • E.A. Evans, R. Skalak, Mechanics and thermodynamics of biomembranes. 2. CRC Crit. Rev. Bioeng. 3 (4) (1979) 331-418.
    • (1979) CRC Crit. Rev. Bioeng , vol.3 , Issue.4 , pp. 331-418
    • Evans, E.A.1    Skalak, R.2
  • 9
    • 0030735760 scopus 로고    scopus 로고
    • Configurations of fluid membranes and vesicles
    • Seifert U. Configurations of fluid membranes and vesicles. Adv. Phys. 1997, 46(1):13-137.
    • (1997) Adv. Phys. , vol.46 , Issue.1 , pp. 13-137
    • Seifert, U.1
  • 11
    • 85189838278 scopus 로고    scopus 로고
    • Dynamics of biomembranes: effect of the bulk fluid, in preparation.
    • A. Bonito, R. Nochetto, M. Pauletti, Dynamics of biomembranes: effect of the bulk fluid, in preparation.
    • Bonito, A.1    Nochetto, R.2    Pauletti, M.3
  • 12
  • 13
    • 34447274993 scopus 로고    scopus 로고
    • Discrete gradient flows for shape optimization and applications
    • Doǧan G., Morin P., Nochetto R., Verani M. Discrete gradient flows for shape optimization and applications. Comput. Methods Appl. Mech. Eng. 2007, 196(37-40):3898-3914.
    • (2007) Comput. Methods Appl. Mech. Eng. , vol.196 , Issue.37-40 , pp. 3898-3914
    • Doǧan, G.1    Morin, P.2    Nochetto, R.3    Verani, M.4
  • 14
    • 54249170447 scopus 로고    scopus 로고
    • Computational parametric Willmore flow
    • Dziuk G. Computational parametric Willmore flow. Numer. Math. 2008, 111(1):55-80.
    • (2008) Numer. Math. , vol.111 , Issue.1 , pp. 55-80
    • Dziuk, G.1
  • 15
    • 25444527546 scopus 로고    scopus 로고
    • An algorithm for the elastic flow of surfaces
    • Rusu R.E. An algorithm for the elastic flow of surfaces. Interfaces Free Bound. 2005, 7(3):229-239.
    • (2005) Interfaces Free Bound. , vol.7 , Issue.3 , pp. 229-239
    • Rusu, R.E.1
  • 16
    • 85189836162 scopus 로고    scopus 로고
    • Parametric approximation of Willmore flow and related geometric evolution equations, preprint.
    • J. Barrett, H. Garcke, R. Nürnberg, Parametric approximation of Willmore flow and related geometric evolution equations, preprint.
    • Barrett, J.1    Garcke, H.2    Nürnberg, R.3
  • 17
    • 10844248239 scopus 로고    scopus 로고
    • A finite element method for surface diffusion: the parametric case
    • Bänsch E., Morin P., Nochetto R. A finite element method for surface diffusion: the parametric case. J. Comput. Phys. 2005, 203(1):321-343.
    • (2005) J. Comput. Phys. , vol.203 , Issue.1 , pp. 321-343
    • Bänsch, E.1    Morin, P.2    Nochetto, R.3
  • 18
    • 85189842398 scopus 로고    scopus 로고
    • Geometrically consistent mesh modification, submitted for publication.
    • A. Bonito, R. Nochetto, M. Pauletti, Geometrically consistent mesh modification, submitted for publication.
    • Bonito, A.1    Nochetto, R.2    Pauletti, M.3
  • 19
    • 3242875567 scopus 로고    scopus 로고
    • A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
    • Du Q., Liu C., Wang X. A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. J. Comput. Phys. 2004, 198(2):450-468.
    • (2004) J. Comput. Phys. , vol.198 , Issue.2 , pp. 450-468
    • Du, Q.1    Liu, C.2    Wang, X.3
  • 20
    • 29144520935 scopus 로고    scopus 로고
    • Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions
    • Du Q., Liu C., Wang X. Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions. J. Comput. Phys. 2006, 212(2):757-777.
    • (2006) J. Comput. Phys. , vol.212 , Issue.2 , pp. 757-777
    • Du, Q.1    Liu, C.2    Wang, X.3
  • 21
    • 72049109265 scopus 로고    scopus 로고
    • Threshold dynamics for high order geometric motions
    • Esedoglu S., Ruuth S., Tsai R. Threshold dynamics for high order geometric motions. Interfaces Free Bound. 2008, 10(3):263-282.
    • (2008) Interfaces Free Bound. , vol.10 , Issue.3 , pp. 263-282
    • Esedoglu, S.1    Ruuth, S.2    Tsai, R.3
  • 22
    • 2542539269 scopus 로고    scopus 로고
    • A level set formulation for Willmore flow
    • Droske M., Rumpf M. A level set formulation for Willmore flow. Interfaces Free Bound. 2004, 6(3):361-378.
    • (2004) Interfaces Free Bound. , vol.6 , Issue.3 , pp. 361-378
    • Droske, M.1    Rumpf, M.2
  • 23
    • 0038541047 scopus 로고    scopus 로고
    • Shapes and geometries
    • Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, (Analysis, differential calculus, and optimization)
    • Delfour M.C., Zolésio J.-P. Shapes and geometries. Advances in Design and Control 2001, vol. 4. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, (Analysis, differential calculus, and optimization).
    • (2001) Advances in Design and Control , vol.4
    • Delfour, M.C.1    Zolésio, J.-P.2
  • 24
    • 33646388390 scopus 로고    scopus 로고
    • Error analysis of a finite element method for the Willmore flow of graphs
    • Deckelnick K., Dziuk G. Error analysis of a finite element method for the Willmore flow of graphs. Interfaces Free Bound. 2006, 8(1):21-46.
    • (2006) Interfaces Free Bound. , vol.8 , Issue.1 , pp. 21-46
    • Deckelnick, K.1    Dziuk, G.2
  • 25
    • 19844369196 scopus 로고    scopus 로고
    • Computation of geometric partial differential equations and mean curvature flow
    • Deckelnick K., Dziuk G., Elliott C. Computation of geometric partial differential equations and mean curvature flow. Acta Numer. 2005, 14:139-232.
    • (2005) Acta Numer. , vol.14 , pp. 139-232
    • Deckelnick, K.1    Dziuk, G.2    Elliott, C.3
  • 26
    • 0000789992 scopus 로고
    • An algorithm for evolutionary surfaces
    • Dziuk G. An algorithm for evolutionary surfaces. Numer. Math. 1991, 58(6):603-611.
    • (1991) Numer. Math. , vol.58 , Issue.6 , pp. 603-611
    • Dziuk, G.1
  • 28
    • 0004027576 scopus 로고
    • An introduction to continuum mechanics
    • Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York
    • Gurtin M. An introduction to continuum mechanics. Mathematics in Science and Engineering 1981, vol. 158. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York.
    • (1981) Mathematics in Science and Engineering , vol.158
    • Gurtin, M.1
  • 29
    • 85189839519 scopus 로고    scopus 로고
    • Calculus of variations. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, (The Lagrangian formalism).
    • M. Giaquinta, S. Hildebrandt, Calculus of variations. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 310, Springer-Verlag, Berlin, 1996 (The Lagrangian formalism).
    • (1996) , vol.310
    • Giaquinta, M.1    Hildebrandt, S.2
  • 30
    • 0035590150 scopus 로고    scopus 로고
    • Finite element discretization of the Navier-Stokes equations with a free capillary surface
    • Bänsch E. Finite element discretization of the Navier-Stokes equations with a free capillary surface. Numer. Math. 2001, 88(2):203-235.
    • (2001) Numer. Math. , vol.88 , Issue.2 , pp. 203-235
    • Bänsch, E.1
  • 31
    • 2342475802 scopus 로고    scopus 로고
    • A finite element method for surface restoration with smooth boundary conditions
    • Clarenz U., Diewald U., Dziuk G., Rumpf M., Rusu R. A finite element method for surface restoration with smooth boundary conditions. Comput. Aided Geom. Des. 2004, 21(5):427-445.
    • (2004) Comput. Aided Geom. Des. , vol.21 , Issue.5 , pp. 427-445
    • Clarenz, U.1    Diewald, U.2    Dziuk, G.3    Rumpf, M.4    Rusu, R.5
  • 32
    • 85189836803 scopus 로고    scopus 로고
    • Isoparametric finite element approximations of curvature on hypersurfaces, preprint from his webpage.
    • C. Heine, Isoparametric finite element approximations of curvature on hypersurfaces, preprint from his webpage.
    • Heine, C.1
  • 33
    • 27744530591 scopus 로고    scopus 로고
    • A posteriori error analysis for the mean curvature flow of graphs
    • (electronic)
    • Lakkis O., Nochetto R. A posteriori error analysis for the mean curvature flow of graphs. SIAM J. Numer. Anal. 2005, 42(5):1875-1898. (electronic).
    • (2005) SIAM J. Numer. Anal. , vol.42 , Issue.5 , pp. 1875-1898
    • Lakkis, O.1    Nochetto, R.2
  • 34
    • 60049098520 scopus 로고    scopus 로고
    • Higher-order finite element methods and pointwise error estimates for elliptic problems on surfaces
    • Demlow A. Higher-order finite element methods and pointwise error estimates for elliptic problems on surfaces. SIAM J. Numer. Anal. 2009, 47(2):805-827.
    • (2009) SIAM J. Numer. Anal. , vol.47 , Issue.2 , pp. 805-827
    • Demlow, A.1
  • 35
    • 85189837660 scopus 로고    scopus 로고
    • Parametric AFEM for Geometric Evolution Equations and Coupled Fluid-Membrane Interaction, Ph.D. Thesis, University of Maryland,
    • M. Pauletti, Parametric AFEM for Geometric Evolution Equations and Coupled Fluid-Membrane Interaction, Ph.D. Thesis, University of Maryland, 2008 http://www.lib.umd.edu/drum/handle/1903/8603.
    • (2008)
    • Pauletti, M.1
  • 36
    • 40049084767 scopus 로고    scopus 로고
    • An adaptive finite element method for the Laplace-Beltrami operator on implicitly defined surfaces
    • (electronic)
    • Demlow A., Dziuk G. An adaptive finite element method for the Laplace-Beltrami operator on implicitly defined surfaces. SIAM J. Numer. Anal. 2007, 45(1):421-442. (electronic).
    • (2007) SIAM J. Numer. Anal. , vol.45 , Issue.1 , pp. 421-442
    • Demlow, A.1    Dziuk, G.2
  • 37
    • 85189836871 scopus 로고    scopus 로고
    • Convergence of Adaptive Finite Element Methods, Ph.D. Thesis, University of Maryland,
    • K. Mekchay, Convergence of Adaptive Finite Element Methods, Ph.D. Thesis, University of Maryland, 2005.
    • (2005)
    • Mekchay, K.1
  • 38
    • 85189839076 scopus 로고    scopus 로고
    • AFEM for the Laplace-Beltrami operator on graphs: design and conditional contraction property, submitted for publication.
    • K. Mekchay, P. Morin, R. Nochetto, AFEM for the Laplace-Beltrami operator on graphs: design and conditional contraction property, submitted for publication.
    • Mekchay, K.1    Morin, P.2    Nochetto, R.3
  • 39
    • 0000947789 scopus 로고
    • A recursive approach to local mesh refinement in two and three dimensions
    • Kossaczký I. A recursive approach to local mesh refinement in two and three dimensions. J. Comput. Appl. Math. 1994, 55(3):275-288.
    • (1994) J. Comput. Appl. Math. , vol.55 , Issue.3 , pp. 275-288
    • Kossaczký, I.1
  • 40
    • 85189836656 scopus 로고    scopus 로고
    • Siebert, Design of adaptive finite element software, Lecture Notes in Computational Science and Engineering, Springer-Verlag, Berlin, 2005 (The finite element toolbox ALBERTA, With 1 CD-ROM (Unix/Linux)).
    • A. Schmidt, K. Siebert, Design of adaptive finite element software, Lecture Notes in Computational Science and Engineering, vol. 42, Springer-Verlag, Berlin, 2005 (The finite element toolbox ALBERTA, With 1 CD-ROM (Unix/Linux)).
    • , vol.42
    • Schmidt, K.1
  • 41
    • 77949313875 scopus 로고    scopus 로고
    • Design of finite element tools for coupled surface and volume meshes
    • Köster D., Kriessl O., Siebert K. Design of finite element tools for coupled surface and volume meshes. Numer. Math. Theor. Methods Appl. 2008, 1(3):245-274.
    • (2008) Numer. Math. Theor. Methods Appl. , vol.1 , Issue.3 , pp. 245-274
    • Köster, D.1    Kriessl, O.2    Siebert, K.3
  • 42
    • 0017644098 scopus 로고
    • Static equilibrium configurations of a model red blood cell
    • Jenkins J. Static equilibrium configurations of a model red blood cell. J. Math. Biol. 1977, 4(2):150-169.
    • (1977) J. Math. Biol. , vol.4 , Issue.2 , pp. 150-169
    • Jenkins, J.1
  • 43
    • 0000924897 scopus 로고
    • Shape transformations of vesicles: phase diagram for spontaneous-curvature and bilayer-coupling models
    • Seifert U., Berndl K., Lipowsky R. Shape transformations of vesicles: phase diagram for spontaneous-curvature and bilayer-coupling models. Phys. Rev. A 1991, 44(2):1182-1202.
    • (1991) Phys. Rev. A , vol.44 , Issue.2 , pp. 1182-1202
    • Seifert, U.1    Berndl, K.2    Lipowsky, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.