메뉴 건너뛰기




Volumn 32, Issue , 2001, Pages 171-188

Geometric aspects of the Simplicial Discretization of Maxwell's equations

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL FORMS; DISCRETE FORMULATIONS; DISCRETIZATIONS; DUAL LATTICES; MAXWELL'S EQUATIONS; WHITNEY;

EID: 79953727476     PISSN: 10704698     EISSN: 15598985     Source Type: Journal    
DOI: 10.2528/PIER00080107     Document Type: Article
Times cited : (15)

References (65)
  • 4
    • 0001777623 scopus 로고
    • Finite-difference approach to the Hodge theory of harmonic forms
    • Dodziuk, J., "Finite-difference approach to the Hodge theory of harmonic forms," Am. J. Math., Vol. 98, No. 1, 79-104, 1976.
    • (1976) Am. J. Math , vol.98 , Issue.1 , pp. 79-104
    • Dodziuk, J.1
  • 5
    • 36749111887 scopus 로고
    • Geometric formulation of electrodynamics and general relativity in discrete space-time
    • Weingarten, D., "Geometric formulation of electrodynamics and general relativity in discrete space-time," J. Math. Phys., Vol. 18, No. 1, 165-170, 1977.
    • (1977) J. Math. Phys , vol.18 , Issue.1 , pp. 165-170
    • Weingarten, D.1
  • 6
    • 0011546533 scopus 로고
    • Analytic torsion and R-torsion of Riemannian manifolds
    • Muller, W., "Analytic torsion and R-torsion of Riemannian manifolds," Advances in Math., Vol. 28, 233-305, 1978.
    • (1978) Advances In Math , vol.28 , pp. 233-305
    • Muller, W.1
  • 7
    • 0039032698 scopus 로고
    • On the mathematical strucuture of a large class of physical theories
    • Tonti, E., "On the mathematical strucuture of a large class of physical theories," Rend. Acc. Lincei, Vol. 52, 48-56, 1972.
    • (1972) Rend Acc. Lincei , vol.52 , pp. 48-56
    • Tonti, E.1
  • 8
    • 0039624934 scopus 로고
    • A mathematical model for physical theories
    • Tonti, E., "A mathematical model for physical theories," Rend. Acc. Lincei, Vol. 52, 175-181, 1972.
    • (1972) Rend Acc. Lincei , vol.52 , pp. 175-181
    • Tonti, E.1
  • 12
    • 36849114079 scopus 로고
    • Differential forms and Maxwell's field: An application of harmonic integrals
    • Ohkuro, S., "Differential forms and Maxwell's field: An application of harmonic integrals," J. Math. Phys., Vol. 11, No. 6, 2005-2012, 1970.
    • (1970) J. Math. Phys , vol.11 , Issue.6 , pp. 2005-2012
    • Ohkuro, S.1
  • 13
    • 0019583846 scopus 로고
    • Electromagnetics and differential forms
    • Deschamps, G. A., "Electromagnetics and differential forms," Proc. IEEE, Vol. 69, No. 6, 676-696, 1981.
    • (1981) Proc. IEEE , vol.69 , Issue.6 , pp. 676-696
    • Deschamps, G.A.1
  • 14
    • 36448999209 scopus 로고
    • The boundary of a boundary principle in field theories and the issue of austerity of the laws of physics
    • Kheyfets, A. and W. A. Miller, "The boundary of a boundary principle in field theories and the issue of austerity of the laws of physics," J. Math. Phys., Vol. 32, No. 11, 3168-3175, 1991.
    • (1991) J. Math. Phys , vol.32 , Issue.11 , pp. 3168-3175
    • Kheyfets, A.1    Miller, W.A.2
  • 15
    • 0024104484 scopus 로고
    • Whitney forms: A new class of finite elements for three-dimensional computations in electromagnetics
    • Bossavit, A., "Whitney forms: a new class of finite elements for three-dimensional computations in electromagnetics," IEE Proc. A, Vol. 135, 493-500, 1988.
    • (1988) IEE Proc. A , vol.135 , pp. 493-500
    • Bossavit, A.1
  • 16
    • 0024771343 scopus 로고
    • Simplicial finite elements for scattering problems in electromagnetism
    • Bossavit, A., "Simplicial finite elements for scattering problems in electromagnetism," Comp. Meth. Appl. Mech. Engineering, Vol. 76, 299-316, 1989.
    • (1989) Comp. Meth. Appl. Mech. Engineering , vol.76 , pp. 299-316
    • Bossavit, A.1
  • 17
  • 18
    • 0002909785 scopus 로고
    • Variational principles for three-dimensional magnetostatics based on helicity
    • Kotiuga, P. R., "Variational principles for three-dimensional magnetostatics based on helicity," J. Appl. Phys., Vol. 63, No. 8, 3360-3362, 1988.
    • (1988) J. Appl. Phys , vol.63 , Issue.8 , pp. 3360-3362
    • Kotiuga, P.R.1
  • 19
    • 0024705021 scopus 로고
    • Helicity functionals and metric invariance in three dimensions
    • Kotiuga, P. R., "Helicity functionals and metric invariance in three dimensions," IEEE Trans. Magn., Vol. 25, No. 4, 2813-2815, 1989.
    • (1989) IEEE Trans. Magn , vol.25 , Issue.4 , pp. 2813-2815
    • Kotiuga, P.R.1
  • 20
    • 0011657714 scopus 로고
    • Analysis of finite-element matrices arising from discretizations of helicity functionals
    • Kotiuga, P. R., "Analysis of finite-element matrices arising from discretizations of helicity functionals," J. Appl. Phys., Vol. 67, No. 9, 5815-5817, 1990.
    • (1990) J. Appl. Phys , vol.67 , Issue.9 , pp. 5815-5817
    • Kotiuga, P.R.1
  • 21
    • 33751047740 scopus 로고
    • Metric dependent aspects of inverse problems and functionals based on helicity
    • Kotiuga, P. R., "Metric dependent aspects of inverse problems and functionals based on helicity," J. Appl. Phys., Vol. 73, No. 10, 5437-5439, 1993.
    • (1993) J. Appl. Phys , vol.73 , Issue.10 , pp. 5437-5439
    • Kotiuga, P.R.1
  • 22
    • 0023979348 scopus 로고
    • Dual energy methods in electromagnetism using tubes and slices
    • Hammond, P. and D. Baldomir, "Dual energy methods in electromagnetism using tubes and slices," IEEE Proc. A, Vol. 135, No. 3, 167-172, 1988.
    • (1988) IEEE Proc. A , vol.135 , Issue.3 , pp. 167-172
    • Hammond, P.1    Baldomir, D.2
  • 23
    • 0000809823 scopus 로고
    • Differential forms and the computation of fields and forces in electromagnetism
    • Bossavit, A., "Differential forms and the computation of fields and forces in electromagnetism," Eur. J. Mech. B, Vol. 10, No. 5, 474-488, 1991.
    • (1991) Eur. J. Mech. B , vol.10 , Issue.5 , pp. 474-488
    • Bossavit, A.1
  • 25
    • 0001469953 scopus 로고    scopus 로고
    • Discrete spaces for Div and Curl-free fields
    • Kettunen, L., K. Forsman, and A. Bossavit, "Discrete spaces for Div and Curl-free fields," IEEE Trans. Magn., Vol. 34, No. 5, 2551-2554, 1998.
    • (1998) IEEE Trans. Magn , vol.34 , Issue.5 , pp. 2551-2554
    • Kettunen, L.1    Forsman, K.2    Bossavit, A.3
  • 26
    • 0033121757 scopus 로고    scopus 로고
    • Some realizations of a discrete Hodge operator: A reinterpretation of finite element techniques
    • Tarhasaari, T., L. Kettunen, and A. Bossavit, "Some realizations of a discrete Hodge operator: A reinterpretation of finite element techniques," IEEE Trans. Magn., Vol. 35, No. 3, 1494-1497, 1999.
    • (1999) IEEE Trans. Magn , vol.35 , Issue.3 , pp. 1494-1497
    • Tarhasaari, T.1    Kettunen, L.2    Bossavit, A.3
  • 27
    • 0033121797 scopus 로고    scopus 로고
    • A posteriori error bounds by 'local corrections' using the dual mesh
    • Bossavit, A., "A posteriori error bounds by 'local corrections' using the dual mesh," IEEE Trans. Magn., Vol. 35, No. 3, 1350-1353, 1999.
    • (1999) IEEE Trans. Magn , vol.35 , Issue.3 , pp. 1350-1353
    • Bossavit, A.1
  • 29
    • 0002672835 scopus 로고
    • The Dirac-Kahler equation and fermions on the lattice
    • Becher, P. and H. Joos, "The Dirac-Kahler equation and fermions on the lattice," Z. Phys. C, Vol. 15, 343-365, 1982.
    • (1982) Z. Phys. C , vol.15 , pp. 343-365
    • Becher, P.1    Joos, H.2
  • 31
    • 0030080007 scopus 로고    scopus 로고
    • A variable metric electrodynamics. The Coulomb and Biot-Savart laws in anisotropic media
    • Jancewicz, B., "A variable metric electrodynamics. The Coulomb and Biot-Savart laws in anisotropic media," Ann. Phys., Vol. 245, 227-274, 1996.
    • (1996) Ann. Phys , vol.245 , pp. 227-274
    • Jancewicz, B.1
  • 32
    • 0031570250 scopus 로고    scopus 로고
    • An analysis of finite volume, finite element, and finite difference methods using some concepts from algebraic topology
    • Mattiussi, C., "An analysis of finite volume, finite element, and finite difference methods using some concepts from algebraic topology," J. Comp. Phys., Vol. 133, 289-309, 1997.
    • (1997) J. Comp. Phys , vol.133 , pp. 289-309
    • Mattiussi, C.1
  • 33
    • 0031077141 scopus 로고    scopus 로고
    • Teaching eletromagnetic field theory using differential forms
    • Warnick, K. F., R. H. Selfridge, and D. V. Arnold, "Teaching eletromagnetic field theory using differential forms," IEEE Trans. Edu., Vol. 40, No. 1, 53-68, 1997.
    • (1997) IEEE Trans. Edu , vol.40 , Issue.1 , pp. 53-68
    • Warnick, K.F.1    Selfridge, R.H.2    Arnold, D.V.3
  • 34
    • 0030652808 scopus 로고    scopus 로고
    • Green forms for anisotropic, inhomogeneous media
    • Warnick, K. F. and D. V. Arnold, "Green forms for anisotropic, inhomogeneous media," J. Electromagn. Waves Appl., Vol. 11, No. 8, 1145-1164, 1997.
    • (1997) J. Electromagn. Waves Appl , vol.11 , Issue.8 , pp. 1145-1164
    • Warnick, K.F.1    Arnold, D.V.2
  • 36
    • 0039491037 scopus 로고    scopus 로고
    • Topological and geometrical considerations for Maxwell's equations on unstructured meshes
    • Montreal, Canada
    • Kraus, C. and R. Ziolkowsky, "Topological and geometrical considerations for Maxwell's equations on unstructured meshes," Proc. URSI Meeting, 714, Montreal, Canada, 1997.
    • (1997) Proc. URSI Meeting , pp. 714
    • Kraus, C.1    Ziolkowsky, R.2
  • 37
    • 0033461694 scopus 로고    scopus 로고
    • Canonical construction of finite elements
    • Hiptmair, R., Canonical construction of finite elements, Math. Computat., Vol. 68, 1325-1346, 1999.
    • (1999) Math. Computat , vol.68 , pp. 1325-1346
    • Hiptmair, R.1
  • 38
    • 0342849182 scopus 로고    scopus 로고
    • Discrete Hodge operators
    • SFB 382, University of Tubingen, Tubingen, Germany
    • Hiptmair, R., "Discrete Hodge operators," Tech. Rep. 126, SFB 382, University of Tubingen, Tubingen, Germany, 1999.
    • (1999) Tech. Rep , pp. 126
    • Hiptmair, R.1
  • 39
    • 0032672917 scopus 로고    scopus 로고
    • Differential forms, metrics, and the reflectionless absorption of electromagnetic waves
    • Teixeira, F. L. and W. C. Chew, "Differential forms, metrics, and the reflectionless absorption of electromagnetic waves," J. Electromagn. Waves Applicat., Vol. 13, No. 5, 665-686, 1999.
    • (1999) J. Electromagn. Waves Applicat , vol.13 , Issue.5 , pp. 665-686
    • Teixeira, F.L.1    Chew, W.C.2
  • 40
    • 0033481261 scopus 로고    scopus 로고
    • Lattice electromagnetic theory from a topological viewpoint
    • Teixeira, F. L. and W. C. Chew, "Lattice electromagnetic theory from a topological viewpoint," J. Math. Phys., Vol. 40, No. 1, 169-187, 1999.
    • (1999) J. Math. Phys , vol.40 , Issue.1 , pp. 169-187
    • Teixeira, F.L.1    Chew, W.C.2
  • 41
    • 0347724675 scopus 로고
    • Construction of convergent simplicial approximations of quantum field on Riemannian manifolds
    • Albeverio, S. and B. Zegarlinski, "Construction of convergent simplicial approximations of quantum field on Riemannian manifolds," Comm. Math. Phys., Vol. 132, 39-71, 1990.
    • (1990) Comm. Math. Phys , vol.132 , pp. 39-71
    • Albeverio, S.1    Zegarlinski, B.2
  • 42
    • 36449000276 scopus 로고
    • Abelian Chern-Simons theory and linking numbers via oscilatory integrals
    • Albeverio, S. and J. Schafer, "Abelian Chern-Simons theory and linking numbers via oscilatory integrals," J. Mat. Phys., Vol. 36, No. 5, 2157-2169, 1995.
    • (1995) J. Mat. Phys , vol.36 , Issue.5 , pp. 2157-2169
    • Albeverio, S.1    Schafer, J.2
  • 44
    • 4243663051 scopus 로고    scopus 로고
    • A double discretization of Abelian Chern-Simons theory
    • Adams, D. H., "A double discretization of Abelian Chern-Simons theory," Phys. Rev. Lett., Vol. 78, No. 22, 4155-4158, 1997.
    • (1997) Phys Rev. Lett , vol.78 , Issue.22 , pp. 4155-4158
    • Adams, D.H.1
  • 45
    • 1542325752 scopus 로고    scopus 로고
    • Geometric discretization scheme applied to the Abelian Chern-Simons theory
    • Sen, S., S. Sen, J. C. Sexton, and D. H. Adams, "Geometric discretization scheme applied to the Abelian Chern-Simons theory," Phys. Rev. E, Vol. 61, No. 3, 3174-3185, 2000.
    • (2000) Phys. Rev. E , vol.61 , Issue.3 , pp. 3174-3185
    • Sen, S.1    Sen, S.2    Sexton, J.C.3    Adams, D.H.4
  • 46
    • 0024703180 scopus 로고
    • Dual mesh approach for semiconductor device simulator
    • Kojima, T., Y. Saito, and R. Dang. "Dual mesh approach for semiconductor device simulator," IEEE Trans. Magn., Vol. 25, No. 4, 2953-2955, 1989.
    • (1989) IEEE Trans. Magn , vol.25 , Issue.4 , pp. 2953-2955
    • Kojima, T.1    Saito, Y.2    Dang, R.3
  • 47
    • 0001047681 scopus 로고    scopus 로고
    • How weak is the 'weak solution' in finite element methods
    • Bossavit, A., "How weak is the 'weak solution' in finite element methods," IEEE Trans. Magn., Vol. 34, No. 5, 2429-2432, 1998.
    • (1998) IEEE Trans. Magn , vol.34 , Issue.5 , pp. 2429-2432
    • Bossavit, A.1
  • 48
    • 0032628755 scopus 로고    scopus 로고
    • Yee-schemes on a tetrahedral mesh, with diagonal lumping
    • Bossavit, A. and L. Kettunen, "Yee-schemes on a tetrahedral mesh, with diagonal lumping," Int. J. Num. Model., Vol. 12, 129-142, 1999.
    • (1999) Int. J. Num. Model , vol.12 , pp. 129-142
    • Bossavit, A.1    Kettunen, L.2
  • 49
    • 0038722672 scopus 로고
    • Topological quantum field theory
    • Witten, E., "Topological quantum field theory," Comm. Math. Phys., Vol. 117, 353-386, 1988.
    • (1988) Comm. Math. Phys , vol.117 , pp. 353-386
    • Witten, E.1
  • 50
    • 21344482750 scopus 로고
    • Lattice topological field theory in two dimensions
    • Fukuma, M., S. Hosono, and H. Kawai, "Lattice topological field theory in two dimensions," Comm. Math. Phys., Vol. 161, 157-175, 1994.
    • (1994) Comm. Math. Phys , vol.161 , pp. 157-175
    • Fukuma, M.1    Hosono, S.2    Kawai, H.3
  • 51
    • 0001388868 scopus 로고
    • Structure of topological lattice field theory in three dimensions
    • Chung, S.-W., M. Fukuma, and A. Shapere, "Structure of topological lattice field theory in three dimensions," Int. J. Mod. Phys., Vol. 9, No. 8, 1305-1360, 1994.
    • (1994) Int. J. Mod. Phys , vol.9 , Issue.8 , pp. 1305-1360
    • Chung, S.-W.1    Fukuma, M.2    Shapere, A.3
  • 52
    • 27844557091 scopus 로고    scopus 로고
    • Quasitopological field theories in two dimensions as soluble models
    • da Cunha, B. G. C. and P. T. Sobrinho, "Quasitopological field theories in two dimensions as soluble models," Int. J. Mod. Phys., Vol. 13, No. 21, 3667-3689, 1998.
    • (1998) Int. J. Mod. Phys , vol.13 , Issue.21 , pp. 3667-3689
    • Da Cunha, B.G.C.1    Sobrinho, P.T.2
  • 53
    • 0001255616 scopus 로고    scopus 로고
    • Conformal boundary conditions and three-dimensional topological field theory
    • Felder, G., J. Frolich, J. Fuchs and C. Schweigert, "Conformal boundary conditions and three-dimensional topological field theory," Phys. Rev. Lett., Vol. 84, No. 8, 1659-1662, 2000.
    • (2000) Phys. Rev. Lett , vol.84 , Issue.8 , pp. 1659-1662
    • Felder, G.1    Frolich, J.2    Fuchs, J.3    Schweigert, C.4
  • 54
    • 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 Trans. Ant. Propagat., Vol. 14, 302-307, 1966.
    • (1966) IEEE Trans. Ant. Propagat , vol.14 , pp. 302-307
    • Yee, K.S.1
  • 56
    • 0021310564 scopus 로고
    • On the numerical solutions of Maxwell's equations and applications in the field of accelerator physics
    • Weiland, T., "On the numerical solutions of Maxwell's equations and applications in the field of accelerator physics," Particle Accelerators, Vol. 15, 245-292, 1984.
    • (1984) Particle Accelerators , vol.15 , pp. 245-292
    • Weiland, T.1
  • 57
    • 0030194949 scopus 로고    scopus 로고
    • Time domain electromagnetic field computations with finite difference methods
    • Weiland, T., "Time domain electromagnetic field computations with finite difference methods," Int. J. Num. Model., Vol. 9, 295-319, 1996.
    • (1996) Int. J. Num. Model , vol.9 , pp. 295-319
    • Weiland, T.1
  • 58
    • 0000544197 scopus 로고
    • Electromagnetic theory on a lattice
    • Chew, W. C., "Electromagnetic theory on a lattice," J. Appl. Phys., Vol. 75, No. 10, 4843-4850, 1994.
    • (1994) J. Appl. Phys , vol.75 , Issue.10 , pp. 4843-4850
    • Chew, W.C.1
  • 59
    • 0033365713 scopus 로고    scopus 로고
    • Full-wave analysis of multiconductor transmission lines on anisotropic inhomogeneous substrates
    • Radhakrishnan, K. and W. C. Chew, "Full-wave analysis of multiconductor transmission lines on anisotropic inhomogeneous substrates," IEEE Trans. Microwave Theory Tech., Vol. 47, No. 9, 1764-1771, 1999.
    • (1999) IEEE Trans. Microwave Theory Tech , vol.47 , Issue.9 , pp. 1764-1771
    • Radhakrishnan, K.1    Chew, W.C.2
  • 60
    • 1542295883 scopus 로고    scopus 로고
    • Finite volume, finite difference, and finite element methods for physical field problems
    • Mattiussi, C., "Finite volume, finite difference, and finite element methods for physical field problems," Advancing Imaging Electron. Phys., Vol. 113, 1-146, 2000.
    • (2000) Advancing Imaging Electron. Phys , vol.113 , pp. 1-146
    • Mattiussi, C.1
  • 61
    • 0024706077 scopus 로고
    • Three dimensional finite difference frequency domain scattering computation using the control region approximation
    • McCartin, B. J. and J. F. DiCello, "Three dimensional finite difference frequency domain scattering computation using the control region approximation," IEEE Trans. Magn., Vol. 25, No. 4, 3092-3094, 1989.
    • (1989) IEEE Trans. Magn , vol.25 , Issue.4 , pp. 3092-3094
    • McCartin, B.J.1    Dicello, J.F.2
  • 62
    • 0026227202 scopus 로고
    • Anisotropic FDFD computed on conformal meshes
    • Rappaport, C. M. and E. B. Smith, "Anisotropic FDFD computed on conformal meshes," IEEE Trans. Magn., Vol. 27, No. 5, 3848-3851, 1991.
    • (1991) IEEE Trans. Magn , vol.27 , Issue.5 , pp. 3848-3851
    • Rappaport, C.M.1    Smith, E.B.2
  • 63
    • 0031071242 scopus 로고    scopus 로고
    • Natural discretization for the divergence, gradient and curl on logically rectangular grids
    • Hyman, J. M. and M. Shashkov, "Natural discretization for the divergence, gradient and curl on logically rectangular grids," Comput. Math. Appl., Vol. 33, 81-104, 1997.
    • (1997) Comput. Math. Appl , vol.33 , pp. 81-104
    • Hyman, J.M.1    Shashkov, M.2
  • 64
    • 0031333803 scopus 로고    scopus 로고
    • Adjoint operators for the natural discretization for the divergence, gradient and curl on logically rectangular grids
    • Hyman, J. M. and M. Shashkov, "Adjoint operators for the natural discretization for the divergence, gradient and curl on logically rectangular grids," Appl. Num. Math., Vol. 25, 413-442, 1997.
    • (1997) Appl. Num. Math , vol.25 , pp. 413-442
    • Hyman, J.M.1    Shashkov, M.2
  • 65
    • 0000397429 scopus 로고    scopus 로고
    • Mimetic discretizations for Maxwell's equations
    • Hyman, J. M. and M. Shashkov, "Mimetic discretizations for Maxwell's equations," J. Comp. Phys., Vol. 151, 881-909, 1999.
    • (1999) J. Comp. Phys , vol.151 , pp. 881-909
    • Hyman, J.M.1    Shashkov, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.