Numerical experiments with the Bloch-Floquet approach in homogenization

International Journal for Numerical Methods in Engineering

Volumn 65, Issue 9, 2006, Pages 1444-1471

  Conca, C ^a   Natesan, S ^b   Vanninathan, M ^c  

^a DEPARTAMENTO DE FÍSICA   (Chile)

^b INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI   (India)

^c TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

Author keywords

Bloch waves; Finite element method; Homogenization; Numerical solution of differential equations; Periodic structures

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; LINEAR EQUATIONS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; WAVES;

BLOCH WAVES; BLOCH-FLOQUET APPROACH; ELLIPTIC LINEAR OPERATORS; HOMOGENIZATION; NUMERICAL EXPERIMENTS; PERIODIC STRUCTURES;

NUMERICAL METHODS;

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; LINEAR EQUATIONS; MATHEMATICAL OPERATORS; NUMERICAL METHODS; PROBLEM SOLVING; WAVES;

EID: 32544453214     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1502     Document Type: Article

References (18)

1. Sánchez-Palencia E. Non-homagenous Media and Vibration Theory. Lecture Notes in Physics, vol. 127. Springer: Berlin, 1980.
2. Allaire G, Conca C, Vanninathan M. Spectral asymptotics of the Helmholtz model in fluid-solid structures. International Journal for Numerical Methods in Engineering 1999; 46:1463-1504.
3. Conca C, Planchard J, Vanninathan M. Fluids and Periodic Structures. Research in Applied Mathematics, vol. 38. Wiley/Masson: New York/Paris, 1995.
4. Bersoussan A. Lions J-L, Papanicolaou G. Asymptotic Analysis for Periodic Structures. North-Holland: Amsterdam 1978.
5. Conca C, Vanninathan M. Homogenization of periodic structures via Bloch decomposition. SIAM Journal on Applied Mathematics 1997; 57:1639-1659.
6. Conca C, Orive R, Vanninathan M. Bloch approximation in homogenization and applications. SIAM Journal on Mathematical Analysis 2002; 33:1166-1198.
7. Allaire G, Conca C. Boundary layers in the homogenization of a spectral problem in fluid-solid structures. SIAM Journal on Mathematical Analysis 1997; 29:343-379.
8. Avellaneda M, Hou T, Papanicolaou G. Finite difference approximations for partial differential equations with rapidly oscillating coefficients. Mathematical Modelling and Numerical Analysis 1991; 25:693-710.
9. Orive R, Zuazua E. Finite difference approximation of homogenization problems for elliptic equations. Multiscale Modeling and Simulation 2005; 4:36-87.
10. Hou TY, Wu XH. A multiscale finite element method for elliptic problems in composite materials and porous media. Journal of Computational Physics 1997; 134:169-189.
11. Avellaneda M, Berlyand L. Clouet J-F. Frequency-dependent acoustics of composites with interfaces. SIAM Journal on Applied Mathematics 2000; 60:2143-2181.
12. Bernardi C, Maday Y. Approximations Spectrales do problémes aux limites elliptiques. Collection Mathéhmatiques and Applications, vol. 10. Springer. Paris, 1993.
13. Gottlieb D, Orzag S. Numerical Analysis of Spectral Methods, Theory and Applications. SIAM Publications: Philadelphia, 1977.
14. Sivaji Ganesh S, Vanninathan M. Bloch wave homogenization of scalar elliptic operators. Asymptotic Analysis 2004; 39:15-44.
15. Bloch F. Über die quantemechanik der electronen in kristallgittern. Zeitschrift Fur Physik 1928; 52: 555-600.
16. Conca C, Natesan S. Numerical methods for elliptic partial differential equations with rapidly oscillating coefficients. Computer Methods in Applied Mechanics and Engineering 2003; 192:47-76.
17. Bourgat J. Numerical experiments of the homogenization method for operators with periodic coefficients. Technical Report 277, Institut de Recherche d'Infornmatique et d'Automatique, Le Chesney, France, 1978.
18. Bourgat J, Lanchon H. Application of the homogenization method to composite materials with periodic structures. Tehnical Report 208, Institut de Recherche d'Informatique et d'Automatique. Le Chesnay, France, 1976.