ce travail permet de résoudre leprobì eme de Helmholtz en l'´ ecrivant sous forme factorisée et en faisant appara??treappara??tre un opérateur d'impédance, dont on peut donner l'expression enétudiantenétudiant sonéquationsonéquation de Riccati ,
Handbook of mathematical functions with formulas, graphs, and mathematical tables, 1992. ,
Dynamic Programming and Partial Differential Equations, IEEE Transactions on Systems, Man, and Cybernetics, vol.3, issue.3, 1971. ,
DOI : 10.1109/TSMC.1973.4309228
Microlocal Diagonalization of Strictly Hyperbolic Pseudodifferential Systems and Application to the Design of Radiation Conditions in Electromagnetism, SIAM Journal on Applied Mathematics, vol.61, issue.6, pp.1877-1905, 2001. ,
DOI : 10.1137/S0036139999353826
URL : https://hal.archives-ouvertes.fr/hal-00347872
Wave propagation, Mathematics and its Applications. D, vol.17, 1986. ,
Applied dynamic programming, 1962. ,
Spectral theory of selfadjoint operators in Hilbert space Mathematics and its Applications (Soviet Series). D, 1987. ,
Coupled mode solution for a cylindrically symmetric oceanic waveguide with a range and depth dependent refractive index and a time varying rough sea surface, The Journal of the Acoustical Society of America, vol.73, issue.3, pp.800-805, 1983. ,
DOI : 10.1121/1.389046
Analyse fonctionnelle Collection Mathématiques Appliquées pour la Ma??triseMa??trise. [Collection of Applied Mathematics for the Master's Degree], Théorie et applications. [Theory and applications], 1983. ,
The linear-quadratic optimal control problem for parabolic systems with boundary control through a Dirichlet condition, Control of distributed parameter systems, pp.87-90, 1982. ,
Méthodes de décomposition de domaine pour lesprobì emes de propagation d'ondes en régime harmonique ; le théorème de Borg pour l'´ equation de Hil vectorielle, Thèse de doctorat, 1991. ,
Multimodal Approach and Optimum Design in Non Uniform Waveguides, Journées Européennes sur les Méthodes Numériques en Electromagnétisme, 2002. ,
Factorization of Second Order Elliptic Boundary Value Problems by Dynamic Programming ,
A Direct Study of the Riccati Equation Appearing in a Factorization Method of Second Order Elliptic oundary Value Problems by Dynamic Programming ,
IntroductionàIntroduction`Introductionà l'analyse mathématique de la propagation d'ondes en régime harmonique, pp.1994-1995 ,
On waves incurved tubes, Uch.Zap.Mosk.Gos.Univ, p.75, 1945. ,
Méthodes mathématiques pour les sciences de l'ingénieur : optimisation et analyse numérique, 1996. ,
IntroductionàIntroduction`Introductionà la théorie spectrale, 2003. ,
Contrôle optimal de systèmes gouvernés par deséquationsdeséquations aux dérivées partielles. Avant propos de P, Lelong. Dunod, 1968. ,
Probì emes aux limites non homogènes et applications, Travaux et Recherches Mathématiques, vol.1, issue.17, 1968. ,
One-way large range step methods for Helmholtz waveguides, J. Comput. Phys, vol.152, issue.1, pp.231-250, 1999. ,
Alternative single scatter approximation for one-way wave propagation, Mathematical and numerical aspects of wave propagation, pp.934-938, 2000. ,
The Riccati Method for the Helmholtz Equation, J. Acoust. Soc. Am, vol.100, issue.3, pp.1432-1446, 1996. ,
Local orthogonal transformation and one-way methods for acoustic waveguides, Wave Motion, vol.34, issue.2, pp.193-207, 2001. ,
DOI : 10.1016/S0165-2125(00)00083-4
An original approach to mode converter optimum design, IEEE Transactions on Microwave Theory and Techniques, vol.46, issue.1, 1998. ,
DOI : 10.1109/22.654916
URL : https://hal.archives-ouvertes.fr/hal-01010737
A generalized impedance method for application of the parabolic approximation to underwater acostics, J. Acoust. Soc. Am, vol.90, issue.1, pp.391-398, 1991. ,
A study of wave propagation in varying cross???section waveguides by modal decomposition. Part I. Theory and validation, The Journal of the Acoustical Society of America, vol.100, issue.4, 1996. ,
DOI : 10.1121/1.417913
Sound propagation in rigid bends : a multimodal approach, J. Acoust. Soc. Am, vol.110, issue.3, 2001. ,
Muldimodal analysis of acoustic propagation in three-dimensional bends, 2002. ,
IntroductionàIntroduction`Introductionà l'analyse numérique deséquationsdeséquations aux dérivées partielles, Collection Mathématiques Appliquées pour la Ma??triseMa??trise. [Collection of Applied Mathematics for the Master's Degree]. Masson, 1983. ,
Riccati differential equations, Mathematics in Science and Engineering, vol.86, 1972. ,
Sur l'´ equation de Riccati stationnaire associée auprobì eme de contróle d'un système parabolique, C. R. Acad. Sci. Paris Sér. A-B, vol.287, issue.6, pp.445-448, 1978. ,
Sur le semi-groupe non linéaire associéassocié`associéà l'´ equation de Riccati, 1981. ,
Superposition laws for solutions of differential matrix Riccati equations arising in control theory, IEEE Transactions on Automatic Control, vol.30, issue.3, pp.266-272, 1985. ,
DOI : 10.1109/TAC.1985.1103934
Worst-case design in the time domain: The maximum principle and the standardH ??? problem, Mathematics of Control, Signals, and Systems, vol.11, issue.4, pp.301-324, 1990. ,
DOI : 10.1007/BF02551373