Champagne, Isabelle (2004) Factorization of wave propagation equations in waveguides. PhD thesis INRIA - Projet Ondes, INRIA - Projet Ondes, EP/X p.237.
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Alternative Locations: http://www.imprimerie.polytechnique.fr/Theses/Files/champagne.pdf
Abstract
This thesis aims at giving a new means of studying the Helmholtz problem inwaveguides. Our method is based on invariant embedding for cylindrical domains: a family of problems, which are similar to the initial one but take place in subdomains, is introduced. This enables us to factorize the Helmholtz equation and to get a decoupled system of differential equations. One of these is a Riccati equation and its solution is a first order differential operator - usually a Dirichlet-to-Neumann one. A representation formula for this solution is then given: introducing a homographic transformation enables us to prove it is similar to a linear semigroup.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Henry/Jacques, |
| Date: | October 2004 |
| Ecole Doctorale: | ED 447 ECOLE DOCTORALE DE L'ECOLE POLYTECHNIQUE |
| Discipline: | INRIA - Projet Ondes |
| Collection (Fonds): | EP/X |
| Institution: | EP/X |
| Department: | INRIA - Projet Ondes |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | Pde, Waveguides, Invariant embedding, Riccati, Helmholtz, Resonances, Dirichlet-to-Neumann, Modal decomposition, Ondes guidées, Plongement invariant, Riccati, Helmholtz, Dirichlet-to-Neumann, Résonances, Décomposition modale, Edp |
Table of content
I - Etude du guide d'ondes cylindrique
1 - Motivations
2 - Factorisation du problème de Helmholtz
3 - Lien avec la théorie du contrôle
4 - Transformation homographique
II - Applications et extensions
5 - Guides avec conditions absorbantes
6 - Factorisation du problème de Helmholtz en section variable
7 - Factorisation du problème de Helmholtz pour un coude
8 - Etude de guides d'ondes composés
| ID Code: | 920 |
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| Deposited By: | Nadine Garnier |
| Deposited On: | 29 November 2004 |
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