Application de méthodes spectrales multi-niveaux à différents problèmes de la physique mathématique
Thèses d'Orsay, no. 521 (1998) , 226 p. 
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     title = {Application de m\'ethodes spectrales multi-niveaux \`a diff\'erents probl\`emes de la physique math\'ematique},
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     year = {1998},
     publisher = {Universit\'e de Paris-Sud Centre d'Orsay},
     number = {521},
     language = {fr},
     url = {https://www.numdam.org/item/BJHTUP11_1998__0521__P0_0/}
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Moebs, Guy. Application de méthodes spectrales multi-niveaux à différents problèmes de la physique mathématique. Thèses d'Orsay, no. 521 (1998), 226 p. https://www.numdam.org/item/BJHTUP11_1998__0521__P0_0/

[1] Adam J.C., Gourdin Seveniere A., Nedelec J.C. et Raviart P.A., Study of an implicit scheme for integrating Maxwell's equations (1974) Computer Methods in Applied Mechanics and Engineering, vol 22, pp 327-346 | MR | Zbl | DOI

[2] Agrawal G.P., Nonlinear Fiber Optics Quantum Electronics, Principles and Applications | Zbl

[3] Alpert B.K. et Rokhlin V., A fast algorithm for the evaluation of Legendre expansion (1991) J. of Scientific and Statistical Computations, vol 12, pp 158-179 | MR | Zbl | DOI

[4] Ben Belgacem F. et Bernardi C., Spectral element discretization of the Maxwell equations (1997) Publication du Laboratoire d'Analyse Numérique, Université Paris 6, vol 16 | MR | Zbl

[5] Benton E. et Platzman G.W., A table of solutions of the one-dimensional Burgers equation (1972) Quarterly Journal of Mechanics and Applied Mathematics, vol 3, pp 201-230. | MR | Zbl

[6] Bernardi C. et Maday Y., Approximations spectrales de problèmes aux limites elliptiques (1992) Mathématiques et Applications, 10, Springer Verlag | MR | Zbl

[7] Blackstock D.T., Convergence of the Keck-Boyer perturbation solution for plane waves of finite amplitude in a viscous fluid (1966) J. Acoust. Soc. Am., vol 39, pp 411-413. | DOI

[8] Bossavit A., Electromagnétisme en vue de la modélisation. (1993) Mathématiques et Applications, 14, Springer Verlag | MR | Zbl

[9] Brigham E.O., The Fast Fourier Transform (1974) Prentice-Hall, Englewood Cliffs, NJ | Zbl

[10] Burgers J.M., A mathematica model illustrating the theory of turbulence (1948) Advances in Applied Mechanics, vol 1, pp 171-199. | MR

[11] Burgers J.M., The Nonlinear Diffusion Equation (1974), Ed. Reidel Boston. | Zbl | DOI

[12] Butcher J.C., The numerical analysis of ordinary differential equations Runge-Kutta and general linear methods (1987), Ed. John Wiley & Sons | MR | Zbl

[13] Canuto C., Hussaini M.Y., Quarteroni A. et Zang T.A., Spectral Methods in Fluid Dynamics (1987) Springer Series in Computational Physics, Springer Verlag | MR | Zbl

[14] Choi H., Temam R., Moin P., Kim J. Feedback Control for unsteady flow and its application to the stochastic Burgers Equation (1993) J. of Fluid Mechanics vol 253, pp 509-544 | MR | Zbl | DOI

[15] Cole J.D., On a quasi-linear parabolic equation occuring in Aerodynamics (1951) Quarterly in Applied Mathematics, vol 9, pp 225-236. | MR | Zbl

[16] Cooley J.W. et Turkey J.W., An algorithm for the Machine Calculation of complex Fourier Series (1965) Mathematics of Computation, vol 19, pp 297-301. | MR | Zbl

[17] Crouzeix M., Sur l'approximation des équations différentielles opérationnelles linéaires. (1975), Thèse Paris

[18] Da Prato G., Debussche A. et Temam R., Stochastic Burgers' Equation (1994) Nonlinear Differential Equations and Applications, vol 1 pp 389-402. | MR | Zbl | DOI

[19] Dautray R et Lions J.L., Analyse numérique matricielle pour les sciences et les techniques, tomes 1,2,3 (1984) Masson, Paris | Zbl

Dautray R et Lions J.L., Analyse numérique matricielle pour les sciences et les techniques, tomes 1,2,3 (1985) Masson, Paris | Zbl

[20] Dekker K. et Verwer J.G., Stability of Runge Kutta methods for stiff nonlinear differential equations (1984) CWI Monograpgs vol 2, North Holland, Amsterdam | MR | Zbl

[21] Deville M., Haldenwang P. et Labrosse G., Comparison of Time Integration (Finite Difference and Spectral) for the Nonlinear Burgers' Equation (1981) Proc 4th GAMM Conf. Numer. Methods in Fluid Mechanics ed Viviand H., Vieweg Braunschweig | Zbl

[22] Deville M., Kleiser L. et Montigny-Rannon F., Pressure and time treatment of Chebychev spectral solution of a Stokes problem (1984) J- of Numerical Methods in Fluids pp 1149-1163 | Zbl | DOI

[23] Dubois Th. Simulation numérique d'écoulements homogènes et non-homogènes par des méthodes spectrales multi-résolution (1993), Thèse Université Orsay - Paris Sud

[24] Fleck J.A., Morris J.R. et Feit M.D., Time Dependent Propagation Of High Energy Laser Beams through the Atmosphere (1976), Applied Physics, vol 10, pp 129-160.

[25] Funaro D., Polynomial Approximation of Differential Equations (1992), Spriger Verlag, Berlin-Heildelberg | MR | Zbl | DOI

[26] Gottlieb D. et Orszag S.A, Numerical Analysis of Spectral Methods : Theory and Applications (1977), SIAM-CBMS 26, Philadelphia | MR | Zbl

[27] Gottlieb D., Communication privée.

[28] Herbst B.M., Morris J.Li. et Mitchell A.R., Numerical experience with the nonlinear Schroedinger Equation (1985), J. of Computational Physics, vol 60, pp 282-305. | MR | Zbl | DOI

[29] Herbst B.M., et Weideman J.A.C., Split Step Methods for the solution of the Nonlinear Schroedinger Equation (1986), SIAM J. of Numerical Analysis, vol 23 num 3, pp 485-507. | MR | Zbl | DOI

[30] Hopf E., The Partial Differential Equation u t + u u x = μ u x x , (1950) Communications in Pure and Applied Mathematics, vol 3, pp 201-230. | MR | Zbl

[31] Jauberteau F., Résolution numérique des équations de Navier-Stokes instationnaires par méthodes spectrales. Méthode de Galerkin non linéaire. (1990), Thèse Université Orsay - Paris Sud

[32] Kim J., Moin P., Moser R., Turbulence statistics in fully developed channel flow at low Reynolds number (1987) J. of Fluids Mechanics, vol 77, pp 133-166. | Zbl | DOI

[33] Kreiss H.O. et Lorentz J., Initial-Boundary Value Problems and the Navier-Stokes Equations (1974), Ed. Academic Press. | Zbl | MR

[34] Kreiss H.O. et Oliger J., Stability of the Fourier Method (1979) SIAM J. Numerical Analysis, vol 16, pp 421-433. | MR | Zbl | DOI

[35] Labrosse G., Communication privée.

[36] Lascaux P. et Theodor R., Analyse numérique matricielle appliquée à l'art de l'ingénieur, tomes 1,2 (1986), Masson, Paris | MR | Zbl

Lascaux P. et Theodor R., Analyse numérique matricielle appliquée à l'art de l'ingénieur, tomes 1,2 (1987), Masson, Paris | MR | Zbl

[37] Lax M., Batteh J.H. et Agrawal G.P., Channeling of intense electromagnetic beams (1981) J. of Applied Physics, vol 52, pp 109-125. | DOI

[38] Lighthill, Viscosity Effects in Sound Waves of Finite amplitude (1956), Cambridge Univ. Press, Cambridge | MR

[39] Peyret R., Introduction to Spectral Methods (1986) Van Karman Institute Lecture Series 1986-04, Rhode-St Genese, Belgique

[40] Sanz-Serna I.M. et Verwer J.G., Conservative and nonconservative schemes for the solution of the nonlinear Schroedinger equation (1986) IMA, J. of Numerical Analysis, vol 6, pp 25-42 | MR | Zbl | DOI

[41] Shen J., Efficient spectral- Galrkin method I. Direct solvers for second- and fourth-order equations by using Legendre polynomials. (1994) SIAM, J. of Scientific Computing, vol 15, pp 1489-1505. | MR | Zbl | DOI

[42] Shen J., Efficient Chebyshev-Legendre Galerkin Methods for Elliptic Problems (1996) Proceedings of the third ICOSAHOM, Houston Journal of Mathematics, University of Houston

[43] Strang G., On the construction and comparison of difference schemes (1968) SIAM, J. of Numerical Analysis, vol 5, pp 506-517 | MR | Zbl | DOI

[44] Strauss W., nonlinear Wave Equation (1989), SIAM-CBMS 73, Philadelphia

[45] Su C.H. Gardner C.S., Korteweg-de-Vries Equation and Generalizations : III Derivation of the Korteweg-de-Vries Equation and Burgers Equation (1969) J. of Mathematical Physics, vol 10, pp 536-539. | MR | Zbl | DOI

[46] Tahar T.R. et Ablowitz M.J., Analytical and Numerical Aspects of certain Nonlinear Evolution Equations. II Numerical, Nonlinear Schroedinger Equation (1984) J. of Computational Physics, vol 55, pp 203-230 | MR | Zbl | DOI

[47] Temam R., Navier-Stokes Equations, Theory and Numerical Analysis (1977), Ed North Holland, Amsterdam | MR | Zbl

[48] Temam R., Navier-Stokes Equations and Nonlinear Functional Analysis (1983) SIAM-CBMS 41, Philadelphia | MR | Zbl

[49] Temam R., Infinite Dimensional Systems in Mechanics and Physics, (1988) Applied Mathematica Sciences 68, Springer Verlag | MR | Zbl

[50] Williamson J.H., Low storage Runge-Kutta schemes (1980), J. of Computational Physics, vol 35, pp 48-56 | MR | Zbl | DOI

[51] Yang B., Gottlieb D. et Hesthaven J.S., Spectral simulations of Electromagnetic Wave Scattering (1997) J. of Computational Physics, vol 134, pp 216-230 | Zbl | DOI

[52] Yee K.S., Numerical simulation of initial boundary value problems involving Maxwell's equations in isotropic media (1966) IEEE Antennas and Propagation, vol 14, pp 302- 307 | Zbl | DOI

[53] Zakaria A., Etude de divers schémas pseudo-spectraux de type collocation pour la résolution des équations aux dérivées partielles. Applications aux équations de Navier-Stokes (1985), Thèse Université de Nice