Component mode synthesis and eigenvalues of second order operators : discretization and algorithm

F. Bourquin

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1992)

  • Volume: 26, Issue: 3, page 385-423
  • ISSN: 0764-583X

How to cite

top

Bourquin, F.. "Component mode synthesis and eigenvalues of second order operators : discretization and algorithm." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 26.3 (1992): 385-423. <http://eudml.org/doc/193669>.

@article{Bourquin1992,
author = {Bourquin, F.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {eigenvalue problems; finite elements; fixed interface method; component mode synthesis; Galerkin method; domain decomposition; eigensolutions; Poincaré-Steklov operator; error bounds; numerical results},
language = {eng},
number = {3},
pages = {385-423},
publisher = {Dunod},
title = {Component mode synthesis and eigenvalues of second order operators : discretization and algorithm},
url = {http://eudml.org/doc/193669},
volume = {26},
year = {1992},
}

TY - JOUR
AU - Bourquin, F.
TI - Component mode synthesis and eigenvalues of second order operators : discretization and algorithm
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1992
PB - Dunod
VL - 26
IS - 3
SP - 385
EP - 423
LA - eng
KW - eigenvalue problems; finite elements; fixed interface method; component mode synthesis; Galerkin method; domain decomposition; eigensolutions; Poincaré-Steklov operator; error bounds; numerical results
UR - http://eudml.org/doc/193669
ER -

References

top
  1. 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. Zbl0683.65097MR972513
  2. J. P. AUBIN[ 1972], Approximation of Elliptic Boundary-Value Problems, Wiley-Interscience, New-York, 1972. Zbl0248.65063MR478662
  3. M. AUFRANC[ 1990], Modeling of junctions between three-dimensional and two-dimensional nonlinearly elastic structures, to appear, 1990. Zbl0754.73034
  4. 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. Zbl0875.65087MR1115240
  5. M. BERNADOU, S. FAYOLLE, F. LENE [ 1988], Numerical analysis of junctions between plates, rapport I.N.R.I.A. n° 865, juillet 1988. Zbl0687.73068MR1020628
  6. 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. Zbl0797.65094
  7. 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. 
  8. G. BEYLKIN, R. COIFMAN, V. ROKHLIN [ 1989], Fast wavelet transform and numerical algorithms II. Preprint. Zbl0722.65022MR1085827
  9. 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. Zbl0615.65113MR865945
  10. 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. Zbl0637.65104MR941627
  11. F. BOURQUIN [ 1989], Synthèse modale d'opérateurs elliptiques du second ordre, C. R. Acad. Sci. Paris, t. 309, Série I, p. 919-922, 1989. Zbl0685.47038MR1055222
  12. F. BOURQUIN [ 1990a], Analysis and comparison of several component mode synthesis methods on one-dimensional domains, Numer. Math., 58, 11-34. Zbl0686.34026MR1069651
  13. F. BOURQUIN [ 1990b], Domain decomposition and eigenvalues of second order operators : convergence analysis, to appear. 
  14. F. BOURQUIN [ 1991], Domain decomposition and eigenvalue approximation for elastic multi-structures, Doctorat dissertation, Université P.-M. Curie. 
  15. 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. Zbl0699.73010MR1026860
  16. F. BOURQUIN, F. D'HENNEZEL [ 1992], to appear in Comput. Math. Appl. Mech. Eng. 
  17. 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. Zbl0595.65111MR829613
  18. 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. MR203254
  19. F. CHATELIN [ 1983], Spectral Approximation of Linear Operators, Academic Press, 1983. Zbl0517.65036MR716134
  20. P. G. CIARLET[ 1978], The finite element method for elliptic problems, North Holland, Amsterdam, 1978. Zbl0383.65058MR520174
  21. 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). Zbl0707.73045MR976852
  22. 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. Zbl0632.73015MR902275
  23. 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. Zbl0661.73013MR1025905
  24. 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. Zbl0181.18303MR233517
  25. COIFMAN [ 1989], private communication. 
  26. R. CRAIG, M. C. C. BAMPTON [ 1968], Coupling of substructures for dynamic analysis, A.I.A.A. J. vol. 6, p. 1313-1321, 1968. Zbl0159.56202
  27. 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. 
  28. 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. Zbl0715.35022MR1053276
  29. R. DAUTRAY, J. L. LIONS [ 1985], Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, vol. 1, Masson, 1985. Zbl0642.35001MR918560
  30. Ph. DESTUYNDER [ 1989], Remarks on dynamic subsiruciuring, Eur. J. Mech. A/Solids, 8, n° 3, 201-218. Zbl0692.73059MR1008130
  31. 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. Zbl0682.65068MR991999
  32. 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. Zbl0753.73008
  33. P. GRISVARD [ 1985], Elliptic Problems in Non-Smooth Domains, Pitman, London, 1985. Zbl0695.35060
  34. G. GRUBB [ 1977], Boundary problems for Systems of partial differential operators of mixed order, J. Funct. Anal., 26, 131-165, 1977. Zbl0368.35030MR501197
  35. W. C. HURTY [ 1965], Dynamic analysis of structural Systems using component modes, A.I.A.A. J., vol. 4 (4), p. 678-685, 1965. 
  36. J. F. IMBERT [ 1979], Calcul des structures par éléments finis, Cépadues, 1979. 
  37. L. JEZEQUEL [ 1985], Synthèse modale : théorie et extensions, thèse d'état, université Claude Bernard, 1985. 
  38. P. LASCAUX, R. THEODOR [ 1989], Analyse Numérique Matricielle Appliquée à l'Art de l'Ingénieur, Masson, Paris, 1986. Zbl0601.65016MR835440
  39. H. LE DRET [ 1987], Modélisation d'une plaque pliée, C. R. Acad. Sci. Paris, Sér. I, J. 305, 581-573, 1987. Zbl0634.73047
  40. K. LEMRABET [ 1977], Régularité de la solution d'un problème de transmission, J. Math. Pures Appl., 56, 1-38, 1977. Zbl0366.35036MR509312
  41. K. LEMRABET [ 1978], An interfaceproblem in a domain of R3, J. Math. Anal. Appl., 63, 549-562, 1978. Zbl0394.35029MR493687
  42. L. MEIROVITCH [ 1980], Computational Methods in Structural Dynamics, Sijthoff & Noordhoff, 1980. Zbl0439.73074MR603443
  43. 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 Zbl0472.65080MR606505
  44. 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. 
  45. 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. Zbl0402.73052
  46. H. POINCARÉ [ 1890], Sur les équations aux dérivées partielles de la physique mathématique, Amer. J. Math. 72, 211-294, 1890. Zbl22.0977.03MR1505534JFM22.0977.03
  47. G. STRANG, G. FIX [ 1973], An Analysis of the Finite Element Method, Prentice Hall, Series in automatic computation, 1973. Zbl0356.65096MR443377
  48. A. E. TAYLOR [ 1958], Introduction to Functional Analysis, Wiley, New-York, 1958. Zbl0081.10202MR98966
  49. 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. Zbl0454.73003
  50. 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. Zbl0485.73032MR657821
  51. 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. 
  52. A. WEINSTEIN, W. STENGER [ 1972], Methods of Intermediate Problems for Eigenvalues. Theory and Ramifications, Academic Press, New-York and London, 1972. Zbl0291.49034MR477971

Citations in EuDML Documents

top
  1. Ulrich L. Hetmaniuk, Richard B. Lehoucq, A special finite element method based on component mode synthesis
  2. Dinh Bao Phuong Huynh, David J. Knezevic, Anthony T. Patera, A Static condensation Reduced Basis Element method : approximation and a posteriori error estimation
  3. Alfredo Bermúdez, Luis Hervella-Nieto, Rodolfo Rodríguez, A modal synthesis method for the elastoacoustic vibration problem
  4. Alfredo Bermúdez, Luis Hervella-Nieto, Rodolfo Rodríguez, A modal synthesis method for the elastoacoustic vibration problem

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.