Cette thèse présente plusieurs nouvelles techniques pour la convergence rapide des solutions aux éléments de frontière de problèmes électromagnétiques. Une attention spéciale a été dédiée aux formulations pertinentes pour les solutions aux problèmes électromagnétiques dans les tissus biologiques à haute et basse fréquence. Pour les basses fréquences, de nouveaux schémas pour préconditionner et accélérer le problème direct de l'électroencéphalographie sont présentés dans cette thèse. La stratégie de régularisation repose sur une nouvelle formule de Calderon, obtenue dans cette thèse, alors que l'accélération exploite le paradigme d'approximation adaptive croisée (ACA). En ce qui concerne le régime haute fréquence, en vue d'applications de dosimétrie, l'attention de ce travail a été concentrée sur l'étude de la régularisation de l'équation intégrale de Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) à l'aide de techniques hiérarchiques. Le travail comprend une analyse complète de l'équation pour des géométries simplement et non-simplement connectées. Cela a permis de concevoir une nouvelle stratégie de régularisation avec une base hiérarchique permettant d'obtenir une équation pour les milieux pénétrable stable pour un large spectre de fréquence. Un cadre de travail propédeutique de discrétisation et une bibliothèque de calcul pour des thèmes de recherches sur les techniques de Calderon en 2D sont proposés en dernière partie de cette thèse. Cela permettra d'étendre nos recherches à l'imagerie par tomographie. / This thesis presents several new techniques for rapidly converging boundary element solutions of electromagnetic problems. A special focus has been given to formulations that are relevant for electromagnetic solutions in biological tissues both at low and high frequencies. More specifically, as pertains the low-frequency regime, this thesis presents new schemes for preconditioning and accelerating the Forward Problem in Electroencephalography (EEG). The regularization strategy leveraged on a new Calderon formula, obtained in this thesis work, while the acceleration leveraged on an Adaptive-Cross-Approximation paradigm. As pertains the higher frequency regime, with electromagnetic dosimetry applications in mind, the attention of this work focused on the study and regularization of the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation via hierarchical techniques. In this effort, a complete analysis of the equation for both simply and non-simply connected geometries has been obtained. This allowed to design a new hierarchical basis regularization strategy to obtain an equation for penetrable media which is stable in a wide spectrum of frequencies. A final part of this thesis work presents a propaedeutic discretization framework and associated computational library for 2D Calderon research which will enable our future investigations in tomographic imaging.

Dans le domaine de l’électromagnétisme computationnel, les équations intégrales de frontière sont très largement utilisées pour résoudre certains des plus grands problèmes directs, grâce à leur grande efficacité. Cependant les équations intégrales du champ électrique et du champ combiné (EFIE et CFIE), deux des formulations les plus employées, souffrent d’instabilités à basse fréquence et à haute discrétisation, ce qui limite leur versatilité. Dans cette thèse différentes approches sont présentées pour obtenir des algorithmes applicables aussi bien à des problèmes de compatibilité électromagnétique qu’à des applications radar. Les solutions présentées incluent (i) l’extension des projecteurs dit quasi-Helmholtz (qH) aux modélisations d’ordre supérieur ; (ii) l’utilisation de ces projecteurs pour stabiliser l’équation intégrale du champ magnétique et former une CFIE extrêmement précise, augmentée par des techniques de type Calderón, qui ne souffre de problèmes ni à basse fréquence ni à haute discrétisation et qui n’est pas sujette aux résonances artificielles ; (iii) le développement d’une EFIE filaire, basée sur des B-splines linéaires et les projecteurs qH, stable aux deux extrémités du spectre. Ces travaux ont été suivis de l’ouverture d’un nouvel axe de recherche visant l’amélioration des techniques de résolution des problèmes inverses en électromagnétique, avec pour objectif principal l’augmentation des performances des interfaces cerveau machine (BCIs). Les premiers résultats obtenus incluent le développement de l’un des premiers systèmes libres de simulation de bout en bout de session de BCI ayant été publié après revue par les pairs. / In computational electromagnetics, boundary integral equations are the scheme of choice for solving extremely large forward electromagnetic problems due to their high efficiency. However, two of the most used of these formulations, the electric and combined field integral equations (EFIE and CFIE), suffer from stability issues at low frequency and dense discretization, limiting their applicability at both ends of the spectrum. This thesis focusses on remedying these issues to obtain full-wave solvers stable from low to high frequencies, capable of handling scenarios ranging from electromagnetic compatibility to radar applications. The solutions presented include (i) extending the quasi-Helmholtz (qH) projectors to higher order modeling thus combining stability with high order convergence rates; (ii) leveraging on the qH projectors to numerically stabilize the magnetic field integral equation and obtain a highly accurate and provably resonance-free Calderón-augmented CFIE immune to both of the aforementioned problems; and(iii) introducing a new low frequency and dense discretization stable wire EFIE based on projectors and linear B-splines. In addition, a research axis focused on enhancing Brain Computer Interface (BCIs) with high resolution electromagnetic modeling of the brain has been opened ; a particular attention is dedicated to the inverse problem of electromagnetics and the associated integral equation-based forward problem. The first results of this new line of investigations include the development of one of the first peer-reviewed, freely available framework for end-to-end simulation of BCI experiments.

Compressive Sensing (CS) is a novel signal-processing paradigm that allows sampling of sparse or compressible signals at lower than Nyquist rate. The past decade has seen substantial research on imaging applications using compressive sensing. In this thesis, CS is combined with the commercial electromagnetic (EM) simulation software newFASANT to improve its efficiency in solving EM scattering problems such as Radar Cross Section (RCS) of complex targets at GHz frequencies. This thesis proposes a CS-RCS approach that allows efficient and accurate recovery of under-sampled RCSs measured from a random set of incident angles using an accelerated iterative soft thresh-holding reconstruction algorithm. The RCS results of a generic missile and a Canadian KingAir aircraft model simulated using Physical Optics (PO) as the EM solver at various frequencies and angular resolutions demonstrate good efficiency and accuracy of the proposed method.

Recent advances in linear quantum optics have involved the development of unbiased, multi-port optical elements for use with pairs of identical photons, or biphotons, for the design of novel quantum devices. The unbiased counterpart of a conventional 50:50 beam-splitter is a particularly useful multiport, thanks to its unique algebraic properties when acting on both classical and quantum states of light. Dubbed the “Grover coin” due to its utility in the Grover’s Search quantum algorithm, the unbiased four-port behaves as a conventional beam splitter, but with two additional ports to provide a photon amplitude with four, equally-probable, spatially distinct paths through which it may propagate. While the Grover coin has been realized in the laboratory in the form of bulk optical elements, the formation of a network of Grover coins is impractical due to the meticulous alignment and large number of elements required for a single component. Therefore, the development of a small, chip-integrated embodiment of the unbiased four-port would enable experimentation with novel quantum optics theories, through the interconnection of multiple Grover coins over a small footprint. This thesis details the design and fabrication of photonic waveguide-based integrated circuit elements through numerical simulation, topology optimization and CMOS-compatible manufacturing processes. / 2025-06-08T00:00:00Z

Modeling and design of high frequency electronic systems such as antennas and microwave devices require the rigorous numerical solution of Maxwell’s equa- tions. The frequency-domain (time-harmonic) tangential vector finite element method (TVFEM) for Maxwell equations results in a second-order dynamical electromagnetic model that must be repeatedly solved for multiple frequencies, excitation or material parameters each design loop. This leads to extremely long design turnaround that often is not optimal. This work will propose an accurate, error controllable and ef- ficient multi-parametric model order reduction scheme that significantly accelerate these parameters sweep. At the core of this work is the proper orthogonal decompo- sition (POD) sampling technique and balanced truncation (BT) algorithm that are used to reduce multi-parameter spaces that include frequency, material parameters and infinite array scan angles. The proposed methodology employs a novel computa- tional scheme based on adaptive POD sampling and the singular value decomposition (SVD) of the low-rank Hankel matrix. Numerical examples confirm the significant time savings and good accuracy of the method for a diverse set of high-frequency electromagnetic systems.

This thesis covers recent advances in the adjoint variable method for the sensitivity estimations through time-domain electromagnetic simulations. It considers both frequency-independent and frequency-dependent response functions, and at the same time, provides a novel adjoint treatment for addressing dispersive sensitivity parameters in the material constitutive relation. With this proposed adjoint technique, response sensitivities with respect to all N sensitivity parameters can be computed through at most one extra simulations regardless of the value of N. This thesis also extends the existing adjoint technique to estimate all N^2 second-order sensitivity entries in the response Hessian matrix through N additional simulations. All adjoint sensitivity techniques presented in this thesis are numerically validated through various practical examples. Comparison shows that our produced adjoint results agree with those produced through central finite-difference approximations or through exact analytical approaches. / Dissertation / Doctor of Engineering (DEng)

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京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24738号 / 情博第826号 / 新制||情||138(附属図書館) / 京都大学大学院情報学研究科先端数理科学専攻 / (主査)教授 磯 祐介, 准教授 吉川 仁, 准教授 藤原 宏志, 教授 西村 直志(京都大学 名誉教授) / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

[EN] Modern communications systems impose stringent requirements on the equipment that operates at microwave frequency, especially in the case of wireless communications. The design of passive components for these applications is contingent upon the availability of accurate electromagnetic (EM) modeling tools that can efficiently handle the complex geometry of these components. Despite the widespread use of mesh-based general-purpose computer-aided engineering (CAE) tools to perform final design verifications, their application during the optimization process is limited. Optimum designs require a large number of simulations, which are computationally expensive when performed by general purpose tools. Instead, microwave designers prefer to employ faster software tools tailored to specific geometries, such as waveguide components, multilayered structures, etc. Therefore, the development of faster and more efficient specialized EM tools has a direct impact on the design of microwave components, both quantitatively and qualitatively. Increasingly complex geometries are modeled more accurately, and may be incorporated into novel designs without penalizing development time and its associated costs. By doing so, passive components become more advanced and are able to fulfill stricter requirements. At the same time, new research and development opportunities arise in order to address the challenges posed by these advanced structures. The present thesis is focused on a specific type of waveguide cavity geometry: bi-dimensional structures of arbitrary shape. Most microwave components based on rectangular waveguides include these elements (bends, T-junctions, tapers, power-dividers, etc.), thus the scope of this work is wide. To characterize these structures, an efficient full-wave modal formulation is developed. Taking into account common properties of bi-dimensional structures, such as its electromagnetic symmetry, the resulting technique is very efficient and accurate. Thanks to the integration of this formulation into a CAE tool, a designer is able to solve complex systems that combine this type of element with components of vastly different shapes. The developed formulation is first applied to the analysis and design of passive components, such as filters, multiplexers and orthomode transducers. These examples are employed to validate the results, as well as to demonstrate the improvement that the proposed analysis technique represents over well-known commercial EM packages. Likewise, this formulation is combined with the tool SPARK3D to predict RF breakdown (multipactor and corona) in selected bi-dimensional structures. Then, novel implementations of waveguide quasi-elliptic filters, based on the interconnection of bi-dimensional cavities, are proposed. Special attention is paid to the realization of multiple transmission zeros (TZs) with tuning-less compact structures. First, a novel family of filters, known as hybrid-folded rectangular waveguide structures, is studied. Simple and flexible methods to prescribe the location of the transmission zeros realized by these structures are presented. Practical aspects related to their physical implementation are also discussed. Secondly, a compact and purely capacitive obstacle, capable of realizing multiple TZs, is presented and discussed. In both cases, multiple examples are given to illustrate the step-by-step process involved in the design of these structures. Finally, a systematic procedure for the design of wideband manifold-coupled multiplexers is proposed. To preven the generation of undesired resonances, stubs that connect the filters to the manifold are removed. Likewise, the manifold length is kept as short as possible. Following a simple procedure, based on analytical formulas and EM simulations, a good starting point for the final optimization of these structures is obtained. It has been applied to a wideband quadruplexer for passive intermodulation measurement at C-band. / [ES] Actualmente, los sistemas de comunicaciones imponen unos requisitos muy estrictos sobre el equipamiento en la banda de microondas. El diseño de estos componentes está supeditado, frecuentemente, a la disponibilidad de herramientas de modelado electromagnético (EM) que sean capaces de analizar geometrías complejas. A pesar del amplio uso de herramientas CAE (computer-aided engineering) de propósito general para la verificación final de prototipos, su potencial aplicación durante el proceso de diseño es limitada. Los diseños óptimos exigen realizar una gran cantidad de simulaciones EM. Dado que las simulaciones con estas técnicas tienen un alto coste computacional, los diseñadores suelen optar por emplear herramientas software especializadas en las estructuras que diseñan. Por tanto, el desarrollo de nuevas herramientas más precisas y eficientes ayudará a reducir el tiempo de diseño de estos productos, y con ello los costes asociados. Además, permitirá abrir nuevas líneas de investigación para responder a los retos que plantean geometrías cada vez más complejas. Esta tesis se centra en el desarrollo de una herramienta de análisis EM para un tipo concreto de estructuras: cavidades bidimensionales de sección arbitraria. Es habitual encontrar este tipo de estructuras en la mayoría de componentes implementados en guía rectangular. Por tanto, el rango de aplicación de la teoría desarrollada en esta tesis es muy amplio. En concreto, se ha desarrollado una nueva formulación basada en métodos modales que permite realizar una caracterización de onda completa de estas estructuras de forma eficiente y precisa. Al aprovechar su simetría geométrica y electromagnética, la herramienta desarrollada puede minimizar los cálculos a realizar, consiguiendo grandes velocidades de computación pero manteniendo una alta precisión. Gracias a la integración de esta formulación dentro de una herramienta CAE basada en métodos modales, se ofrece la posibilidad a los diseñadores de resolver sistemas muy complejos que combinan este tipo de cavidades con otros componentes de geometrías distintas. Esta formulación se aplica, en primer lugar, al análisis y diseño de componentes pasivos comunes, tales como filtros, multiplexores y OMTs. Estos ejemplo validan la herramienta desarrollada, y demuestran la significativa mejora que supone el uso de esta nueva técnica con respecto a otros paquetes software de análisis electromagnético. Asimismo, al combinar esta formulación con la herramienta SPARK3D se abre la posibilidad de predecir la aparición de fenómenos de descarga de alta potencia en determinadas estructuras bidimensionales. A continuación, se proponen nuevas formas de implementar filtros cuasi-elípticos basados en la interconexión de cavidades bi-dimensionales. Se hace especial hincapié en la realización de múltiples ceros de transmisión mediante estructuras compactas que no requieran sintonía. Por una parte se estudian los filtros hybrid-folded rectangular waveguide. Este trabajo incluye una discusión en profundidad sobre distintas implementaciones de este tipo de filtros. En ella se consideran aspectos prácticos relacionados con su uso e implementación física, que ofrecen al diseñador unos criterios claros para elegir la estructura que más se ajuste a sus especificaciones. Por otra parte se presenta un nuevo obstáculo de naturaleza capacitiva muy compacto, que permite la realización de múltiples ceros de transmisión incluso en estructuras en línea. En ambos casos se incluyen ejemplos de aplicación y se describe la metodología seguida para su diseño. Finalmente, se expone un procedimiento sistemático para diseñar multiplexores de banda ancha. Para prevenir la generación de resonancias indeseadas se evitan, en la medida de lo posible, las interconexiones mediante tramos cortos de guía. Siguiendo una metodología simple se consigue un excelente punto inicial para su optimización. La te / [CA] Els actuals sistemes de comunicacions sense fils imposen uns requisits molt estrictes sobre l'equipament de la banda de microones. El disseny d'aquests components està supeditat, frequentment, a la disponibilitat de ferramentes de modelatge electromagèntic (EM) que siguen capaços de gestionar geometries complexes. Tot i l'ampli ús de ferramentes CAE (computer-aided engineering) de propòsit general per a la verificació final de prototips, la seua aplicació durant el procés de disseny és limitada. Els dissenys òptims exigeixen realitzar una gran quantitat de simulacions. Les simulacions amb aquestes tècniques tenen un alt cost computacional, per tant els dissenyadors solen optar per utilitzar ferramentes software especialitzades en les estructures que dissenyen. Per tant, el desenvolupament de noves tècniques d'anàlisi més precises i eficients ajudarà a reduir el temps de desenvolupament d'aquests productes, i dels seus costos associats. A més permetrà obrir noves línies d'investigació per respondre els reptes que plantegen geometries cada vegada més complexes. Aquesta tesi es centra en el desenvolupament d'una ferramenta d'anàlisi EM per a un tipus concret d'estructures: cavitats bidimensionals de forma arbitraria. És habitual trobar aquestes estructures en la majoria de components implementats en guia rectangular. Per tant, l'àmbit d'aplicació de la teoria presentada en esta tesi és molt ampli. En concret, s'ha desenvolupat una nova formulació basada en mètodes modals que permet realitzar una caracterització d'ona completa d'aquestes estructures de forma eficient i precisa. Aprofitant la seua simetria geomètrica i electromagnètica, la ferramenta desenvolupada pot minimitzar els càlculs a realitzar, aconseguint grans velocitats de càlcul mantenint una alta precisió. Gràcies a la integració d'aquesta formulació dins d'una ferramenta CAE basada en mètodes modals, s'ofereix la possibilitat als dissenyadors de resoldre sistemes molt complexos que combinen aquest tipus de cavitats amb altres components de diferent geometria. Aquesta formulació s'aplica, en primer lloc, a l'anàlisi i disseny de components passius comuns: filtres, multiplexors i OMTs. Aquests exemples serveixen per a validar la ferramenta desenvolupada, així com demostrar la significativa millora que suposa l'ús d'aquesta nova tècnica respecte d'altres paquets software d'anàlisi electromagnètic. Així mateix, mitjançant la combinació d'aquesta formulació amb la ferramenta SPARK3D s'obri la possibilitat de predir l'aparició de fenòmens de descàrrega d'alta potència en estructures bidimensionals. A continuació, es proposen noves formes d'implementar filtres quasi el-líptics en guia d'ona basats en la interconnexió de cavitats bidimensionals. Es fa especial èmfasi en la realització de múltiples zeros de transmissió mitjançant estructures compactes que no requereixen de sintonia. D'una banda s'estudien els filtres hybrid folded rectangular waveguide. Aquest treball inclou una discussió en profunditat sobre diferents implementacions d'aquest tipus de filtres. S'hi consideren aspectes pràctics relacionats amb el seu ús i implementació física, que ofereixen al dissenyador uns criteris clars per triar l'estructura que més s'ajuste a les seues especificacions. D'altra banda es presenta un nou obstacle de naturalesa capacitiva extremadament compacte, que permet la realització de múltiples zeros de transmissió fins i tot en estructures en línia. En els dos casos s'inclouen exemples d'aplicació i es descriu la metodologia seguida per al seu disseny. Finalment, s'exposa un procediment sistemàtic per dissenyar multiplexors de banda ampla. Per prevenir la generació de ressonàncies no desitjades s'eviten les interconnexions amb trams de guia curts. Seguint una metodologia simple, basada en fórmules analítiques i simulacions electromagnètiques, s'aconsegueix un excel-lent punt inicial per a l'optimització. / Carceller Candau, C. (2016). Full-wave characterization of bi-dimensional cavities and its application to the design of waveguide filters and multiplexers [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/64089