Concept de zoom adaptatif en architecture multigrille locale ; étude comparative des méthodes L.D.C., F.A.C. et F.I.C.
Khadra, K. ; Angot, Ph. ; Caltagirone, J. P. ; Morel, P.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 30 (1996), p. 39-82 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1996-01-01
@article{M2AN_1996__30_1_39_0,
     author = {Khadra, K. and Angot, Ph. and Caltagirone, J. P. and Morel, P.},
     title = {Concept de zoom adaptatif en architecture multigrille locale ; \'etude comparative des m\'ethodes L.D.C., F.A.C. et F.I.C.},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {30},
     year = {1996},
     pages = {39-82},
     mrnumber = {1378611},
     zbl = {0851.65088},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/M2AN_1996__30_1_39_0}
}

Khadra, K.; Angot, Ph.; Caltagirone, J. P.; Morel, P. Concept de zoom adaptatif en architecture multigrille locale ; étude comparative des méthodes L.D.C., F.A.C. et F.I.C.. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 30 (1996) pp. 39-82. http://gdmltest.u-ga.fr/item/M2AN_1996__30_1_39_0/

[1] Ph. Angot et J. P. Caltagirone, 1988, Homogénéisation numérique en thermique des structures hétérogènes périodiques, Actes EUROTHERM n°4, Nancy, pp. 122-126.

[2] Ph. Angot, 1989, Contribution à l'étude des transferts thermiques dans des systèmes complexes; Application aux composants électroniques, Thèse de Doctorat de l'Université Bordeaux I, Spécialité Mécanique.

[3] Ph. Angot and J. P. Caltagirone, 1990, New graphical and computational architecture concept for numerical simulation on supercomputers, Proc, 2-nd World Congress on Computational Mechanics, Stuttgart, pp. 973-976.

[4] Ph. Angot, J. P. Caltagirone et K. Khadra, 1992, Une méthode adaptative de raffinement local : la Correction du Flux à l'Interface, C. R. Acad. Sci. Paris, 315, Série I, pp.739-745. | MR 1183814 | Zbl 0755.65120

[5] Ph. Angot, J. P. Caltagirone, K. Khadra et P. Morel, 1992, Concept de zoom en architecture de calcul; Etude comparative de trois méthodes adaptatives de raffinement local : L.D.C., F.A.C. et F.I.C., Rapport interne IMST 92-04, juin.

[6] Ph. Angot, 1994, Parallel multi-level and domain decomposition methods, Calculateurs parallèles, L.T.CP, 6, pp. 9-14.

[7] Ph. Angot et M. Laugier, 1994, La méthode F.I.C, de raccordement conservatif de sous-domaines emboîtés pour un modèle de circulation océanique, C. R. Acad.Sci. Paris, 319, Série II, pp. 993-1000.

[8] Ph. Angot and M. Laugier, 1995, Conservative matching of non-conforming grids on nested subdomains; Application to an ocean circulation model, Comput. Meth. Appl. Mech. Engrg., soumis.

[9] D. Bai and A. Brandt, 1987, Local mesh refinement muitilevel techniques, SIAM J. Sci.Stat Comput, 8, pp. 109-134. | MR 879406 | Zbl 0619.65091

[10] R. E. Bank and A. Weiser, 1985, Some a posteriori error estimates for elliptic partial differential equations, Math. Comp., 44, pp. 283-301. | MR 777265 | Zbl 0569.65079

[11] R. E. Bank, 1986, A posteriori error estimates, adaptive local mesh refinement and multigrid iteration, Lecture Notes in Mathematics, W. Hackbusch and UTrottenberg, eds., Springer-Verlag, 1228,pp. 7-23. | MR 896055 | Zbl 0619.65092

[12] R. E. Bank, T. F. Dupont and H. Yserentant, 1988, The hierarchical basis multigrid methods, Numer. Math., 52, pp.427-458 | MR 932709 | Zbl 0645.65074

[13] M. J. Berger and J. Oliger, 1984, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput Phys., 53, pp.484-512. | MR 739112 | Zbl 0536.65071

[14] C. Bernardi, Y. Maday and A. Patera, 1989, A new nonconforming approach to domain decomposition : the mortar element method, Nonlinear Partial Differential Equations and their Applications, H, Brezis and J. L. Lions, eds., Pitman Research. | Zbl 0797.65094

[15] P. E. Bjorstad and O. B. Widlund, 1986, Iterative methods for the solution of elliptic problems on regions partitioned into substructures, SIAM J. Numer. Anal, 23, pp. 1097-1120. | MR 865945 | Zbl 0615.65113

[16] J. H. Bramble, J. E. Pasciak and A. H. Schatz, 1986, An iterative method for elliptic problems on regions partitioned into substructures, Math. Comp,, 46,pp. 361-369. | MR 829613 | Zbl 0595.65111

[17] J. H. Bramble, R. E. Ewing, J. E. Pasciak and A. H. Schatz, 1988, A preconditioning technique for the efficient solution of problems with local grid refinement, Comput Meth. Appl. Mech, Engrg,, 67, pp. 149-159. | Zbl 0619.76113

[18] J. H. Bramble, J. E. Pasciak and J. Xu, 1990, Parallel multilevel preconditioners, Math. Comp., 55, pp. 1-22. | MR 1023042 | Zbl 0703.65076

[19] A. Brandt, 1973, Multi-Level Adaptive Techniques (MLAT) for fast numerical solution to boundary value problems, Lecture Notes in Physics, H. Cabannes and R. Temam, eds., Springer-Verlag, 18, pp. 82-89. | Zbl 0259.76013

[20] A. Brandt, 1977, Multi-level adaptive solution to boundary-value problems, Math. Comp., 31, pp.333-390. | MR 431719 | Zbl 0373.65054

[21] J. P. Caltagirone, K. Khadra et Ph. Angot, 1995, Sur une méthode de raffinement local multigrille pour la résolution des équations de Navier-Stokes, CR. Acad. Sci Paris, 320, Série IIb, pp. 295-302. | Zbl 0834.76065

[22] M. El Ganaoui, 1993, Etude de schémas multigrilles adaptatifs pour un problème d'advection-diffusion, D.E.A. de Mécanique, Université Aix-Marseille II,juillet.

[23] W. Hackbusch and U. Trqttenberg, 1982, eds., Multigrid Methods, Lecture Notes in Mathematics, 960, Springer-Verlag. | MR 685772

[24] W. Hackbusch, 1984, Local Defect Correction Method and Domain Decomposition Techniques, in Defect Correction Methods, Theory and Applications, K. Böhmer and H. J. Stetter, eds., Computing Supplementum, Springer-Verlag, 5, pp. 89-113. | MR 782692 | Zbl 0552.65070

[25] W. Hackbusch, 1985, Multi-Grid Methods and Applications, Series in Computational Mathematics, Springer-Verlag. | Zbl 0595.65106

[26] K. Khadra, Ph. Angot and J. P. Caltagirone, 1993, A comparison of locally adaptive multigrid methods ; L.D.C., F.A.C, and F.I.C., NASA Conf.Publ 3224, 6th Copper Mountain Conference on Multigrid Methods, N. D. Melson, S. F. McCormick and T. A. Manteuffel, eds., 1, pp.275-292.

[27] K. Khadra, 1994, Méthodes adaptatives de raffinement local multigrille; Applications aux équations de Navier-Stokes et de l'énergie, Thèse de Doctorat de l'Université Bordeaux I, Spécialité Mathématiques Appliquées, mars.

[28] P. Le Tallec, 1994, Domain decomposition methods in computational mechanics, Comput. Mech. Adv., 1, pp. 121-220. | MR 1263805 | Zbl 0802.73079

[29] S. F. Mccormick, 1984, Fast Adaptive Composite Grid (F.A.C.) Methods : theory for the variational case, in Defect Correction Methods, Theory and Applications, K. Böhmer and H. J. Stetter, eds., Computing Supplementum, Springer-Verlag, 5, pp. 115-121. | MR 782693 | Zbl 0552.65071

[30] S. F. Mccormick, ed., 1987, Multigrid Methods, Frontiers in Appl., Math., 3, SIAM, Philadelphie | MR 972752 | Zbl 0659.65094

[31] S. F. Mccormick, 1989, Multilevel adaptive methods for partial differential equations, Frontiers in Appl. Math,, 6, SIAM, Philadelphia. | MR 1056696 | Zbl 0707.65080

[32] S. V. Patankar, 1980, Numerical heat transfer and fluid flow, Hemisphère Publishing Corporation, New-York. | Zbl 0521.76003

[33] U. Rüde, 1993, Fully adaptive multigrid methods, SIAM J. Numer. AnaL, 30,pp. 230-248. | MR 1202664 | Zbl 0849.65090

[34] J. Xu, 1992, Iterative methods by space decomposition and subspace correction, SIAM Rev., 34, pp, 581-613. | MR 1193013 | Zbl 0788.65037