In this dissertation, a Method of Moments (MoM) Volume Integral Equation (VIE)-based modeling approach suitable for a patch or slot antenna on a thin finite dielectric substrate is developed and validated. Two new key features of this method are the use of proper dielectric basis functions and proper VIE conditioning, close to the metal surface, where the surface boundary condition of the zero tangential-component must be extended into adjacent tetrahedra. The extended boundary condition is the exact result for the piecewise-constant dielectric basis functions. The latter operation allows one to achieve a good accuracy with one layer of tetrahedra for a thin dielectric substrate and thereby greatly reduces computational cost. The use of low-order basis functions also implies the use of low-order integration schemes and faster filling of the impedance matrix. For some common patch/slot antennas, the VIE-based modeling approach is found to give an error of about 1% or less in the resonant frequency for one-layer tetrahedral meshes with a relatively small number of unknowns. This error is obtained by comparison with fine finite- element method (FEM) simulations, or with measurements, or with the analytical mode matching approach. Hence it is competitive with both the method of moments surface integral equation approach and with the FEM approach for the printed antennas on thin dielectric substrates. Along with the MoM development, the dissertation also presents the models and design procedures for a number of practical antenna configurations. They in particular include: i. a compact linearly polarized broadband planar inverted-F antenna (PIFA); ii. a circularly polarized turnstile bowtie antenna. Both the antennas are designed to operate in the low UHF band and used for indoor positioning/indoor geolocation.

Various error estimation and adaptive refinement techniques for the solution of electromagnetic integral equations were developed. Residual based error estimators and h-refinement implementations were done for the Method of Moments (MoM) solution of electromagnetic integral equations for a number of different problems. Due to high computational cost associated with the MoM, a cheaper solution technique known as the Locally-Corrected Nyström (LCN) method was explored. Several explicit and implicit techniques for error estimation in the LCN solution of electromagnetic integral equations were proposed and implemented for different geometries to successfully identify high-error regions. A simple p-refinement algorithm was developed and implemented for a number of prototype problems using the proposed estimators. Numerical error was found to significantly reduce in the high-error regions after the refinement. A simple computational cost analysis was also presented for the proposed error estimation schemes. Various cost-accuracy trade-offs and problem-specific limitations of different techniques for error estimation were discussed. Finally, a very important problem of slope-mismatch in the global error rates of the solution and the residual was identified. A few methods to compensate for that mismatch using scale factors based on matrix norms were developed.

La formation, l’évolution et la structure des planètes géantes font parties des grandesproblématiques de l’astrophysique moderne. Les planète géantes ont un rôle majeur carelles possèdent la plupart de la masse des systèmes planétaires et donc influencent leursévolutions dynamiques. Mon travail de thèse s’inscrit dans une démarche observationnellequi est essentielle pour apporter des contraintes sur la diversité des systèmes exoplanétaires.Mes premiers résultats de thèse sont issus d’une campagne d’observations sur trois ansréalisées avec l’instrument NaCo au VLT. Mes observations de HD142527 excluent laprésence d’une planète géante dans le disque et favoriseraient plutôt un système multiplede faible masse pour expliquer les structures de ce disque de transition. J’ai égalementdétecté une planète géante autour de HD95086. Cette planète possède des propriétés atmosphériquesparticulières. Sa présence fait de HD95086 un rare exemple de systèmesimagés possédant un disque de débris et une planète géante. Enfin, j’ai réalisé une étudestatistique sur l’ensemble du relevé et montré que les planètes géantes sur des orbiteséloignées sont rares (10 − 20 %) et ne peuvent pas s’être formées majoritairement pareffondrement direct du gaz dans un disque instable.La dernière partie de mon travail de thèse a été consacrée à l’étude du mode d’imageriedifférentielle simultanée spectrale. J’ai identifié les biais particuliers liés à la réductionde ce type de données et ai montré que leurs analyses nécessitent l’utilisation de modèlesd’évolution. Cette étude permettra d’exploiter les données de l’instrument IRDISde SPHERE installé au VLT. / How giant exoplanet form, evolve and are made of is one of the biggest challenge of modernastronomy. They play an important role as they carry most of the planetary systemmasses. Therefore, they strongly impact their dynamics and the fate of these systems tohost life. My PhD thesis falls within an observational approach that is mandatory to bringconstraints on the diversity of planetary systems.I got my first results from a three-year survey, with NaCo at VLT. My observations ofHD142527 excluded the presence of massive giants planets to explain the structures of thistransitional disk and might favor a light multiple system. I also detected a giant planetaround HD95086 and I showed that it has particular atmospheric properties. Finally, Icarried out a statistical analysis of the whole survey to show that giant planets on wideorbitsare rare (10 − 20 %) and could not be formed via direct collapse of unstable disks.I dedicated the last part of my work to investigate the spectral simultaneous differentialimaging mode. I pointed out the biases associated to the reduction of these data andshowed that evolutionary models have to be used to analyze them. This study might helpto exploit the full potential of SPHERE/IRDIS data.