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Volumn 230, Issue 2, 2011, Pages 305-328

The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes

Author keywords

Div curl equations; Magnetostatics; Mimetic finite differences; Polyhedral mesh

Indexed keywords

ALGEBRA; DEGREES OF FREEDOM (MECHANICS); FINITE DIFFERENCE METHOD; MESH GENERATION; NUMERICAL METHODS;

EID: 78149411899     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.09.007     Document Type: Article
Times cited : (68)

References (49)
  • 2
    • 37449025866 scopus 로고    scopus 로고
    • A residual based error estimator for the mimetic finite difference method
    • Beirão da Veiga L.
    • Beirão da Veiga L. A residual based error estimator for the mimetic finite difference method. Numer. Math. 2008, 108(3):387-406.
    • (2008) Numer. Math. , vol.108 , Issue.3 , pp. 387-406
  • 3
    • 77950190438 scopus 로고    scopus 로고
    • A mimetic finite difference method for linear elasticity
    • Beirão da Veiga L.
    • Beirão da Veiga L. A mimetic finite difference method for linear elasticity. M2AN: Math. Model. Numer. Anal. 2010, 44(2):231-250.
    • (2010) M2AN: Math. Model. Numer. Anal. , vol.44 , Issue.2 , pp. 231-250
  • 4
    • 71549140062 scopus 로고    scopus 로고
    • Convergence analysis of the high-order mimetic finite difference method
    • Beirão da Veiga L., Lipnikov K., Manzini G.
    • Beirão da Veiga L., Lipnikov K., Manzini G. Convergence analysis of the high-order mimetic finite difference method. Numer. Math. 2009, 113(3):325-356.
    • (2009) Numer. Math. , vol.113 , Issue.3 , pp. 325-356
  • 5
    • 68549140230 scopus 로고    scopus 로고
    • A higher-order formulation of the mimetic finite difference method
    • Beirão da Veiga L, Manzini G.
    • Beirão da Veiga L., Manzini G. A higher-order formulation of the mimetic finite difference method. SIAM, J. Sci. Comput. 2008, 31(1):732-760.
    • (2008) SIAM, J. Sci. Comput. , vol.31 , Issue.1 , pp. 732-760
  • 6
    • 60949113471 scopus 로고    scopus 로고
    • An a-posteriori error estimator for the mimetic finite difference approximation of elliptic problems
    • Beirão da Veiga L., Manzini G. An a-posteriori error estimator for the mimetic finite difference approximation of elliptic problems. Int. J. Numer. Meth. Eng. 2008, 76(11):1696-1723.
    • (2008) Int. J. Numer. Meth. Eng. , vol.76 , Issue.11 , pp. 1696-1723
    • Beirão da Veiga, L.1    Manzini, G.2
  • 7
    • 33646719455 scopus 로고    scopus 로고
    • Principle of mimetic discretizations of differential operators
    • Springer-Verlag, D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides, M. Shashkov (Eds.) Compatible discretizations
    • Bochev P., Hyman J.M. Principle of mimetic discretizations of differential operators. Proceedings of IMA hot topics workshop on compatible discretizations, IMA 2006, vol. 142. Springer-Verlag. D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides, M. Shashkov (Eds.).
    • (2006) Proceedings of IMA hot topics workshop on compatible discretizations, IMA , vol.142
    • Bochev, P.1    Hyman, J.M.2
  • 8
    • 0024104484 scopus 로고
    • Whitney forms: a class of finite elements for three dimensional computation in electromagnetism
    • Bossavit A. Whitney forms: a class of finite elements for three dimensional computation in electromagnetism. IEE Proc. 1988, 135:493-500.
    • (1988) IEE Proc. , vol.135 , pp. 493-500
    • Bossavit, A.1
  • 9
    • 77955232524 scopus 로고    scopus 로고
    • Innovative mimetic discretizations for electromagnetic problems
    • Brezzi F., Buffa A. Innovative mimetic discretizations for electromagnetic problems. J. Comput. Appl. Math. 2010, 234(6):1980-1987.
    • (2010) J. Comput. Appl. Math. , vol.234 , Issue.6 , pp. 1980-1987
    • Brezzi, F.1    Buffa, A.2
  • 12
    • 26944484259 scopus 로고    scopus 로고
    • Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes
    • Brezzi F., Lipnikov K., Shashkov M. Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes. SIAM J. Numer. Anal. 2005, 43:1872-1896.
    • (2005) SIAM J. Numer. Anal. , vol.43 , pp. 1872-1896
    • Brezzi, F.1    Lipnikov, K.2    Shashkov, M.3
  • 13
    • 34447101360 scopus 로고    scopus 로고
    • A new discretization methodology for diffusion problems on generalized polyhedral meshes
    • Brezzi F., Lipnikov K., Shashkov M., Simoncini V. A new discretization methodology for diffusion problems on generalized polyhedral meshes. Comput. Methods Appl. Mech. Eng. 2007, 196:3682-3692.
    • (2007) Comput. Methods Appl. Mech. Eng. , vol.196 , pp. 3682-3692
    • Brezzi, F.1    Lipnikov, K.2    Shashkov, M.3    Simoncini, V.4
  • 14
    • 25144443045 scopus 로고    scopus 로고
    • A family of mimetic finite difference methods on polygonal and polyhedral meshes
    • Brezzi F., Lipnikov K., Simoncini V. A family of mimetic finite difference methods on polygonal and polyhedral meshes. Math. Models Methods Appl. Sci. 2005, 15:1533-1553.
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1533-1553
    • Brezzi, F.1    Lipnikov, K.2    Simoncini, V.3
  • 15
    • 0035922232 scopus 로고    scopus 로고
    • A tensor artificial viscosity using a mimetic finite difference algorithm
    • Campbell J.C., Shashkov M.J. A tensor artificial viscosity using a mimetic finite difference algorithm. J. Comput. Phys. 2001, 172(2):739-765.
    • (2001) J. Comput. Phys. , vol.172 , Issue.2 , pp. 739-765
    • Campbell, J.C.1    Shashkov, M.J.2
  • 16
    • 36949012302 scopus 로고    scopus 로고
    • Flux reconstruction and pressure post-processing in mimetic finite difference methods
    • Cangiani A., Manzini G. Flux reconstruction and pressure post-processing in mimetic finite difference methods. Comput. Methods Appl. Mech. Eng. 2008, 197(9-12):933-945.
    • (2008) Comput. Methods Appl. Mech. Eng. , vol.197 , Issue.9-12 , pp. 933-945
    • Cangiani, A.1    Manzini, G.2
  • 17
    • 84863818794 scopus 로고    scopus 로고
    • Convergence analysis of the mimetic finite difference method for elliptic problems
    • Cangiani A., Manzini G., Russo A. Convergence analysis of the mimetic finite difference method for elliptic problems. SIAM J. Numer. Anal. 2009, 47(4):2612-2637.
    • (2009) SIAM J. Numer. Anal. , vol.47 , Issue.4 , pp. 2612-2637
    • Cangiani, A.1    Manzini, G.2    Russo, A.3
  • 19
    • 67649319152 scopus 로고    scopus 로고
    • A 3D discrete duality finite volume method for non linear elliptic problem, in: A. Handlovicov, P. Frolkovic, K. Mikula, D. Sevcovic (Eds.), Proceedings of Algoritmy 2009
    • Y. Coudière, F. Hubert, A 3D discrete duality finite volume method for non linear elliptic problem, in: A. Handlovicov, P. Frolkovic, K. Mikula, D. Sevcovic (Eds.), Proceedings of Algoritmy 2009, 2009, pp. 51-60.
    • (2009) , pp. 51-60
    • Coudière, Y.1    Hubert, F.2
  • 20
    • 77649097647 scopus 로고    scopus 로고
    • The discrete duality finite volume method for convection-diffusion problems
    • Coudière Y., Manzini G. The discrete duality finite volume method for convection-diffusion problems. SIAM J. Numer. Anal. 2010, 47(6):4163-4192.
    • (2010) SIAM J. Numer. Anal. , vol.47 , Issue.6 , pp. 4163-4192
    • Coudière, Y.1    Manzini, G.2
  • 21
    • 46949102178 scopus 로고    scopus 로고
    • A discrete duality finite volume approach to Hodge decomposition and div-curl problems on almost arbitrary two-dimensional meshes
    • Delcourte S., Domelevo K., Omnes P. A discrete duality finite volume approach to Hodge decomposition and div-curl problems on almost arbitrary two-dimensional meshes. SIAM J. Numer. Anal. 2007, 45(3):1142-1174.
    • (2007) SIAM J. Numer. Anal. , vol.45 , Issue.3 , pp. 1142-1174
    • Delcourte, S.1    Domelevo, K.2    Omnes, P.3
  • 22
    • 33750488420 scopus 로고    scopus 로고
    • A mixed finite volume scheme for anisotropic diffusion problems on any grid
    • Droniou J., Eymard R. A mixed finite volume scheme for anisotropic diffusion problems on any grid. Numer. Math. 2006, 105(1):35-71.
    • (2006) Numer. Math. , vol.105 , Issue.1 , pp. 35-71
    • Droniou, J.1    Eymard, R.2
  • 23
    • 77951574038 scopus 로고    scopus 로고
    • A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods
    • Droniou J., Eymard R., Gallouët T., Herbin R. A unified approach to mimetic finite difference, hybrid finite volume and mixed finite volume methods. Math. Models Methods Appl. Sci. (M3AS) 2010, 20(2):265-295.
    • (2010) Math. Models Methods Appl. Sci. (M3AS) , vol.20 , Issue.2 , pp. 265-295
    • Droniou, J.1    Eymard, R.2    Gallouët, T.3    Herbin, R.4
  • 24
    • 77956592107 scopus 로고    scopus 로고
    • Discretization of heterogeneous and anisotropic diffusion problems on general non-conforming meshes, SUSHI: a scheme using stabilisation and hybrid interfaces, doi:10.1093/imanum/drn084
    • R. Eymard, T. Gallouët, R. Herbin, Discretization of heterogeneous and anisotropic diffusion problems on general non-conforming meshes, SUSHI: a scheme using stabilisation and hybrid interfaces, 2009. doi:10.1093/imanum/drn084.
    • (2009)
    • Eymard, R.1    Gallouët, T.2    Herbin, R.3
  • 26
    • 50249099733 scopus 로고    scopus 로고
    • High-order mimetic finite difference method for diffusion problems on polygonal meshes
    • Gyrya V., Lipnikov K. High-order mimetic finite difference method for diffusion problems on polygonal meshes. J. Comput. Phys. 2008, 227:8841-8854.
    • (2008) J. Comput. Phys. , vol.227 , pp. 8841-8854
    • Gyrya, V.1    Lipnikov, K.2
  • 27
    • 67649340811 scopus 로고    scopus 로고
    • A finite volume method for approximating 3d diffusion operators on general meshes
    • Hermeline F. A finite volume method for approximating 3d diffusion operators on general meshes. J. Comput. Phys. 2009, 228(16):5763-5786.
    • (2009) J. Comput. Phys. , vol.228 , Issue.16 , pp. 5763-5786
    • Hermeline, F.1
  • 28
    • 0035788953 scopus 로고    scopus 로고
    • Discrete Hodge operators
    • Hiptmair R. Discrete Hodge operators. Numer. Math. 2001, 90(2):265-289.
    • (2001) Numer. Math. , vol.90 , Issue.2 , pp. 265-289
    • Hiptmair, R.1
  • 29
    • 84875677944 scopus 로고    scopus 로고
    • Mimetic discretisations of Maxwell's equations and the equations of magnetic diffusion
    • Hyman J., Shashkov M. Mimetic discretisations of Maxwell's equations and the equations of magnetic diffusion. Prog. Electromagnet. Res. 2001, 32:89-121.
    • (2001) Prog. Electromagnet. Res. , vol.32 , pp. 89-121
    • Hyman, J.1    Shashkov, M.2
  • 30
    • 0031333803 scopus 로고    scopus 로고
    • Adjoint operators for the natural discretizations of the divergence gradient and curl on logically rectangular grids
    • Hyman J.M., Shashkov M. Adjoint operators for the natural discretizations of the divergence gradient and curl on logically rectangular grids. Appl. Numer. Math. 1997, 25(4):413-442.
    • (1997) Appl. Numer. Math. , vol.25 , Issue.4 , pp. 413-442
    • Hyman, J.M.1    Shashkov, M.2
  • 31
    • 0031071242 scopus 로고    scopus 로고
    • Natural discretizations of the divergence gradient and curl on logically rectangular grids
    • Hyman J.M., Shashkov M. Natural discretizations of the divergence gradient and curl on logically rectangular grids. Comput. Math. Appl. 1997, 33(4):81-104.
    • (1997) Comput. Math. Appl. , vol.33 , Issue.4 , pp. 81-104
    • Hyman, J.M.1    Shashkov, M.2
  • 32
    • 0002058288 scopus 로고    scopus 로고
    • The orthogonal decomposition theorems for mimetic finite difference methods
    • Hyman J.M., Shashkov M. The orthogonal decomposition theorems for mimetic finite difference methods. SIAM J. Numer. Anal. 1999, 36(3):788-818.
    • (1999) SIAM J. Numer. Anal. , vol.36 , Issue.3 , pp. 788-818
    • Hyman, J.M.1    Shashkov, M.2
  • 33
    • 0038136552 scopus 로고    scopus 로고
    • New mixed finite element method on polygonal and polyhedral meshes
    • Kuznetsov Yu., Repin S. New mixed finite element method on polygonal and polyhedral meshes. Russ. J. Numer. Anal. Math. Model. 2003, 18(3):261-278.
    • (2003) Russ. J. Numer. Anal. Math. Model. , vol.18 , Issue.3 , pp. 261-278
    • Kuznetsov, Y.1    Repin, S.2
  • 35
    • 33750701771 scopus 로고    scopus 로고
    • A family of H1-conforming finite element spaces for calculations on 3D grids with pinch-outs
    • Lyons S.L., Parashkevov R.R., Wu X.H. A family of H1-conforming finite element spaces for calculations on 3D grids with pinch-outs. Numer. Linear Algebra Appl. 2006, 13(9):789-799.
    • (2006) Numer. Linear Algebra Appl. , vol.13 , Issue.9 , pp. 789-799
    • Lyons, S.L.1    Parashkevov, R.R.2    Wu, X.H.3
  • 37
    • 0031570250 scopus 로고    scopus 로고
    • An analysis of finite volume, finite element, and finite difference methods using some concepts of algebraic topology
    • Matiussi C. An analysis of finite volume, finite element, and finite difference methods using some concepts of algebraic topology. J. Comput. Phys. 1997, 133:289-309.
    • (1997) J. Comput. Phys. , vol.133 , pp. 289-309
    • Matiussi, C.1
  • 39
    • 34250103285 scopus 로고
    • A new family of mixed finite elements in R3
    • Nédélec J.-C. A new family of mixed finite elements in R3. Numer. Math. 1986, 50(1):57-81.
    • (1986) Numer. Math. , vol.50 , Issue.1 , pp. 57-81
    • Nédélec, J.-C.1
  • 40
    • 0032361315 scopus 로고    scopus 로고
    • Convergence analysis of a covolume scheme for Maxwell's equations in three dimensions
    • Nicolaides R.A., Wang D.-Q. Convergence analysis of a covolume scheme for Maxwell's equations in three dimensions. Math. Comput. 1998, 67(223):947-963.
    • (1998) Math. Comput. , vol.67 , Issue.223 , pp. 947-963
    • Nicolaides, R.A.1    Wang, D.-Q.2
  • 41
    • 0026822185 scopus 로고
    • Direct discretization of planar div-curl problems
    • Nicolaides R.A. Direct discretization of planar div-curl problems. SIAM J. Numer. Anal. 1992, 29(1):32-56.
    • (1992) SIAM J. Numer. Anal. , vol.29 , Issue.1 , pp. 32-56
    • Nicolaides, R.A.1
  • 42
    • 0001389991 scopus 로고    scopus 로고
    • Covolume solutions of three-dimensional div-curl equations
    • Nicolaides R.A., Wu X. Covolume solutions of three-dimensional div-curl equations. SIAM J. Numer. Anal. 1997, 34(6):2195-2203.
    • (1997) SIAM J. Numer. Anal. , vol.34 , Issue.6 , pp. 2195-2203
    • Nicolaides, R.A.1    Wu, X.2
  • 43
    • 33750299447 scopus 로고    scopus 로고
    • Higher-order mimetic methods for unstructured meshes
    • Perot J.B., Subramanian V. Higher-order mimetic methods for unstructured meshes. J. Comput. Phys. 2006, 219(1):68-85.
    • (2006) J. Comput. Phys. , vol.219 , Issue.1 , pp. 68-85
    • Perot, J.B.1    Subramanian, V.2
  • 44
    • 0030525010 scopus 로고    scopus 로고
    • Solving diffusion equations with rough coefficients in rough grids
    • Shashkov M., Steinberg S. Solving diffusion equations with rough coefficients in rough grids. J. Comput. Phys. 1996, 129(2):383-405.
    • (1996) J. Comput. Phys. , vol.129 , Issue.2 , pp. 383-405
    • Shashkov, M.1    Steinberg, S.2
  • 45
    • 84976700678 scopus 로고
    • Reentrant polygon clipping
    • Sutherland I.E., Hodgman G.W. Reentrant polygon clipping. Commun. ACM 1974, 17(1):32-42.
    • (1974) Commun. ACM , vol.17 , Issue.1 , pp. 32-42
    • Sutherland, I.E.1    Hodgman, G.W.2
  • 46
    • 34447504567 scopus 로고    scopus 로고
    • Application of polygonal finite elements in linear elasticity
    • Tabarraei A., Sukumar N. Application of polygonal finite elements in linear elasticity. Int. J. Comput. Methods 2006, 3(4):503-520.
    • (2006) Int. J. Comput. Methods , vol.3 , Issue.4 , pp. 503-520
    • Tabarraei, A.1    Sukumar, N.2
  • 47
    • 35448995164 scopus 로고    scopus 로고
    • Extended finite element method on polygonal and quadtree meshes
    • Tabarraei A., Sukumar N. Extended finite element method on polygonal and quadtree meshes. Comput. Methods Appl. Mech. Eng. 2007, 197(5):425-438.
    • (2007) Comput. Methods Appl. Mech. Eng. , vol.197 , Issue.5 , pp. 425-438
    • Tabarraei, A.1    Sukumar, N.2
  • 48
    • 55049089695 scopus 로고    scopus 로고
    • Inner products in covolume and mimetic methods
    • Trapp K.A. Inner products in covolume and mimetic methods. M2AN: Math. Model. Numer. Anal. 2008, 42:941-959.
    • (2008) M2AN: Math. Model. Numer. Anal. , vol.42 , pp. 941-959
    • Trapp, K.A.1
  • 49
    • 84894021661 scopus 로고
    • Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media
    • Yee K.S. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE T. Antenn. Propag. 1966, 14:302-307.
    • (1966) IEEE T. Antenn. Propag. , vol.14 , pp. 302-307
    • Yee, K.S.1


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