no. 3
Component mode synthesis and eigenvalues of second order operators : discretization and algorithm
ESAIM: Modélisation mathématique et analyse numérique, Tome 26 (1992) no. 3, pp. 385-423. 
@article{M2AN_1992__26_3_385_0,
     author = {Bourquin, F.},
     title = {Component mode synthesis and eigenvalues of second order operators : discretization and algorithm},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {385--423},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {26},
     number = {3},
     year = {1992},
     mrnumber = {1160133},
     zbl = {0765.65100},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1992__26_3_385_0/}
}
TY  - JOUR
AU  - Bourquin, F.
TI  - Component mode synthesis and eigenvalues of second order operators : discretization and algorithm
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1992
SP  - 385
EP  - 423
VL  - 26
IS  - 3
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://www.numdam.org/item/M2AN_1992__26_3_385_0/
LA  - en
ID  - M2AN_1992__26_3_385_0
ER  - 
%0 Journal Article
%A Bourquin, F.
%T Component mode synthesis and eigenvalues of second order operators : discretization and algorithm
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1992
%P 385-423
%V 26
%N 3
%I AFCET - Gauthier-Villars
%C Paris
%U http://www.numdam.org/item/M2AN_1992__26_3_385_0/
%G en
%F M2AN_1992__26_3_385_0
Bourquin, F. Component mode synthesis and eigenvalues of second order operators : discretization and algorithm. ESAIM: Modélisation mathématique et analyse numérique, Tome 26 (1992) no. 3, pp. 385-423. http://www.numdam.org/item/M2AN_1992__26_3_385_0/

V. I. Agoshkov[ 1988], Poincaré-Steklov's operators and domain decomposition methods in finite dimensional spaces, in R. Glowinski, G. H. Golub, J. Periaux, eds, Proceedings of the 1rst international symposium on decomposition methods for partial differential equations, Paris, SIAM editor, Philadelphia 1988. | MR | Zbl

J. P. Aubin[ 1972], Approximation of Elliptic Boundary-Value Problems, Wiley-Interscience, New-York, 1972. | MR | Zbl

M. Aufranc[ 1990], Modeling of junctions between three-dimensional and two-dimensional nonlinearly elastic structures, to appear, 1990. | Zbl

I. Babuska, J. E. Osborn [ 1990], Eigenvalue problems, to appear in Handbook of Numerical Analysis, North Holland, P. G. Ciarlet and J. L. Lions editors, 1990. | MR | Zbl

M. Bernadou, S. Fayolle, F. Lene [ 1988], Numerical analysis of junctions between plates, rapport I.N.R.I.A. n° 865, juillet 1988. | MR | Zbl

C. Bernardi, Y. Maday, T. Patera [ 1989a], A new nonconforming approach to domain decomposition : the mortar element method ; Report 89027 of the Laboratoire d'Analyse Numérique de l'université Pierre et Marie Curie. | Zbl

C. Bernardi, Y. Maday, C. Mavriplis, T. Patera [ 1989b], Nonconforming coupling of variational discretizations, Part I : The mortar element method applied to spectral discretizations, to appear in the Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, Huntsville, 1989.

G. Beylkin, R. Coifman, V. Rokhlin [ 1989], Fast wavelet transform and numerical algorithms II. Preprint. | MR

P. E. Bjorstad, O. B. Widlund [ 1986], Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal. 23, 1097-1120. | MR | Zbl

J. F. Bourgat, R. Glowinski, P. Le Tallec[ 1988], Formulation variationnelle et algorithme de décomposition de domaines pour les problèmes elliptiques, C. R. Acad. Sci. Paris, t. 306, Série I, p. 569-572, 1988. | MR | Zbl

F. Bourquin [ 1989], Synthèse modale d'opérateurs elliptiques du second ordre, C. R. Acad. Sci. Paris, t. 309, Série I, p. 919-922, 1989. | MR | Zbl

F. Bourquin [ 1990a], Analysis and comparison of several component mode synthesis methods on one-dimensional domains, Numer. Math., 58, 11-34. | MR | Zbl

F. Bourquin [ 1990b], Domain decomposition and eigenvalues of second order operators : convergence analysis, to appear.

F. Bourquin [ 1991], Domain decomposition and eigenvalue approximation for elastic multi-structures, Doctorat dissertation, Université P.-M. Curie.

F. Bourquin, P. G. Ciarlet [ 1989], Modeling and justification of eigenvalue problems for junctions between elastic structures, J, Funct. Anal., vol, 87, 2, p. 392-427, dec. 1989. | MR | Zbl

F. Bourquin, F. D'Hennezel [ 1992], to appear in Comput. Math. Appl. Mech. Eng.

J. H. Bramble, J. E. Pasciak, A. H. Schatz [ 1986], An iterative method for elliptic problems on regions partitioned into substructures. Math. Comp. 46, 361-369. | MR | Zbl

A. P. Calderon [ 1963], Boundary value problems for elliptic equations, in « Proc. Joint Soviet-American Symp. on Part, Diff. Eqns. » p. 1-4, Novosibirsk, 1963. | MR

F. Chatelin [ 1983], Spectral Approximation of Linear Operators, Academic Press, 1983. | MR | Zbl

P. G. Ciarlet[ 1978], The finite element method for elliptic problems, North Holland, Amsterdam, 1978. | MR | Zbl

P. G. Ciarlet[ 1987], Modeling and numerical analysis of junctions between elastic structures, to appear in Proceedings, First International Conference on Industrial and Applied Mathematics (Paris, June 29-July 3, 1987). | MR | Zbl

P. G. Ciarlet, H. Le Dret, R. Nzengwa [ 1987], Modélisation de la jonction entre un corps élastique tridimensionnel et une plaque, C. R. Acad. Sci. Paris, Série I, 305, 55-58, 1987. | MR | Zbl

P. G. Ciarlet, H. Le Dret, R. Nzengwa [ 1989], Junctions between three-dimensional and two-dimensional linearly elastic structures, J. Math. Pures Appl., 68, 261-295. | MR | Zbl

P. G. Ciarlet, M. H. Schultz, R. S. Varga [ 1968], Numerical methods of high-order accuracy for non-linear boundary value problems, III : Eigenvalue problems. Numer. Math., 12, 120-133, 1968. | MR | Zbl

Coifman [ 1989], private communication.

R. Craig, M. C. C. Bampton [ 1968], Coupling of substructures for dynamic analysis, A.I.A.A. J. vol. 6, p. 1313-1321, 1968. | Zbl

R. R. Craig Jr [ 1985], A review of time domain and frequency domain component mode synthesis methods, joint ASCE/ASME mechanics conference, Albuquerque, New Mexico, June 24-26, A.M.D. vol 67, 1985.

M. Dauge [ 1989], Problèmes mixtes pour le Laplacien dans des domaines polyédraux courbes, C.R. Acad. Sci. Paris, t. 309, Série I, p. 553-558, 1989. | MR | Zbl

R. Dautray, J. L. Lions [ 1985], Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, vol. 1, Masson, 1985. | MR | Zbl

Ph. Destuynder [ 1989], Remarks on dynamic subsiruciuring, Eur. J. Mech. A/Solids, 8, n° 3, 201-218. | MR | Zbl

M. Door [ 1989], On the discretization of Interdomain coupling in elliptic boundary value problems, Domain decomposition methods, T. Chan, R. Glowinski, J. Périaux, O. Widlund editors, SIAM, proceedings of the second international symposium on domain decomposition methods, Los Angeles, California, Janv. 1988. | MR | Zbl

R. J. Gibert [ 1988], Vibrations des Structures, Interactions avec les fluides, Sources d'excitations aléatoires, cours de l'école d'été d'analyse numérique CEA INRIA EDF, 1986, collection de la Direction des Etudes et Recherches d'Electricité de France, Eyrolles, 1988. | Zbl

P. Grisvard [ 1985], Elliptic Problems in Non-Smooth Domains, Pitman, London, 1985. | Zbl

G. Grubb [ 1977], Boundary problems for Systems of partial differential operators of mixed order, J. Funct. Anal., 26, 131-165, 1977. | MR | Zbl

W. C. Hurty [ 1965], Dynamic analysis of structural Systems using component modes, A.I.A.A. J., vol. 4 (4), p. 678-685, 1965.

J. F. Imbert [ 1979], Calcul des structures par éléments finis, Cépadues, 1979.

L. Jezequel [ 1985], Synthèse modale : théorie et extensions, thèse d'état, université Claude Bernard, 1985.

P. Lascaux, R. Theodor [ 1989], Analyse Numérique Matricielle Appliquée à l'Art de l'Ingénieur, Masson, Paris, 1986. | MR | Zbl

H. Le Dret [ 1987], Modélisation d'une plaque pliée, C. R. Acad. Sci. Paris, Sér. I, J. 305, 581-573, 1987. | Zbl

K. Lemrabet [ 1977], Régularité de la solution d'un problème de transmission, J. Math. Pures Appl., 56, 1-38, 1977. | MR | Zbl

K. Lemrabet [ 1978], An interfaceproblem in a domain of R3, J. Math. Anal. Appl., 63, 549-562, 1978. | MR | Zbl

L. Meirovitch [ 1980], Computational Methods in Structural Dynamics, Sijthoff & Noordhoff, 1980. | MR | Zbl

B. Mercier, J. E. Osborn, J. Rappaz, P. A. Raviart [ 1981], Eigenvalue approximation by mixed and hybrid methods, Math. Comp., 36, p. 427-453, 1981 | MR | Zbl

H. Morand [ 1977], Méthodes de détermination approchée des modes propres de vibration en calcul des structures ; sous-structuration dynamique, ONERA R.T. n° 2 | 3238 RY OOOR, 1977.

H. Morand, R. Ohayon [ 1979], Substructure variational analysis of the vibrations of coupled fluid-structure Systems. Finite element results, Internat. J. Numer. Methods Engrg., vol. 14, 741-755, 1979. | Zbl

H. Poincaré [ 1890], Sur les équations aux dérivées partielles de la physique mathématique, Amer. J. Math. 72, 211-294, 1890. | JFM | MR

G. Strang, G. Fix [ 1973], An Analysis of the Finite Element Method, Prentice Hall, Series in automatic computation, 1973. | MR | Zbl

A. E. Taylor [ 1958], Introduction to Functional Analysis, Wiley, New-York, 1958. | MR | Zbl

R. Valid [ 1977], La mécanique des Milieux continus et le calcul des structures, Collection de la Direction des Etudes et Recherches d'Électricité de France, Eyrolles, 1977. | Zbl

R. Valid [ 1982], Une méthode de calcul des structures au flambage par sous-structuration et synthèse modale, C.R. Acad. Sci. Paris, t. 294, série II, p. 299-302. | MR | Zbl

R. Valid, R. Ohayon [ 1974], Influence du ballottement dans les réservoirs des bouts d'ailes sur les modes propres de vibration d'un avion, Rech. Aérospat., 1974-75, p. 319-325.

A. Weinstein, W. Stenger [ 1972], Methods of Intermediate Problems for Eigenvalues. Theory and Ramifications, Academic Press, New-York and London, 1972. | MR | Zbl