References
- Avellaneda , M. , Hou , T. and Papanicolaou , G. 1991 . Finite difference approximations for partial differential equations with rapidly oscillating coefficients . Math. Modell. Numer. Anal. , 25 ( No. 6 ) : 693 – 710 .
- Bensoussan , A. , Lions , J. L. and Papanicolaou , G. 1978 . Studies in Mathematics and Its Applications , Vol. 5 , Amsterdam : North-Holland . Asymptotic Analysis for Periodic Structures
- Berggren , S. , Lukkassen , D. and Meidell , A. 2001 . A new method for numerical solution of checkerboard fields . Journal of Applied Mathematics , 1 ( No. 4 ) : 157 – 173 .
- Bloch , F. , . 1928 . Über die quantenmechanik der electronen in kristallgittern . Z. Phys. , 52 : 555 – 600 .
- Cioranescu , D. and Donato , P. 1999 . An Introduction to Homogenization , Oxford : Oxford University Press .
- Conca , C. and Natesan , S. 2003 . Numerical methods for elliptic partial differential equations with rapidly oscillating coefficients . Comput. Methods Appl. Mech. Engrg. , 192 : 47 – 76 .
- Conca , C. and Vanninathan , M. 1997 . Homogenization of periodic structures via Bloch decomposition . SIAM J. Appl. Math. , 57 ( No. 6 ) : 1639 – 1659 .
- Dorobantu , M. and Engquist , B. 1998 . W avelet-based numerical homogenization . SIAM Journal on Numerical Analysis , 35 ( No. 2 ) : 540 – 559 .
- Floquet , G. , . 1883 . Sur les équations différentielles linéaries à coefficients périodique . Ann. École Norm. Sup. , 12 : 47 – 88 .
- Guenneau , S. and Zolla , F. 2000 . Homogenization of three-dimensional finite photonic crystals . Progress In Electromagnetics Research , PIER 27 : 91 – 127 .
- Hou , T. Y. , Wu , X. H. and Cai , Z. 1999 . on vergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients . Mathematics of Computation , 68 ( 227 ) : 913 – 943 .
- Jikov , V. V. , Kozlov , S. M. and Oleinik , O. A. 1994 . Homogenization of Differential Operators and Integral Functionals , Berlin : Springer-Verlag .
- Johnson , S. G. and Joannopoulos , J. D. 2001 . Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis . Opt. Express , 8 ( No. 3 ) : 173 – 190 .
- Kittel , C. 1986 . Introduction to Solid State Physics , 6th edition , New York : John Wiley & Sons .
- Kristensson , G. , . 2003 . Homogenization of spherical inclusions . Progress In Electromagnetics Research , PIER 42 : 1 – 25 .
- Kristensson , G. , . 2005 . Homogenization of corrugated interfaces in electromagnetics . Progress In Electromagnetics Research , PIER 55 : 1 – 31 .
- Odeh , F. and Keller , J. B. 1964 . Partial differential equations with periodic coefficients and Bloch waves . J. Math. Phys. , 5 : 1499 – 1504 .
- Saad , Y. 1996 . Iterative Methods for Sparse Linear Systems , Boston : PWS Publishing Company .
- Sjöberg , D. , . 2005 . Homogenization of dispersive material parameters for Maxwell's equations using a singular value decomposition . Multiscale Modeling and Simulation , 4 ( No. 3 ) : 760 – 789 .
- Sjöberg , D. , . 2006 . Exact and asymptotic dispersion relations for homogenization of stratified media with two phases . Journal of Electromagn. Waves and Appl. , 20 ( No. 6 ) : 781 – 792 .
- Sjöberg , D. , Engström , C. , Kristensson , G. , Wall , D. J. N. and Wellander , N. 2005 . A Floquet-Bloch decomposition of Maxwell's equations,applied to homogenization . Multiscale Modeling and Simulation , 4 ( No. 1 ) : 149 – 171 .
- Wilcox , C. H. , . 1978 . Theory of Bloch waves . Journal d'Analyse Mathématique , 33 : 146 – 167 .