Neumann-Neumann algorithms for spectral elements in three dimensions
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 31 (1997) no. 4, p. 471-493
@article{M2AN_1997__31_4_471_0,
     author = {Pavarino, Luca F.},
     title = {Neumann-Neumann algorithms for spectral elements in three dimensions},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {31},
     number = {4},
     year = {1997},
     pages = {471-493},
     zbl = {0881.65121},
     mrnumber = {1457457},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1997__31_4_471_0}
}
Pavarino, Luca F. Neumann-Neumann algorithms for spectral elements in three dimensions. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 31 (1997) no. 4, pp. 471-493. http://www.numdam.org/item/M2AN_1997__31_4_471_0/

[1] C. Bernardi and Y. Maday, 1992, Approximations Spectrales de Problèmes aux Limites Elliptiques, vol. 10 of Mathématiques & Applications, Springer Verlag France, Paris. | MR 1208043 | Zbl 0773.47032

[2] J. H. Bramble and J. Xu, 1991, Some estimates for a weighted L2 projection, Math. Comp., 56, pp. 463-476. | MR 1066830 | Zbl 0722.65057

[3] C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, 1988, Spectral Methods in Fluid Dynamics, Springer-Verlag. | MR 917480 | Zbl 0658.76001

[4] M. Casarin, 1995, Quasi-optimal Schwarz methods for the conforming spectral element discretization, in 1995 Copper Mountain Conference on Multignd Methods, N. D. Melson, T. A. Manteuffel and S. F. McCormick, eds., NASA, 1995. | Zbl 0889.65123

[5] T. F. Chan and T. P. Mathew, 1994, Domain decomposition algorithms, Acta Numerica, Cambridge University Press, pp. 61-143. | MR 1288096 | Zbl 0809.65112

[6] M. Dryja, B. F. Smith and O. B. Widlund, 1994, Schwarz analysis of itérative substructunng algorithms for elliptic problems in three dimensions, SIAM J. Numer. Anal., 31, pp. 1662-1694. | MR 1302680 | Zbl 0818.65114

[7] M. Dryja and O. B. Widlund, 1990, Towards a unified theory of domain décomposition algorithms for elliptic problems, in Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, T. Chan, R. Glowinski, J. Pénaux and O. Widlund, eds., SIAM, Philadelphia, PA, pp. 3-21. | MR 1064335 | Zbl 0719.65084

[8] M. Dryja and O. B. Wldlund, 1995, Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems, Comm. Pure Appl. Math., 48, pp. 121-155. | MR 1319698 | Zbl 0824.65106

[9] P. F. Fischer and E. M. Rønquist, 1994, Spectral element methods for large scale parallel Navier-Stokes calculations, Comp. Meth. Appl. Mech. Engr., 116, pp. 69-76. | MR 1286514 | Zbl 0826.76060

[10] P. Le Tallec, 1994, Domain decomposition methods in computational mechanics, in Computational Mechanics Advances, J. T. Oden, ed., vol 1 (2), North-Holland, pp. 121-220. | MR 1263805 | Zbl 0802.73079

[11] P. Le Tallec, Y.-H. De Roeck and M. Vidrascu, 1991, Domain-decomposition methods for large linearly elliptic three dimensional problems, J. of Computational and Applied Mathematics, 35. | Zbl 0719.65083

[12] J. Mandel, Balancing domain decomposition, 1993, Comm. Numer. Meth. Engrg., 9, pp. 233-241. | MR 1208381 | Zbl 0796.65126

[13] J. Mandel and M. Brezina, 1993, Balancing domain decomposition : Theory and computations in two and three dimensions, tech. rep., Computational Mathematics Group, University of Colorado at Denver, UCD/CCM TR 2.

[14] S. S. Pahl, Schwarz type domain decomposition methods for spectral element discretizations, Master's thesis, Department of Computational and Applied Mathematics, University of Wittwatersrand, Johannesburg, South Africa, December 1993.

[15] L. F. Pavarino and O. B. Wldlund, 1997, Iterative substructuring methods for spectral elements : Problems in three dimensions based on numerical quadrature. Computers & Mathematics with Applications, 33, pp. 193-209. | MR 1442072 | Zbl 0871.41020

[16] L. F. Pavarino and O. B. Wldlund, 1996, A polylogarithmic bound for an itérative substructuring method for spectral elements in three dimensions, SIAM J. Numer. Anal., 33, pp. 1303-1335. | MR 1403547 | Zbl 0856.41007

[17] L. F. Pavarino and O. B. Wldlund, 1995, Preconditioned conjugate gradient solvers for spectral elements in 3D, in Solution Techniques for Large Scale CFD Problems, W. Habashi, ed., John Wiley & Sons, pp. 249-270.

[18] E. M. Rønquist, 1992, A domain decomposition method for elliptic boundary value problems : Application to unsteady incompressible fluid flow, in Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, T. F. Chan, D. E. Keyes, G. A. Meurant, J. S. Scroggs and R. G. Voigt, eds., Philadelphia, PA, SIAM. | MR 1189558 | Zbl 0767.76056

[19] E. M. Rønquist, 1995, A domain decomposition solver for the steady Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg. To appear.

[20] B. F. Smtth, P. E. Bjørstad and W. D. Gropp, 1996, Domain Decomposition : Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press. | MR 1410757 | Zbl 0857.65126