메뉴 건너뛰기




Volumn 19, Issue 8, 2013, Pages 1386-1404

The Helmholtz-Hodge decomposition - A survey

Author keywords

boundary conditions; Helmholtz Hodge decomposition; incompressibility; Vector fields

Indexed keywords

CURL-FREE COMPONENTS; FUNDAMENTAL THEOREMS; HELMHOLTZ-HODGE DECOMPOSITION; INCOMPRESSIBILITY; RESEARCH COMMUNITIES; TOPOLOGICAL ANALYSIS; TRANSFER OF KNOWLEDGE; VECTOR FIELDS;

EID: 84879233699     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/TVCG.2012.316     Document Type: Review
Times cited : (269)

References (102)
  • 2
    • 34447282031 scopus 로고    scopus 로고
    • A primal formulation for the helmholtz decomposition
    • E. Ahusborde, M. Azaiez, and J.-P. Caltagirone, "A Primal Formulation for the Helmholtz Decomposition," J. Computational Physics, vol. 225, no. 1, pp. 13-19, 2007.
    • (2007) J. Computational Physics , vol.225 , Issue.1 , pp. 13-19
    • Ahusborde, E.1    Azaiez, M.2    Caltagirone, J.-P.3
  • 4
    • 79952313965 scopus 로고    scopus 로고
    • Regularisation of the helmholtz decomposition and its application to geomagnetic field modelling
    • M. Akram and V. Michel, "Regularisation of the Helmholtz Decomposition and its Application to Geomagnetic Field Modelling," Int'l J. Geomath., vol. 1, no. 1, pp. 101-120, 2010.
    • (2010) Int'l J. Geomath. , vol.1 , Issue.1 , pp. 101-120
    • Akram, M.1    Michel, V.2
  • 6
    • 0039955832 scopus 로고
    • Grobli's solution of the three- vortex problem
    • H. Aref, N. Rott, and H. Thomann, "Grobli's Solution of the Three- Vortex Problem," Ann. Rev. Fluid Mechanics, vol. 24, pp. 1-21, 1992.
    • (1992) Ann. Rev. Fluid Mechanics , vol.24 , pp. 1-21
    • Aref, H.1    Rott, N.2    Thomann, H.3
  • 8
    • 0009964350 scopus 로고
    • Potential representation of incompressible vector fields
    • SIAM
    • G. Auchmuty, "Potential Representation of Incompressible Vector Fields," Nonlinear Problems in Applied Mathematics, pp. 43-49, SIAM, 1995.
    • (1995) Nonlinear Problems in Applied Mathematics , pp. 43-49
    • Auchmuty, G.1
  • 9
    • 0001608079 scopus 로고
    • A second order projection method for the incompressible navier-stokes equations
    • J.B. Bell, P. Colella, and H.M. Glaz, "A Second Order Projection Method for the Incompressible Navier-Stokes Equations," J. Computational Physics, vol. 85, pp. 257-283, 1989.
    • (1989) J. Computational Physics , vol.85 , pp. 257-283
    • Bell, J.B.1    Colella, P.2    Glaz, H.M.3
  • 10
    • 0001373981 scopus 로고
    • A second-order projection method for variable-density flows
    • J.B. Bell and D.L. Marcus, "A Second-Order Projection Method for Variable-Density Flows," J. Computational Physics, vol. 101, pp. 334-348, 1992.
    • (1992) J. Computational Physics , vol.101 , pp. 334-348
    • Bell, J.B.1    Marcus, D.L.2
  • 12
    • 0043160823 scopus 로고
    • Uber die zerlegung unendlicher vektorfelder
    • O. Blumenthal, "Uber Die Zerlegung Unendlicher Vektorfelder," Mathematische Annalen, vol. 61, no. 2, 235-250, 1905.
    • (1905) Mathematische Annalen , vol.61 , Issue.2 , pp. 235-250
    • Blumenthal, O.1
  • 13
    • 0026105813 scopus 로고
    • Tomographic reconstruction of vector fields
    • Feb
    • H. Braun and A. Hauck, "Tomographic Reconstruction of Vector Fields," IEEE Trans. Signal Processing, vol. 39, no. 2, pp. 464-471, Feb. 1991.
    • (1991) IEEE Trans. Signal Processing , vol.39 , Issue.2 , pp. 464-471
    • Braun, H.1    Hauck, A.2
  • 15
    • 0000135764 scopus 로고    scopus 로고
    • Accurate projection methods for the incompressible navier-stokes equations
    • DOI 10.1006/jcph.2001.6715, PII S0021999101967154
    • D.L. Brown, R. Cortez, and M.L. Minion, "Accurate Projection Methods for the Incompressible Navier-Stokes Equations," J. Computational Physics, vol. 168, pp. 464-499, 2001. (Pubitemid 33663736)
    • (2001) Journal of Computational Physics , vol.168 , Issue.2 , pp. 464-499
    • Brown, D.L.1    Cortez, R.2    Minion, M.L.3
  • 18
    • 0036341189 scopus 로고    scopus 로고
    • Vector calculus and the topology of domains in 3-space
    • J. Cantarella, D. DeTurck, and H. Gluck, "Vector Calculus and the Topology of Domains in 3-Space," Am. Math. Monthly, vol. 109, no. 5, pp. 409-442, 2002.
    • (2002) Am. Math. Monthly , vol.109 , Issue.5 , pp. 409-442
    • Cantarella, J.1    Deturck, D.2    Gluck, H.3
  • 19
    • 40449093496 scopus 로고
    • A numerical method for solving incompressible viscous flow problems
    • A.J. Chorin, "A Numerical Method for Solving Incompressible Viscous Flow Problems," J. Computational Physics, vol. 2, pp. 12-26, 1967.
    • (1967) J. Computational Physics , vol.2 , pp. 12-26
    • Chorin, A.J.1
  • 20
    • 84968510911 scopus 로고
    • Numerical solution of the navier-stokes equations
    • A.J. Chorin, "Numerical Solution of the Navier-Stokes Equations," Math. Computations, vol. 22, pp. 745-762, 1968.
    • (1968) Math. Computations , vol.22 , pp. 745-762
    • Chorin, A.J.1
  • 21
    • 84968483581 scopus 로고
    • On the convergence of discrete approximations to the navier-stokes equations
    • A.J. Chorin, "On the Convergence of Discrete Approximations to the Navier-Stokes equations," Math. Computations, vol. 23, pp. 341- 353, 1969.
    • (1969) Math. Computations , vol.23 , pp. 341-353
    • Chorin, A.J.1
  • 23
    • 33748415769 scopus 로고    scopus 로고
    • Computing a null divergence velocity field using smoothed particle hydrodynamics
    • DOI 10.1016/j.jcp.2006.01.021, PII S0021999106000295
    • F. Colin, R. Egli, and F. Lin, "Computing a Null Divergence Velocity Field Using Smoothed Particle Hydrodynamics," J. Computational Physics, vol. 217, no. 2, pp. 680-692, 2006. (Pubitemid 44340992)
    • (2006) Journal of Computational Physics , vol.217 , Issue.2 , pp. 680-692
    • Colin, F.1    Egli, R.2    Lin, F.Y.3
  • 25
    • 84980076280 scopus 로고
    • On the solution of nonlinear hyperbolic differential equations by finite differences
    • R. Courant, E. Isaacson, and M. Rees, "On the Solution of Nonlinear Hyperbolic Differential Equations by Finite Differences," Comm. Pure and Applied Math., vol. 5, pp. 243-255, 1952.
    • (1952) Comm. Pure and Applied Math. , vol.5 , pp. 243-255
    • Courant, R.1    Isaacson, E.2    Rees, M.3
  • 27
    • 0038596999 scopus 로고    scopus 로고
    • On the application of the Helmholtz-Hodge decomposition in projection methods for incompressible flows with general boundary conditions
    • DOI 10.1002/fld.598
    • F.M. Denaro, "On the Application of the Helmholtz-Hodge Decomposition in Projection Methods for Incompressible Flows with General Boundary Conditions," Int'l J. Numerical Methods in Fluids, vol. 43, pp. 43-69, 2003. (Pubitemid 37065756)
    • (2003) International Journal for Numerical Methods in Fluids , vol.43 , Issue.1 , pp. 43-69
    • Denaro, F.M.1
  • 28
    • 31744448320 scopus 로고    scopus 로고
    • Divergence-free and curl-free wavelets in two dimensions and three dimensions: Application to turbulent flows
    • DOI 10.1080/14685240500260547
    • E. Deriaz and V. Perrier, "Divergence-Free and Curl-Free Wavelets in 2D and 3D, Application to Turbuent Flows," J. Turbulence, vol. 7, no. 3, pp. 1-37, 2006. (Pubitemid 43174651)
    • (2006) Journal of Turbulence , vol.7 , pp. 1-37
    • Deriaz, E.1    Perrier, V.2
  • 29
    • 84865601057 scopus 로고    scopus 로고
    • Direct numerical simulation of turbulence using divergence-free wavelets
    • E. Deriaz and V. Perrier, "Direct Numerical Simulation of Turbulence Using Divergence-Free Wavelets," Multiscale Modeling and Simulation, vol. 7, no. 3, pp. 1101-1129, 2008.
    • (2008) Multiscale Modeling and Simulation , vol.7 , Issue.3 , pp. 1101-1129
    • Deriaz, E.1    Perrier, V.2
  • 30
    • 59649103603 scopus 로고    scopus 로고
    • Orthogonal helmholtz decomposition in arbitrary dimension using divergence-free and curl-free wavelets
    • E. Deriaz and V. Perrier, "Orthogonal Helmholtz Decomposition in Arbitrary Dimension using Divergence-Free and Curl-Free Wavelets," Applied and Computational Harmonic Analysis, vol. 26, no. 2, pp. 249-269, 2009.
    • (2009) Applied and Computational Harmonic Analysis , vol.26 , Issue.2 , pp. 249-269
    • Deriaz, E.1    Perrier, V.2
  • 31
    • 0000213656 scopus 로고
    • Projection method i: Convergence and numerical boundary layers
    • W. Weinan and J.G. Liu, "Projection Method I: Convergence and Numerical Boundary Layers," SIAM J. Numerical Analysis, vol. 32, no. 4, pp. 1017-1057, 1995.
    • (1995) SIAM J. Numerical Analysis , vol.32 , Issue.4 , pp. 1017-1057
    • Weinan, W.1    Liu, J.G.2
  • 36
    • 0001696546 scopus 로고
    • An lr theorem of the helmholtz decomposition of vector fields
    • D. Fujiwara and H. Morimoto, "An Lr Theorem of the Helmholtz Decomposition of Vector Fields," J. Faculty of Science, vol. 44, pp. 685-700, 1977.
    • (1977) J. Faculty of Science , vol.44 , pp. 685-700
    • Fujiwara, D.1    Morimoto, H.2
  • 39
    • 77955510600 scopus 로고    scopus 로고
    • The neumann problem and helmholtz decomposition in convex domains
    • J. Geng and Z. Shen, "The Neumann Problem and Helmholtz Decomposition in Convex Domains," J. Functional Analysis, vol. 259, pp. 2147-2164, 2010.
    • (2010) J. Functional Analysis , vol.259 , pp. 2147-2164
    • Geng, J.1    Shen, Z.2
  • 43
    • 13544263205 scopus 로고    scopus 로고
    • Efficient Hodge-Helmholtz decomposition of motion fields
    • DOI 10.1016/j.patrec.2004.08.008, PII S0167865504001886, ICARP 2003
    • Q. Guo, M.K. Mandal, and M.Y. Li, "Efficient Hodge-Helmholtz Decomposition of Motion Fields," Pattern Recognition Letters, vol. 26, no. 4, pp. 493-501, 2005. (Pubitemid 40220144)
    • (2005) Pattern Recognition Letters , vol.26 , Issue.4 , pp. 493-501
    • Guo, Q.1    Mandal, M.K.2    Li, M.Y.3
  • 44
    • 28444438458 scopus 로고    scopus 로고
    • Cardiac video analysis using Hodge-Helmholtz field decomposition
    • DOI 10.1016/j.compbiomed.2004.06.011, PII S001048250400109X
    • Q. Guo, M.K. Mandal, G. Liu, and K.M. Kavanagh, "Cardiac Video Analysis Using Hodge-Helmholtz Field Decomposition," Computers in Biology and Medicine, vol. 36, no. 1, pp. 1-20, 2006. (Pubitemid 41735393)
    • (2006) Computers in Biology and Medicine , vol.36 , Issue.1 , pp. 1-20
    • Guo, Q.1    Mandal, M.K.2    Liu, G.3    Kavanagh, K.M.4
  • 45
    • 13644274503 scopus 로고    scopus 로고
    • Stability of approximate projection methods on cell-centered grids
    • DOI 10.1016/j.jcp.2004.09.005, PII S0021999104003900
    • R. Guy and A. Fogelson, "Stability of Approximate Projection Methods on Cell-Centered Grids," J. Computational Physics, vol. 203, pp. 517-538, 2005. (Pubitemid 40233515)
    • (2005) Journal of Computational Physics , vol.203 , Issue.2 , pp. 517-538
    • Guy, R.D.1    Fogelson, A.L.2
  • 46
    • 33749190078 scopus 로고
    • Numerical calculation of time- dependent viscous incompressible flow of fluid with free surface
    • F.H. Harlow and J.E. Welch, "Numerical Calculation of Time- Dependent Viscous Incompressible Flow of Fluid with Free Surface," Physics of Fluids, vol. 8, no. 12, pp. 2182-2189, 1965.
    • (1965) Physics of Fluids , vol.8 , Issue.12 , pp. 2182-2189
    • Harlow, F.H.1    Welch, J.E.2
  • 48
    • 0009228516 scopus 로고
    • On the fundamental equations of electromagnetism
    • W. Hauser, "On the Fundamental Equations of Electromagnetism," Am. J. Physics, vol. 38, no. 1, pp. 80-85, 1970.
    • (1970) Am. J. Physics , vol.38 , Issue.1 , pp. 80-85
    • Hauser, W.1
  • 50
    • 84943471869 scopus 로고
    • Uber Integrale der Hydrodynamischen Gleichungen, Welche den Wirbelbewegungen Entsprechen
    • Jan
    • H. Helmholtz, "Uber Integrale der Hydrodynamischen Gleichungen, Welche den Wirbelbewegungen Entsprechen," J. fur die reine und angewandte Mathematik, vol. 1858, no. 55, pp. 25-55, Jan. 1858.
    • (1858) J. fur Die Reine und Angewandte Mathematik , vol.1858 , Issue.55 , pp. 25-55
    • Helmholtz, H.1
  • 51
    • 0000001774 scopus 로고
    • On integrals of the hydrodynamical equations, which express vortex-motion
    • H. Helmholtz, "On Integrals of the Hydrodynamical Equations, which Express Vortex-Motion," Philosophical Magazine and J. Science, vol. 33, no. 226, pp. 485-512, 1867.
    • (1867) Philosophical Magazine and J. Science , vol.33 , Issue.226 , pp. 485-512
    • Helmholtz, H.1
  • 54
    • 0001610179 scopus 로고    scopus 로고
    • A galerkin implementation of the generalized helmholtz decomposition for vorticity formulations
    • DOI 10.1006/jcph.2001.6724, PII S0021999101967245
    • M.S. Ingber and S.N. Kempka, "A Galerkin Implementation of the Generalized Helmholtz Decomposition for Vorticity Formulations," J. Computational Physics, vol. 169, no. 1, pp. 215-237, 2001. (Pubitemid 33653345)
    • (2001) Journal of Computational Physics , vol.169 , Issue.1 , pp. 215-237
    • Ingber, M.S.1    Kempka, S.N.2
  • 57
    • 33749235507 scopus 로고    scopus 로고
    • Helmholtz decomposition coupling rotational to irrotational flow of a viscous fluid
    • DOI 10.1073/pnas.0605792103
    • D.D. Joseph, "Helmholtz Decomposition Coupling Rotational to Irrotational Flow of a Viscous Fluid," Proc. Nat'l Academy of Sciences of USA, vol. 103, no. 39, pp. 14272-14277, 2006. (Pubitemid 44484739)
    • (2006) Proceedings of the National Academy of Sciences of the United States of America , vol.103 , Issue.39 , pp. 14272-14277
    • Joseph, D.D.1
  • 58
    • 46549092989 scopus 로고
    • Application of a fractional-step method to incompressible navier-stokes equations
    • J. Kim and P. Moin, "Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations," J. Computational Physics, vol. 59, no. 2, pp. 308-323, 1985.
    • (1985) J. Computational Physics , vol.59 , Issue.2 , pp. 308-323
    • Kim, J.1    Moin, P.2
  • 59
    • 0001203006 scopus 로고
    • Helmholtz theorem for antisymmetric second-rank tensor fields and electromagnetism with magnetic monopoles
    • D.H. Kobe, "Helmholtz Theorem for Antisymmetric Second-Rank Tensor Fields and Electromagnetism with Magnetic Monopoles," Am. J. Physics, vol. 52, no. 4, pp. 354-358, 1984.
    • (1984) Am. J. Physics , vol.52 , Issue.4 , pp. 354-358
    • Kobe, D.H.1
  • 60
    • 1842573396 scopus 로고
    • Helmholtz's theorem revisited
    • D.H. Kobe, "Helmholtz's Theorem Revisited," Am. J. Physics, vol. 54, no. 6, pp. 552-554, 1986.
    • (1986) Am. J. Physics , vol.54 , Issue.6 , pp. 552-554
    • Kobe, D.H.1
  • 61
    • 0001591178 scopus 로고
    • Harmonic fields in riemannian manifolds
    • K. Kodaira, "Harmonic Fields in Riemannian Manifolds," Annals of Math., vol. 50, pp. 587-665, 1949.
    • (1949) Annals of Math. , vol.50 , pp. 587-665
    • Kodaira, K.1
  • 63
    • 0004168443 scopus 로고
    • sixth ed. Cambridge Univ. Press
    • H. Lamb, Hydrodynamics, sixth ed. Cambridge Univ. Press, 1932.
    • (1932) Hydrodynamics
    • Lamb, H.1
  • 64
    • 84877612238 scopus 로고    scopus 로고
    • Simulating water and smoke with an octree data structure
    • F. Losasso, F. Gibou, and R. Fedkiw, "Simulating Water and Smoke with an Octree Data Structure," ACM Trans. Graphics, vol. 23, pp. 457-462, 2004.
    • (2004) ACM Trans. Graphics , vol.23 , pp. 457-462
    • Losasso, F.1    Gibou, F.2    Fedkiw, R.3
  • 65
    • 0001765873 scopus 로고
    • A numerical approach to the testing of the fission hypothesis
    • L.B. Lucy, "A Numerical Approach to the Testing of the Fission Hypothesis," The Astronomical J., vol. 82, pp. 1013-1024, 1977.
    • (1977) The Astronomical J. , vol.82 , pp. 1013-1024
    • Lucy, L.B.1
  • 69
    • 14544299611 scopus 로고    scopus 로고
    • On learning vector-valued functions
    • DOI 10.1162/0899766052530802
    • C.A. Micchelli and M. Pontil, "On Learning Vector-Valued Functions," Neural Computation, vol. 17, pp. 177-204, 2005. (Pubitemid 40305887)
    • (2005) Neural Computation , vol.17 , Issue.1 , pp. 177-204
    • Micchelli, C.A.1    Pontil, M.2
  • 70
    • 34047194750 scopus 로고
    • Interpretations from helmholtz theorem in classical electromagnetism
    • B.P. Miller, "Interpretations from Helmholtz Theorem in Classical Electromagnetism," Am. J. Physics, vol. 52, p. 948, 1984.
    • (1984) Am. J. Physics , vol.52 , pp. 948
    • Miller, B.P.1
  • 71
    • 33750690657 scopus 로고    scopus 로고
    • A second order accurate projection method for the incompressible Navier-Stokes equations on non-graded adaptive grids
    • DOI 10.1016/j.jcp.2006.07.019, PII S0021999106003366
    • C. Min and F. Gibou, "A Second Order Accurate Projection Method for the Incompressible Navier-Stokes Equations on Non- Graded Adaptive Grids," J. Computational Physics, vol. 219, pp. 912-929, 2006. (Pubitemid 44696133)
    • (2006) Journal of Computational Physics , vol.219 , Issue.2 , pp. 912-929
    • Min, C.1    Gibou, F.2
  • 72
    • 33748524485 scopus 로고    scopus 로고
    • A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids
    • DOI 10.1016/j.jcp.2006.01.046, PII S0021999106000635
    • C. Min, F. Gibou, and H.D. Ceniceros, "A Supra-Convergent Finite Difference Scheme for the Variable Coefficient Poisson Equation on Non-Graded Grids," J. Computational Physics, vol. 218, no. 1, pp. 123-140, 2006. (Pubitemid 44364185)
    • (2006) Journal of Computational Physics , vol.218 , Issue.1 , pp. 123-140
    • Min, C.1    Gibou, F.2    Ceniceros, H.D.3
  • 73
    • 77951153799 scopus 로고    scopus 로고
    • Spatial reasoning for robot navigation using the helmholtz-hodge decomposition of omnidirectional optical flow
    • Y. Mochizuki and A. Imiya, "Spatial Reasoning for Robot Navigation Using the Helmholtz-Hodge Decomposition of Omnidirectional Optical Flow," Proc. 24th Int'l Conf. Image and Vision Computing (IVCNZ), pp. 1-6, 2009.
    • (2009) Proc. 24th Int'l Conf. Image and Vision Computing (IVCNZ) , pp. 1-6
    • Mochizuki, Y.1    Imiya, A.2
  • 75
    • 0002337338 scopus 로고
    • Helmholtz decomposition revisited: Vorticity generation and trailing edge condition
    • L. Morino, "Helmholtz Decomposition Revisited: Vorticity Generation and Trailing Edge Condition," Computational Mechanics, vol. 1, pp. 65-90, 1986.
    • (1986) Computational Mechanics , vol.1 , pp. 65-90
    • Morino, L.1
  • 76
    • 84968510026 scopus 로고
    • Generalized hermite interpolation via matrix-valued conditionally positive definite functions
    • F.J. Narcowich and J.D. Ward, "Generalized Hermite Interpolation Via Matrix-Valued Conditionally Positive Definite Functions," Math. of Computations, vol. 63, no. 208, pp. 661-687, 1994.
    • (1994) Math. of Computations , vol.63 , Issue.208 , pp. 661-687
    • Narcowich, F.J.1    Ward, J.D.2
  • 77
    • 0036995655 scopus 로고    scopus 로고
    • Physically based modeling and animation of fire
    • D.Q. Nguyen, R. Fedkiw, and H.W. Jensen, "Physically based Modeling and Animation of Fire," ACM Trans. Graphics, vol. 21, pp. 721-728, 2002.
    • (2002) ACM Trans. Graphics , vol.21 , pp. 721-728
    • Nguyen, D.Q.1    Fedkiw, R.2    Jensen, H.W.3
  • 78
    • 0024573076 scopus 로고
    • Tomographic reconstruction of 2-D vector fields: Applications to flow imaging
    • S.J. Norton, "Tomographic Reconstruction of 2-D Vector Fields: Applications to Flow Imaging," Geophysics J. Int'l, vol. 97, no. 1, pp. 161-168, 1988.
    • (1988) Geophysics J. Int'l , vol.97 , Issue.1 , pp. 161-168
    • Norton, S.J.1
  • 79
    • 0026897948 scopus 로고
    • Unique tomographic reconstruction of vector fields using boundary data
    • July
    • S.J. Norton, "Unique Tomographic Reconstruction of Vector Fields Using Boundary Data," IEEE Trans. Image Processing, vol. 1, no. 3, pp. 406-412, July 1992.
    • (1992) IEEE Trans. Image Processing , vol.1 , Issue.3 , pp. 406-412
    • Norton, S.J.1
  • 80
    • 33646729076 scopus 로고    scopus 로고
    • Applications of the discrete hodge-helmholtz decomposition to image and video processing
    • S. Pal, S. Bandyopadhyay, and S. Biswas, eds.
    • B. Palit, A. Basu, and M. Mandal, "Applications of the Discrete Hodge-Helmholtz Decomposition to Image and Video Processing," Proc. First Int'l Conf. Pattern Recognition and Machine Intelligence, S. Pal, S. Bandyopadhyay, and S. Biswas, eds., pp. 497-502, 2005.
    • (2005) Proc. First Int'l Conf. Pattern Recognition and Machine Intelligence , pp. 497-502
    • Palit, B.1    Basu, A.2    Mandal, M.3
  • 84
    • 13544250158 scopus 로고    scopus 로고
    • Identifying vector fields singularities using a discrete Hodge decomposition
    • H.C. Hege, K. Polthier, eds. Springer
    • K. Polthier and E. Preuß, "Identifying Vector Fields Singularities Using a Discrete Hodge Decomposition," Mathematical Visualization III, H.C. Hege, K. Polthier, eds., pp. 112-134, Springer, 2003.
    • (2003) Mathematical Visualization III , pp. 112-134
    • Polthier, K.1    Preuß, E.2
  • 85
    • 0141515637 scopus 로고    scopus 로고
    • Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries
    • DOI 10.1016/S0021-9991(03)00298-5
    • S. Popinet, "A Tree-Based Adaptive Solver for the Incompressible Euler Equations in Complex Geometries," J. Computational Physics, vol. 190, pp. 572-600, 2003. (Pubitemid 37141667)
    • (2003) Journal of Computational Physics , vol.190 , Issue.2 , pp. 572-600
    • Popinet, S.1
  • 86
    • 0030269648 scopus 로고    scopus 로고
    • Convolution backprojection formulas for 3-D vector tomography with application to MRI
    • PII S1057714996060289
    • J.L. Prince, "Convolution Backprojection Formulas for 3-D Vector Tomography with Application to MRI," IEEE Trans. Image Processing, vol. 5, no. 10, pp. 1462-1472, Oct. 1996. (Pubitemid 126782832)
    • (1996) IEEE Transactions on Image Processing , vol.5 , Issue.10 , pp. 1462-1472
    • Prince, J.L.1
  • 87
    • 84963549647 scopus 로고
    • Helmholtz decomposition of surface electric current in electromagnetic scattering problems
    • R. Scharstein, "Helmholtz Decomposition of Surface Electric Current in Electromagnetic Scattering Problems," Proc. 23rd Southeastern Symp. System Theory, pp. 424-426, 1991.
    • (1991) Proc. 23rd Southeastern Symp. System Theory , pp. 424-426
    • Scharstein, R.1
  • 88
    • 84879218331 scopus 로고
    • Differential forms as a basis for vector analysis - With applications to electrodynamics
    • N. Schleifer, "Differential Forms as a Basis for Vector Analysis - with Applications to Electrodynamics," Am. J. Physics, vol. 51, no. 45, p. 1983, 1983.
    • (1983) Am. J. Physics , vol.51 , Issue.45 , pp. 1983
    • Schleifer, N.1
  • 91
    • 77249131799 scopus 로고    scopus 로고
    • On helmholtz decompositions and their generalizations - An overview
    • W. Sprossig, "On Helmholtz Decompositions and their Generalizations - An Overview," Math. Methods in the Applied Sciences, vol. 33, pp. 374-383, 2010.
    • (2010) Math. Methods in the Applied Sciences , vol.33 , pp. 374-383
    • Sprossig, W.1
  • 93
    • 0011052009 scopus 로고    scopus 로고
    • A simple fluid solver based on the FFT
    • J. Stam, "A Simple Fluid Solver Based on the FFT," J. Graphics Tools, vol. 6, pp. 43-52, 2002.
    • (2002) J. Graphics Tools , vol.6 , pp. 43-52
    • Stam, J.1
  • 94
    • 0029182696 scopus 로고
    • Depicting fire and other gaseous phenomena using diffusion processes
    • J. Stam and E. Fiume, "Depicting Fire and Other Gaseous Phenomena Using Diffusion Processes," Proc. ACM SIGGRAPH '95, pp. 129-136, 1995.
    • (1995) Proc. ACM SIGGRAPH '95 , pp. 129-136
    • Stam, J.1    Fiume, E.2
  • 95
    • 0034377153 scopus 로고    scopus 로고
    • Realistic solar convection simulations
    • R. Stein and A. Nordlund, "Realistic Solar Convection Simulations," Solar Physics, vol. 192, pp. 91-108, 2000.
    • (2000) Solar Physics , vol.192 , pp. 91-108
    • Stein, R.1    Nordlund, A.2
  • 96
    • 0043028725 scopus 로고
    • A finite difference galerkin formulation for the incompressible navier-stokes equations
    • A.B. Stephens, J.B. Bell, J.M. Solomon, and L.B. Hackerman, "A Finite Difference Galerkin Formulation for the Incompressible Navier-Stokes Equations," J. Computational Physics, vol. 53, pp. 152-172, 1984.
    • (1984) J. Computational Physics , vol.53 , pp. 152-172
    • Stephens, A.B.1    Bell, J.B.2    Solomon, J.M.3    Hackerman, L.B.4
  • 97
    • 1542325749 scopus 로고    scopus 로고
    • Discrete multiscale vector field decomposition
    • Y. Tong, S. Lombeyda, A. Hirani, and M. Desbrun, "Discrete Multiscale Vector Field Decomposition," ACM Trans. Graphics, vol. 22, no. 3, pp. 445-452, 2003.
    • (2003) ACM Trans. Graphics , vol.22 , Issue.3 , pp. 445-452
    • Tong, Y.1    Lombeyda, S.2    Hirani, A.3    Desbrun, M.4
  • 98
    • 0000674333 scopus 로고
    • A second-order accurate pressure-correction scheme for viscous incompressible flow
    • J. van Kan, "A Second-Order Accurate Pressure-Correction Scheme for Viscous Incompressible Flow," SIAM J. Scientific and Statistical Computing, vol. 7, no. 3, pp. 870-891, 1986.
    • (1986) SIAM J. Scientific and Statistical Computing , vol.7 , Issue.3 , pp. 870-891
    • Van Kan, J.1
  • 99
    • 33749240363 scopus 로고    scopus 로고
    • Edge subdivision schemes and the construction of smooth vector fields
    • DOI 10.1145/1141911.1141991, ACM Transactions on Graphics - Proceedings of ACM SIGGRAPH 2006
    • K. Wang Weiwei, Y. Tong, M. Desburn, and P. Schroder, "Edge Subdivision Schemes and the Construction of Smooth Vector Fields," ACM Trans. Graphics, vol. 25, no. 3, pp. 1041-1048, 2006. (Pubitemid 44481066)
    • (2006) ACM Transactions on Graphics , vol.25 , Issue.3 , pp. 1041-1048
    • Wang, K.1    Weiwei2    Tong, Y.3    Desbrun, M.4    Schroder, P.5
  • 100
    • 84967491274 scopus 로고
    • The method of orthogonal projection in potential theory
    • H. Weyl, "The Method of Orthogonal Projection in Potential Theory," Duke Math. J., vol. 7, no. 7, pp. 411-444, 1940.
    • (1940) Duke Math. J. , vol.7 , Issue.7 , pp. 411-444
    • Weyl, H.1
  • 102
    • 85047697530 scopus 로고    scopus 로고
    • Computation of localized flow for steady and unsteady vector fields and its applications
    • DOI 10.1109/TVCG.2007.1036
    • A. Wiebel, C. Garth, and G. Scheuermann, "Computation of Localized Flow for Steady and Unsteady Vector Fields and its Applications," IEEE Trans. Visualization and Computer Graphics, vol. 13, no. 4, pp. 641-651, July/Aug. 2007. (Pubitemid 47289541)
    • (2007) IEEE Transactions on Visualization and Computer Graphics , vol.13 , Issue.4 , pp. 641-651
    • Wiebel, A.1    Garth, C.2    Scheuermann, G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.