Techn. University, Diss., 2007--Darmstadt.

Chemnitz, Techn. University Diss., 2005. / Erscheinungsjahr an der Haupttitelstelle: 1998.

Darmstadt, Techn. Universiẗat, Diss., 2008. / Dateien im PDF-Format.

Darmstadt, Techn. University, Diss., 2007.

Le retournement temporel exploite la réversibilité temporelle de l’équation d’onde dans les milieux sans perte. Cela implique qu’une onde émise par une source peut rebrousser chemin et se focaliser sur sa source originale par le biais d’un miroir à retournement temporel. Cette focalisation permet de situer l’emplacement de cette source. Le but de cette thèse est d’exploiter le phénomène de retournement temporel d’ondes électromagnétiques en vue de la localisation et la caractérisation partielle d’objets diffractants enfouis dans un milieu sans perte. Notre étude est menée dans le domaine temporel large bande en se basant sur une modélisation numérique par la technique d’intégration finie.Le domaine temporel est un domaine assez peu exploré dans la littérature contrairement au domaine fréquentiel. La principale problématique est la détermination de l’instant de focalisation qui nous permet de choisir la distribution des champs à partir de laquelle les objets diffractants seront localisés. Nous introduisons dans ce manuscrit un critère de choix d’instant de focalisation qui est comparé tout au long des études entreprises au critère du minimum d’entropie.La démarche empruntée exploite l’analyse de cartographies d’énergie électromagnétique en deux et trois dimensions. Elle est validée dans un premier temps par l’analyse de configurations canoniques exploitant des données synthétiques obtenues par simulation. L’influence de divers paramètres relatifs aux objets diffractants est étudiée de même que l’impact du nombre d’émetteurs récepteurs du miroir à retournement temporel. Dans une seconde étape une expérimentation contrôlée en chambre anéchoïque à SUPELEC est réalisée en utilisant des antennes en régime harmonique et en régime impulsionnel. / Time reversal is, as is now well-known, exploiting the temporal reversibility of the wave equation in assumed lossless media. To summarize, it implies that a wave emitted by a given source may turn back and thereupon focus onto its original source by means of a so-called Time Reversal Mirror (TRM), which operation, properly simulated from field data acquired in a given measurement domain, could enable us to locate the source indeed. The aim of this thesis is to exploit the phenomenon of time reversal for the localization and the partial characterization, whenever possible, of diffracting objects (dielectric and conducting scatterers, in which sources are induced by given antennas, usually dipole-like) that are buried in a lossless medium (it can be a free space or a half-space) within a fully 3-D transient electromagnetic context. Time-domain certainly is a less explored area in the literature than frequency-domain, and this 3-D context (even if some 2-D validation studies are led also in the present work) is particularly demanding, computatinally speaking as well as at the level of real laboratory experiments. In addition, it requires that we be able to accurately compute the vector electromagnetic field in this time domain in an appropriate wideband situation, as well as whatever field is time reversed during the experiments, which are tasks performed via a full-wave Finite Integration Technique (FIT) developed at LGEP as is validated and discussed in some length in the manuscript. The main problem however is the determination of the moment of focus which would enable us determine the location of the scatterers at least to some extent. Here, to that effect, we introduce and discuss in depth a new criterion of choice of the instant of focus, which is in particular compared throughout the studies undertaken to the usually employed minimum entropy criterion. Influences of the various parameters of the scatterers themselves and of the measurement set-ups are thoroughly discussed on the way. Let us emphasize that what matters to us is the behavior of the (time-reversed) electromagnetic energy and not only of the electric field as standard, that is, the approach taken builds and uses the analysis of energy maps obtained by the aforementioned 3-D numerical modeling. Beyond the modeling of pure synthetic field data and discussions thereof, much attention is also given to leading controlled experiments on canonical targets using both transient and frequency-diverse time-harmonic sources within an anechoic chamber which was made available to us in SUPELEC.

This work is concerned with the applicability of several approximation methods (finite section method, Galerkin and collocation methods with maximum defect splines for uniform and non uniform meshes) to operators belonging to the closed subalgebra generated by operators of multiplication bz piecewise continuous functions and convolution operators also with piecewise continuous generating function.

This work is concerned with the applicability of several approximation methods (finite section method, Galerkin and collocation methods with maximum defect splines for uniform and non uniform meshes) to operators belonging to the closed subalgebra generated by operators of multiplication bz piecewise continuous functions and convolution operators also with piecewise continuous generating function.

Diese Arbeit widmet sich der Simulation von elektrischen/elektronischen Schaltungen welche um elektromagnetische Bauelemente erweitert werden. Im Fokus stehen unterschiedliche Kopplungen der Schaltungsgleichungen, modelliert mit der modifizierten Knotenanalyse, und den elektromagnetischen Bauelementen mit deren verfeinerten Modell basierend auf den vollen Maxwell-Gleichungen in der Lorenz-geeichten A-V Formulierung welche durch Finite-Integrations-Technik räumlich diskretisiert werden. Eine numerische Analyse erweitert die topologischen Kriterien für den Index der resultierenden differential-algebraischen Gleichungen, wie sie bereits in anderen Arbeiten mit ähnlichen Feld/Schaltkreis-Kopplungen hergeleitet wurden. Für die Simulation werden sowohl ein monolithischer Ansatz als auch Waveform-Relaxationsmethoden untersucht. Im Mittelpunkt stehen dabei Zeitintegration, Skalierungsmethoden, strukturelle Eigenschaften und ein hybride Ansatz zur Lösung der zugrundeliegenden linearen Gleichungssysteme welcher den Einsatz spezialisierter Löser für die jeweiligen Teilsysteme erlaubt. Da die vollen Maxwell-Gleichungen zusätzliche Ableitungen in der Kopplungsstruktur verursachen, sind bisher existierende Konvergenzaussagen für die Waveform-Relaxation von gekoppelten differential-algebraischen Gleichungen nicht anwendbar und motivieren eine neue Konvergenzanalyse. Auf dieser Analyse aufbauend werden hinreichende topologische Kriterien entwickelt, welche eine Konvergenz von Gauß-Seidel- und Jacobi-artigen Waveform-Relaxationen für die gekoppelten Systeme garantieren. Schließlich werden numerische Benchmarks zur Verfügung gestellt, um die eingeführten Methoden und Theoreme dieser Abhandlung zu unterstützen. / This work is devoted to the simulation of electrical/electronic circuits incorporating electromagnetic devices. The focus is on different couplings of the circuit equations, modeled with the modified nodal analysis, and the electromagnetic devices with their refined model based on full-wave Maxwell's equations in Lorenz gauged A-V formulation which are spatially discretized by the finite integration technique. A numerical analysis extends the topological criteria for the index of the resulting differential-algebraic equations, as already derived in other works with similar field/circuit couplings. For the simulation, both a monolithic approach and waveform relaxation methods are investigated. The focus is on time integration, scaling methods, structural properties and a hybrid approach to solve the underlying linear systems of equations with the use of specialized solvers for the respective subsystems. Since the full-Maxwell approach causes additional derivatives in the coupling structure, previously existing convergence statements for the waveform relaxation of coupled differential-algebraic equations are not applicable and motivate a new convergence analysis. Based on this analysis, sufficient topological criteria are developed which guarantee convergence of Gauss-Seidel and Jacobi type waveform relaxation schemes for introduced coupled systems. Finally, numerical benchmarks are provided to support the introduced methods and theorems of this treatise.