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Volumn 4, Issue 1, 2005, Pages 149-171

A Floquet-Bloch decomposition of Maxwell's equations applied to homogenization

Author keywords

Bloch waves; Eigenvalue problem; Homogenization; Maxwell's equations

Indexed keywords

DIFFERENTIATION (CALCULUS); EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS; VECTORS;

EID: 33644684621     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/040607034     Document Type: Article
Times cited : (57)

References (27)
  • 1
    • 0031994541 scopus 로고    scopus 로고
    • Bloch wave homogenization and spectral asymptotic analysis
    • G. Allaire and C. Conca, Bloch wave homogenization and spectral asymptotic analysis, J. Math. Pures Appl, (9), 77 (1998), pp. 153-208.
    • (1998) J. Math. Pures Appl , vol.77 , Issue.9 , pp. 153-208
    • Allaire, G.1    Conca, C.2
  • 2
    • 0035304043 scopus 로고    scopus 로고
    • Nonlinear photonic crystals: I. Quadratic nonlinearity
    • A. Babin and A. Figotin, Nonlinear photonic crystals: I. Quadratic nonlinearity, Waves Random Media, 11 (2001), pp. R31-R102.
    • (2001) Waves Random Media , vol.11
    • Babin, A.1    Figotin, A.2
  • 3
    • 0003529370 scopus 로고
    • Asymptotic Analysis for Periodic Structures
    • North-Holland, Amsterdam
    • A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, Stud. Math. Appl. 5, North-Holland, Amsterdam, 1978.
    • (1978) Stud. Math. Appl. , vol.5
    • Bensoussan, A.1    Lions, J.L.2    Papanicolaou, G.3
  • 4
    • 34250940025 scopus 로고
    • Über die Quantenmechanik der Electronen in Kristallgittern
    • F. Bloch, Über die Quantenmechanik der Electronen in Kristallgittern, Z. Phys., 52 (1928), pp. 555-600.
    • (1928) Z. Phys. , vol.52 , pp. 555-600
    • Bloch, F.1
  • 6
    • 0037414944 scopus 로고    scopus 로고
    • Numerical methods for elliptic partial differential equations with rapidly oscillating coefficients
    • C. Conca and S. Natesan, Numerical methods for elliptic partial differential equations with rapidly oscillating coefficients, Comput. Methods Appl. Mech. Engrg., 192 (2003), pp. 47-76.
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 47-76
    • Conca, C.1    Natesan, S.2
  • 7
    • 0036375626 scopus 로고    scopus 로고
    • Bloch approximation in homogenization and applications
    • C. Conca, R. Orive, and M. Vanninathan, Bloch approximation in homogenization and applications, SIAM J. Math. Anal., 33 (2002), pp. 1166-1198.
    • (2002) SIAM J. Math. Anal. , vol.33 , pp. 1166-1198
    • Conca, C.1    Orive, R.2    Vanninathan, M.3
  • 8
    • 0031352502 scopus 로고    scopus 로고
    • Homogenization of periodic structures via Bloch decomposition
    • C. Conca and M. Vanninathan, Homogenization of periodic structures via Bloch decomposition, SIAM J. Appl. Math., 57 (1997), pp. 1639-1659.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1639-1659
    • Conca, C.1    Vanninathan, M.2
  • 9
    • 0000404778 scopus 로고    scopus 로고
    • An efficient method for band structure calculations in 3D photonic crystals
    • D. C. Dobson, J. Gopalakrishnan, and J. E. Pasciak, An efficient method for band structure calculations in 3D photonic crystals, J. Comput. Phys., 161 (2000), pp. 668-679.
    • (2000) J. Comput. Phys. , vol.161 , pp. 668-679
    • Dobson, D.C.1    Gopalakrishnan, J.2    Pasciak, J.E.3
  • 10
    • 33747989822 scopus 로고    scopus 로고
    • A general environment for the treatment of discrete problems and its application to the finite element method
    • P. Dular, C. Geuzaine, F. Henrotte, and W. Legros, A general environment for the treatment of discrete problems and its application to the finite element method, IEEE Trans. Magnetics, 34 (1998), pp. 3395-3398.
    • (1998) IEEE Trans. Magnetics , vol.34 , pp. 3395-3398
    • Dular, P.1    Geuzaine, C.2    Henrotte, F.3    Legros, W.4
  • 11
    • 33644701992 scopus 로고    scopus 로고
    • A Comparison of Two Numerical Methods for Homogenization of Maxwell's Equations
    • Tech. Report LUTEDX/(TEAT-7121)/1-10/(2004), Lund Institute of Technology, Department of Electroscience, Lund, Sweden
    • C. Engström and D. Sjöberg, A Comparison of Two Numerical Methods for Homogenization of Maxwell's Equations, Tech. Report LUTEDX/ (TEAT-7121)/1-10/(2004), Lund Institute of Technology, Department of Electroscience, Lund, Sweden, 2004, http://www.es.lth.se.
    • (2004)
    • Engström, C.1    Sjöberg, D.2
  • 12
    • 0003001490 scopus 로고
    • Sur les équations différentielles linéaries à coefficients périodique
    • G. Floquet, Sur les équations différentielles linéaries à coefficients périodique, Ann. École Norm. Sup., 12 (1883), pp. 47-88.
    • (1883) Ann. École Norm. Sup. , vol.12 , pp. 47-88
    • Floquet, G.1
  • 13
    • 84887472217 scopus 로고    scopus 로고
    • Homogenization of three-dimensional finite photonic crystals
    • S. Guenneau and F. Zolla, Homogenization of three-dimensional finite photonic crystals, Progress in Electromagnetics Research, 27 (2000), pp. 91-127.
    • (2000) Progress in Electromagnetics Research, , vol.27 , pp. 91-127
    • Guenneau, S.1    Zolla, F.2
  • 14
    • 0003284894 scopus 로고
    • The Analysis of Linear Partial Differential Operators I
    • Springer-Verlag, Berlin, Heidelberg
    • L. Hörmander, The Analysis of Linear Partial Differential Operators I, Grundlehren Math. Wiss. 256, Springer-Verlag, Berlin, Heidelberg, 1983.
    • (1983) Grundlehren Math. Wiss. , vol.256
    • Hörmander, L.1
  • 15
    • 0000278298 scopus 로고    scopus 로고
    • Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis
    • S. G. Johnston and J. D. Joannopoulos, Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis, Opt. Express, 8 (2001), pp. 173-190.
    • (2001) Opt. Express , vol.8 , pp. 173-190
    • Johnston, S.G.1    Joannopoulos, J.D.2
  • 18
    • 85069074933 scopus 로고
    • 3rd ed., Butterworth-Heinemann, Linacre House, Jordan Hill, Oxford, UK
    • L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1, 3rd ed., Butterworth-Heinemann, Linacre House, Jordan Hill, Oxford, UK, 1980.
    • (1980) Statistical Physics , Issue.PART 1
    • Landau, L.D.1    Lifshitz, E.M.2
  • 19
    • 0038902126 scopus 로고    scopus 로고
    • The essential spectrum of the nonself-adjoint Maxwell operator in a bounded domain
    • M. Lassas, The essential spectrum of the nonself-adjoint Maxwell operator in a bounded domain, J. Math. Anal. Appl., 224 (1998), pp. 201-217.
    • (1998) J. Math. Anal. Appl. , vol.224 , pp. 201-217
    • Lassas, M.1
  • 20
    • 0037020945 scopus 로고    scopus 로고
    • Homogeneous models for bianisotropic crystals
    • S. Ponti, J. A. Reyes, and C. Oldano, Homogeneous models for bianisotropic crystals, J. Phys.-Condensed Matter, 14 (2002), pp. 10173-10182.
    • (2002) J. Phys.-Condensed Matter , vol.14 , pp. 10173-10182
    • Ponti, S.1    Reyes, J.A.2    Oldano, C.3
  • 21
    • 0026204381 scopus 로고
    • A dispersive effective medium for wave propagation in periodic composites
    • F. Santosa and W. W. Symes, A dispersive effective medium for wave propagation in periodic composites, SIAM J. Appl. Math., 51 (1991), pp. 984-1005.
    • (1991) SIAM J. Appl. Math. , vol.51 , pp. 984-1005
    • Santosa, F.1    Symes, W.W.2
  • 22
    • 33644664190 scopus 로고
    • Asymptotic expansion of the solution of a second-order elliptic equation with periodic rapidly oscillating coefficients
    • (in Russian); Math. USSR-Sb., 43 (1982), pp. 181-198 (in English)
    • E. V. Sevost'yanova, Asymptotic expansion of the solution of a second-order elliptic equation with periodic rapidly oscillating coefficients, Mat. Sb. (N.S.), 115 (1981), pp, 204-222 (in Russian); Math. USSR-Sb., 43 (1982), pp. 181-198 (in English).
    • (1981) Mat. Sb. (N.S.) , vol.115 , pp. 204-222
    • Sevost'yanova, E.V.1
  • 25
    • 0038344178 scopus 로고    scopus 로고
    • Homogenization of the Maxwell equations: Case I. Linear theory
    • N. Wellander, Homogenization of the Maxwell equations: Case I. Linear theory, Appl. Math., 46 (2001), pp. 29-51.
    • (2001) Appl. Math. , vol.46 , pp. 29-51
    • Wellander, N.1
  • 26
    • 1842458239 scopus 로고    scopus 로고
    • Homogenization of the Maxwell equations at fixed frequency
    • N. Wellander and G. Kristensson, Homogenization of the Maxwell equations at fixed frequency, SIAM J. Appl. Math., 64 (2003), pp. 170-195.
    • (2003) SIAM J. Appl. Math. , vol.64 , pp. 170-195
    • Wellander, N.1    Kristensson, G.2
  • 27
    • 51249187120 scopus 로고
    • Theory of Bloch waves
    • C. H. Wilcox, Theory of Bloch waves, J. Analyse Math., 33 (1978), pp. 146-167.
    • (1978) J. Analyse Math. , vol.33 , pp. 146-167
    • Wilcox, C.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.