메뉴 건너뛰기




Volumn 187, Issue 3-4, 2000, Pages 365-383

A discrete operator calculus for finite difference approximations

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONTINUUM MECHANICS; DATA STRUCTURES; EQUATIONS OF STATE OF GASES; EQUATIONS OF STATE OF SOLIDS; FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; TENSORS; VECTORS;

EID: 0034235159     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(00)80001-8     Document Type: Article
Times cited : (69)

References (49)
  • 1
    • 0040599659 scopus 로고
    • The Convergence of difference Schemes for two-dimensional equations of acoustics and Maxwell's equations
    • Ardelyan N.V. The Convergence of difference Schemes for two-dimensional equations of acoustics and Maxwell's equations. USSR Comput. Math. Math. Phys. 23:1983;93-99.
    • (1983) USSR Comput. Math. Math. Phys. , vol.23 , pp. 93-99
    • Ardelyan, N.V.1
  • 2
    • 0343457031 scopus 로고
    • Convergence of difference schemes for two-dimensional gas-dynamic equations in acoustics approximations with gravitation taken into account
    • Ardelyan N.V., Chernigovskii S.V. Convergence of difference schemes for two-dimensional gas-dynamic equations in acoustics approximations with gravitation taken into account. Diff. Eqns. 28:1988;57-63.
    • (1988) Diff. Eqns. , vol.28 , pp. 57-63
    • Ardelyan, N.V.1    Chernigovskii, S.V.2
  • 3
    • 0343457032 scopus 로고
    • DPDC: A second-order monotone scheme for advection
    • Lawrence Livermore National Laboratory
    • Beason C.W., Margolin L.G. DPDC: a second-order monotone scheme for advection. Report UCRL-99731. 1988;Lawrence Livermore National Laboratory.
    • (1988) Report UCRL-99731
    • Beason, C.W.1    Margolin, L.G.2
  • 4
    • 0026923198 scopus 로고
    • Computational methods in Lagrangian and Eulerian hydrocodes
    • See in particular p. 250 (Eq. 2.4.2.6.).
    • Benson D.J. Computational methods in Lagrangian and Eulerian hydrocodes. Comput. Meth. Appl. Mech. Eng. 99:1991;235-394. See in particular p. 250 (Eq. 2.4.2.6.).
    • (1991) Comput. Meth. Appl. Mech. Eng. , vol.99 , pp. 235-394
    • Benson, D.J.1
  • 5
    • 0041587520 scopus 로고
    • The pressure term in the anelastic model: A symmetric elliptic solver for a C-Arakawa grid in generalized coordinates
    • Bernardet P. The pressure term in the anelastic model: a symmetric elliptic solver for a C-Arakawa grid in generalized coordinates. Mon. Wea. Rev. 123:1995;2474.
    • (1995) Mon. Wea. Rev. , vol.123 , pp. 2474
    • Bernardet, P.1
  • 6
    • 0000890297 scopus 로고    scopus 로고
    • Elimination of artificial grid distortion and hourglass-type motions by means of Lagrangian subzonal masses and pressures
    • Caramana E.J., Shashkov M.J. Elimination of artificial grid distortion and hourglass-type motions by means of Lagrangian subzonal masses and pressures. J. Comput. Phys. 142:1998;521-561.
    • (1998) J. Comput. Phys. , vol.142 , pp. 521-561
    • Caramana, E.J.1    Shashkov, M.J.2
  • 7
    • 0001840838 scopus 로고    scopus 로고
    • Formulation of artificial viscosity for multi-dimensional shock wave problems
    • Caramana E.J., Shashkov M.J., Whalen P.P. Formulation of artificial viscosity for multi-dimensional shock wave problems. J. Comput. Phys. 144:1998;70-97.
    • (1998) J. Comput. Phys. , vol.144 , pp. 70-97
    • Caramana, E.J.1    Shashkov, M.J.2    Whalen, P.P.3
  • 8
    • 0000142136 scopus 로고    scopus 로고
    • The construction of compatible hydrodynamics algorithms utilizing conservation of total energy
    • Caramana E.J., Burton D.E., Shashkov M.J., Whalen P.P. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy. J. Comput. Phys. 146:1998;227-262.
    • (1998) J. Comput. Phys. , vol.146 , pp. 227-262
    • Caramana, E.J.1    Burton, D.E.2    Shashkov, M.J.3    Whalen, P.P.4
  • 10
    • 0000935266 scopus 로고
    • A difference scheme for numerical computation of discontinuous solutions of equations in fluid dynamics
    • Godunov S.K. A difference scheme for numerical computation of discontinuous solutions of equations in fluid dynamics. Math. Sbornik. 47:1959;271-306.
    • (1959) Math. Sbornik , vol.47 , pp. 271-306
    • Godunov, S.K.1
  • 12
    • 0003753516 scopus 로고
    • Time Dependent Problems and Difference Methods
    • New York: Wiley/Interscience
    • Gustafsson B., Kreiss H.O., Oliger J. Time Dependent Problems and Difference Methods. Chapter 11. 1995;445-495 Wiley/Interscience, New York.
    • (1995) Chapter 11 , pp. 445-495
    • Gustafsson, B.1    Kreiss, H.O.2    Oliger, J.3
  • 13
    • 33749725182 scopus 로고
    • Uniformly high-order accurate essentially non-oscillatory schemes III
    • Harten A., Engquist B., Osher S., Chakravarthy S.R. Uniformly high-order accurate essentially non-oscillatory schemes III. J. Comput. Phys. 71:1987;231-303.
    • (1987) J. Comput. Phys. , vol.71 , pp. 231-303
    • Harten, A.1    Engquist, B.2    Osher, S.3    Chakravarthy, S.R.4
  • 14
    • 17144456156 scopus 로고
    • An arbitrary Lagrangian-Eulerian computing method for all flow speeds
    • Hirt C.W., Amsden A.A., Cook J.L. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14:1974;227.
    • (1974) J. Comput. Phys. , vol.14 , pp. 227
    • Hirt, C.W.1    Amsden, A.A.2    Cook, J.L.3
  • 15
    • 0000536753 scopus 로고    scopus 로고
    • The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
    • Hyman J., Shashkov M., Steinberg S. The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials. J. Comput. Phys. 132:1997;130-148.
    • (1997) J. Comput. Phys. , vol.132 , pp. 130-148
    • Hyman, J.1    Shashkov, M.2    Steinberg, S.3
  • 16
    • 0031071242 scopus 로고    scopus 로고
    • Natural discretizations for the divergence, gradient, and curl on logically rectangular grids
    • Hyman J.M., Shashkov M. Natural discretizations for the divergence, gradient, and curl on logically rectangular grids. Comput. Math. Appl. 33:1997;81-104.
    • (1997) Comput. Math. Appl. , vol.33 , pp. 81-104
    • Hyman, J.M.1    Shashkov, M.2
  • 17
    • 0031333803 scopus 로고    scopus 로고
    • The adjoint operators for natural discretizations for the divergence gradient and curl on logically rectangular grids
    • Hyman J.M., Shashkov M. The adjoint operators for natural discretizations for the divergence gradient and curl on logically rectangular grids. IMACS J. Appl. Numer. Math. 25:1997;413-442.
    • (1997) IMACS J. Appl. Numer. Math. , vol.25 , pp. 413-442
    • Hyman, J.M.1    Shashkov, M.2
  • 18
    • 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. 36:1999;788-818.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 788-818
    • Hyman, J.M.1    Shashkov, M.2
  • 19
    • 0032167141 scopus 로고    scopus 로고
    • The approximation of boundary conditions for mimetic finite difference methods
    • Hyman J.M., Shashkov M. The approximation of boundary conditions for mimetic finite difference methods. Comput. Math. Appl. 36:1998;79-99.
    • (1998) Comput. Math. Appl. , vol.36 , pp. 79-99
    • Hyman, J.M.1    Shashkov, M.2
  • 20
    • 0000397429 scopus 로고    scopus 로고
    • Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion
    • Hyman J.M., Shashkov M. Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion. J. Comput. Phys. 151:1999;881-909.
    • (1999) J. Comput. Phys. , vol.151 , pp. 881-909
    • Hyman, J.M.1    Shashkov, M.2
  • 21
    • 0343457022 scopus 로고    scopus 로고
    • Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion
    • DeSanto J.A. Golden, Colorado: SIAM, Philadelphai. Mathematical and and Numerical Aspects of Wave Propagations
    • Hyman J.M., Shashkov M. Mimetic discretizations for Maxwell's equations and equations of magnetic diffusion. DeSanto J.A. Proceedings of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation. 1-5 June 1998;561-563 SIAM, Philadelphai, Golden, Colorado. Mathematical and and Numerical Aspects of Wave Propagations.
    • (1998) Proceedings of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation , pp. 561-563
    • Hyman, J.M.1    Shashkov, M.2
  • 22
    • 0011654556 scopus 로고
    • Variational approach to the construction of finite-difference schemes for the diffusion equations for magnetic field
    • Korshiya T., Tishkin V., Favorskii A., Shashkov M. Variational approach to the construction of finite-difference schemes for the diffusion equations for magnetic field. Diff. Eqns. 18:1982;863-872.
    • (1982) Diff. Eqns. , vol.18 , pp. 863-872
    • Korshiya, T.1    Tishkin, V.2    Favorskii, A.3    Shashkov, M.4
  • 23
    • 0011601576 scopus 로고
    • A variational approach to the construction of difference schemes on curvilinear meshes for the heat-conduction equation
    • Korshiya T., Tishkin V., Favorskii A., Shashkov M. A variational approach to the construction of difference schemes on curvilinear meshes for the heat-conduction equation. USSR Comput. Maths. Math. Phys. 20:1980;135-155.
    • (1980) USSR Comput. Maths. Math. Phys. , vol.20 , pp. 135-155
    • Korshiya, T.1    Tishkin, V.2    Favorskii, A.3    Shashkov, M.4
  • 24
    • 0342587095 scopus 로고
    • Turbulence modeling in the SHALE code
    • Lawrence Livermore National Laboratory
    • Leith C.E., Margolin L.G. Turbulence modeling in the SHALE code. Report UCRL-ID-103271. 1990;Lawrence Livermore National Laboratory.
    • (1990) USSR Comput. Maths. Math. Phys.
    • Leith, C.E.1    Margolin, L.G.2
  • 25
    • 0000030024 scopus 로고    scopus 로고
    • Introduction to an arbitrary Lagrangian-Eulerian computing methods for all flow speeds
    • Margolin L.G. Introduction to an arbitrary Lagrangian-Eulerian computing methods for all flow speeds. J. Comput. Phys. 135:1997;198-202.
    • (1997) J. Comput. Phys. , vol.135 , pp. 198-202
    • Margolin, L.G.1
  • 26
    • 0039769455 scopus 로고
    • Spatial differencing for finite difference codes
    • Los Alamos National Laboratory
    • Margolin L.G., Adams T.F. Spatial differencing for finite difference codes. Report LA-10249. 1985;Los Alamos National Laboratory.
    • (1985) Report LA-10249
    • Margolin, L.G.1    Adams, T.F.2
  • 27
    • 0342587089 scopus 로고
    • Antidifussive velocities for multipass donor cell advection
    • Report UCID-21866. Lawrence Livermore National Laboratory. to appear.
    • Margolin L.G., Smolarkiewicz P.K. Antidifussive velocities for multipass donor cell advection. Report UCID-21866 SIAM J. Sci. Comput. 1989;Lawrence Livermore National Laboratory. to appear.
    • (1989) SIAM J. Sci. Comput.
    • Margolin, L.G.1    Smolarkiewicz, P.K.2
  • 29
    • 0001965060 scopus 로고    scopus 로고
    • A Local Support-operator diffusion discretization scheme for quadrilateral r-z meshes
    • Morel J.E., Roberts R.M., Shashkov M. A Local Support-operator diffusion discretization scheme for quadrilateral r-z meshes. J. Comput. Phys. 144:1998;17-51.
    • (1998) J. Comput. Phys. , vol.144 , pp. 17-51
    • Morel, J.E.1    Roberts, R.M.2    Shashkov, M.3
  • 30
    • 0040599653 scopus 로고
    • Stability of variational-difference schemes for the problems of gas-dynamics with heat conduction
    • Sabitova A., Samarskaya E.A. Stability of variational-difference schemes for the problems of gas-dynamics with heat conduction. Diff. Eqns. 21:1985;861-864.
    • (1985) Diff. Eqns. , vol.21 , pp. 861-864
    • Sabitova, A.1    Samarskaya, E.A.2
  • 31
    • 0040006469 scopus 로고
    • Employment of the reference-operations method in the construction of finite-difference analogs of tensor operators
    • Samarskii A., Tishkin V., Favorskii A., Shashkov M. Employment of the reference-operations method in the construction of finite-difference analogs of tensor operators. Diff. Eqns. 18:1982;881-885.
    • (1982) Diff. Eqns. , vol.18 , pp. 881-885
    • Samarskii, A.1    Tishkin, V.2    Favorskii, A.3    Shashkov, M.4
  • 33
    • 0001367435 scopus 로고
    • Support-operators finite-difference algorithms for general elliptic problems
    • Shashkov M., Steinberg S. Support-operators finite-difference algorithms for general elliptic problems. J. Comput. Phys. 118:1995;131-151.
    • (1995) J. Comput. Phys. , vol.118 , pp. 131-151
    • Shashkov, M.1    Steinberg, S.2
  • 35
    • 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. 129:1996;383-405.
    • (1996) J. Comput. Phys. , vol.129 , pp. 383-405
    • Shashkov, M.1    Steinberg, S.2
  • 36
    • 0020918558 scopus 로고
    • A simple positive definite advection scheme with small implicit diffusion
    • Smolarkiewicz P.K. A simple positive definite advection scheme with small implicit diffusion. Mon. Wea. Rev. 111:1983;479-486.
    • (1983) Mon. Wea. Rev. , vol.111 , pp. 479-486
    • Smolarkiewicz, P.K.1
  • 37
    • 0001097416 scopus 로고
    • A fully multidimensional positive difinite advection transport algorithm with small implicit diffusion
    • Smolarkiewicz P.K. A fully multidimensional positive difinite advection transport algorithm with small implicit diffusion. J. Comput. Phys. 54:1984;325-362.
    • (1984) J. Comput. Phys. , vol.54 , pp. 325-362
    • Smolarkiewicz, P.K.1
  • 38
    • 33749522108 scopus 로고
    • The multidimensional positive definite advection transport algorithm: Further development and applications
    • Smolarkiewicz P.S., Clark T.L. The multidimensional positive definite advection transport algorithm: further development and applications. J. Comput. Phys. 67:1986;396-438.
    • (1986) J. Comput. Phys. , vol.67 , pp. 396-438
    • Smolarkiewicz, P.S.1    Clark, T.L.2
  • 39
    • 0026273789 scopus 로고
    • On forward-in-time differencing for fluids
    • Smolarkiewicz P.K. On forward-in-time differencing for fluids. Mon. Wea. Rev. 119:1991;2505-2510.
    • (1991) Mon. Wea. Rev. , vol.119 , pp. 2505-2510
    • Smolarkiewicz, P.K.1
  • 40
    • 0000686029 scopus 로고
    • A class of monotone interpolation schemes
    • Smolarkiewicz P.K., Grell G.A. A class of monotone interpolation schemes. J. Comput. Phys. 101:1992;431-440.
    • (1992) J. Comput. Phys. , vol.101 , pp. 431-440
    • Smolarkiewicz, P.K.1    Grell, G.A.2
  • 41
    • 0027795504 scopus 로고
    • On forward-in-time differencing for fluids: Extension to a curvilinear framework
    • Smolarkiewicz P.K., Margolin L.G. On forward-in-time differencing for fluids: extension to a curvilinear framework. Mon. Wea. Rev. 121:1993;1847-1859.
    • (1993) Mon. Wea. Rev. , vol.121 , pp. 1847-1859
    • Smolarkiewicz, P.K.1    Margolin, L.G.2
  • 42
    • 77953525929 scopus 로고    scopus 로고
    • On forward-in-time differencing for fluids: An Eulerian/semi-Lagrangian nonhydrostatic model for stratified flows
    • Smolarkiewicz P.K., Margolin L.G. On forward-in-time differencing for fluids: an Eulerian/semi-Lagrangian nonhydrostatic model for stratified flows. Atmos-Ocean Special. 35:1997;127-157.
    • (1997) Atmos-Ocean Special , vol.35 , pp. 127-157
    • Smolarkiewicz, P.K.1    Margolin, L.G.2
  • 43
    • 0000037511 scopus 로고
    • The multidimensional positive definite advection transport algorithm: Nonoscillatory option
    • Smolarkiewicz P.K., Grabowski W.W. The multidimensional positive definite advection transport algorithm: nonoscillatory option. J. Comput. Phys. 86:1990;355.
    • (1990) J. Comput. Phys. , vol.86 , pp. 355
    • Smolarkiewicz, P.K.1    Grabowski, W.W.2
  • 44
    • 0001567858 scopus 로고    scopus 로고
    • MPDATA: A finite-difference solver for geophysical flows
    • Smolarkiewicz P.K., Margolin L.G. MPDATA: a finite-difference solver for geophysical flows. J. Comput. Phys. 140:1998;459.
    • (1998) J. Comput. Phys. , vol.140 , pp. 459
    • Smolarkiewicz, P.K.1    Margolin, L.G.2
  • 45
    • 0001518684 scopus 로고
    • On the construction and comparison of difference schemes
    • Strang G. On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5:1968;506.
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 506
    • Strang, G.1
  • 46
    • 0021513424 scopus 로고
    • High resolution schemes using flux limiters for hyperbolic conservation laws
    • Sweby P.K. High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21:1984;995-1011.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 995-1011
    • Sweby, P.K.1
  • 47
    • 0342587081 scopus 로고
    • CSQ - A two-dimensional hydrodynamic program with energy flow and material strength
    • Sandia National Laboratories
    • Thompson S.L. CSQ - a two-dimensional hydrodynamic program with energy flow and material strength. Report SAND74-0122. 1974;Sandia National Laboratories.
    • (1974) Report SAND74-0122
    • Thompson, S.L.1
  • 48
    • 0001440358 scopus 로고
    • A standard test set for numerical approximations to the shallow water equations on the sphere
    • Williamson D.L., Drake J.B., Hack J.J., Jakob R., Swarztrauber P.N. A standard test set for numerical approximations to the shallow water equations on the sphere. J. Comput. Phys. 102:1992;211-224.
    • (1992) J. Comput. Phys. , vol.102 , pp. 211-224
    • Williamson, D.L.1    Drake, J.B.2    Hack, J.J.3    Jakob, R.4    Swarztrauber, P.N.5
  • 49
    • 3743101779 scopus 로고
    • Fully multidimensional flux-corrected transport algorithms for fluids
    • Zalesak S.T. Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys. 31:1979;335-362.
    • (1979) J. Comput. Phys. , vol.31 , pp. 335-362
    • Zalesak, S.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.