Overview of Large-Scale Computing: The Past, the Present, and the Future

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Elements of Theory for Electromagnetic Compatibility and Systems

International audienceThe purpose of this book is to submit a formalism constructed on the base of Kron's tensorial analysis of networks, and able to abord systems modeling. It was used to model electronic systems for electromagnetic compatibility. It appears that many systems can be analyzed through this approach. The author presents here personal proposals to analyze theoretically the complex systems

Kron's method and cell complexes for magnetomotive and electromotive forces

Starting from topological principles we first recall the elementary ones giving Kirchhoff's laws for current conservation. Using in a second step the properties of spaning tree, we show that currents are under one hypothesis intrinsically boundaries of surfaces flux. Naturally flux appears as the object from which the edge comes from. The current becomes the magnetomotive force (mmf) that creates the flux in the magnetostatic representation. Using a metric and an Hodge's operator, this flux creates an electromotive force (emf). This emf is finally linked with the current to give the fundamental tensor - or "metric" - of the Kron's tensorial analysis of networks. As it results in a link between currents of cycles (surface boundaries) and energy sources in the network, we propose to symbolize this cross talk using chords between cycles in the graph structure on which the topology is based. Starting then from energies relations we show that this metric is the Lagrange's operator of the circuit. But introducing moment space, the previous results can be extended to non local interactions as far field one. And to conclude, we use the same principle to create general relation of information exchange between networks as functors between categories.Comment: 21 page

De l'expérimentation sur des systèmes complexes en compatibilité électromagnétique, à leurs représentations et leurs analyses dans un espace géométrique abstrait.

La compatibilité électromagnétique (CEM) est un métier récent et difficile. Récent car c'est un métier apparu après guerre, même si quelques modèles (la diaphonie par exemple) sont plus anciens. Difficile car il met en jeu des systèmes complexes tel que nous le verrons, suivant la même problématique quelque part que d'autres sciences récentes telle l'écologie.La compatibilité électromagnétique implique les équations de l'électromagnétisme comme on peut s'en douter par sa dénomination, mais au sens général. Ce sont ainsi les équations de Maxwell qui déterminent les comportements des champs électromagnétiques mais aussi les équations des semi-conducteurs qui gèrent les flux de particules dans les composants. Ce système d'équations multiphysiques couplées ne permet pourtant que de modéliser l'échelle la plus petite des systèmes électroniques. A une échelle supérieure il faut considérer les équations de la logique et au plus hautes échelles toutes les techniques de la cybernétique : théorie des jeux, automatisme, etc.Je présente dans ce mémoire mon expérience en compatibilité électromagnétique dans les deux contextes industriel (depuis 1986) mais aussi partiellement académique (depuis 1995). Cette expérience conduit à une certaine compréhension des défaillances possibles des systèmes, ou en tout cas permet d'acquérir un recul nécessaire à l'étude des systèmes complexes en CEM. Pour analyser ces systèmes j'en suis venu à inventer une méthode à partir d'une autre, originellement conçue pour la modélisation des machines électriques, dite “ méthode de KRON ” (du nom de son auteur Gabriel KRON). Cette construction constitue depuis 1992 le thème récurrent de mes travaux scientifiques personnels. En la décrivant je réalise quelque part ma propre psychanalyse de chercheur, étape obligée avant de prétendre pouvoir travailler avec d'autres chercheurs.Il n'est pas possible de relater ici tous les travaux que j'ai pu mener de façon à adapter la méthode de KRON pour la CEM. J'ai choisi d'en présenter 4 parmi les travaux de recherche en CEM que j'ai pu aborder pour lesquels les apports de l'usage de la méthode de KRON sont, il me semble, les plus significatifs et aussi ceux pour lesquels l'effort de recherche a été pour moi le plus conséquent. Ces travaux portent sur :1. la modélisation des interactions en champ proche ;2. la modélisation pour la CEM des électroniques de puissance ;3. comment considérer les interactions dans des guides ou des cavités ;4. la modélisation des systèmes.Je balaie chacune de ces expériences de recherche après avoir évoqué l'origine du besoin de trouver une méthode autre que celles disponibles en 1986 quand je débutais en CEM

1-D broadside-radiating leaky-wave antenna based on a numerically synthesized impedance surface

A newly-developed deterministic numerical technique for the automated design of metasurface antennas is applied here for the first time to the design of a 1-D printed Leaky-Wave Antenna (LWA) for broadside radiation. The surface impedance synthesis process does not require any a priori knowledge on the impedance pattern, and starts from a mask constraint on the desired far-field and practical bounds on the unit cell impedance values. The designed reactance surface for broadside radiation exhibits a non conventional patterning; this highlights the merit of using an automated design process for a design well known to be challenging for analytical methods. The antenna is physically implemented with an array of metal strips with varying gap widths and simulation results show very good agreement with the predicted performance

Beam scanning by liquid-crystal biasing in a modified SIW structure

A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium

LEGO : linear embedding via Green's operators

Reduction of lead time has long been an important target in product development. Owing to the advance of computer power product optimization has been moved from the production stage to the preceding design stage. In particular, the full electromagnetic behavior of the final product can now be predicted through numerical methods. However, for the tuning of device parameters in the optimization stage, commercial software packages often rely on brute-force parameter sweeps. Further, for each set of parameter values a full recomputation of the entire configuration is usually required. In case of stringent product specifications or large complex structures, the computational burden may become severe. Recently, "marching on in anything" has been introduced to accelerate parameter sweeps. Nevertheless, it remains necessary to further reduce the computational costs of electromagnetic device design. This is the main goal in this thesis. As an alternative to existing electromagnetic modeling methods, we propose a modular modeling technique called linear embedding via Green’s operators (LEGO). It is a so-called diakoptic method based on the Huygens principle, involving equivalent boundary current sources by which simply connected scattering domains of arbitrary shape may fully be characterized. Mathematically this may be achieved using either Love’s or Schelkunoff’s equivalence principles, LEP or SEP, respectively. LEGO may be considered as the electromagnetic generalization of decomposing an electric circuit into a system of multi-port subsystems. We have captured the pertaining equivalent current distributions in terms of a lucid Green’s operator formalism. For instance, our scattering operator expresses the equivalent sources that would produce the scattered field exterior to a scattering domain in terms of the equivalent sources that would produce the incident field inside that domain. The enclosed scattering objects may be of arbitrary shape and composition. The scattering domains together with their scattering operators constitute the LEGO building blocks. We have employed various alternative electromagnetic solution methods to construct the scattering operators. In its most elementary form, LEGO is a generalization of an embedding procedure introduced in inverse scattering to describe multiple scattering be tween adjacent blocks, by considering one of the blocks as the environment of the other and vice versa. To establish an interaction between current distributions on disjoint domain boundaries we define a source transfer operator. Through such transfer operators we obtain a closed loop that connects the scattering operators of both domains, which describes the total field including the multiple scattering. Subsequently, a combined scattering block is composed by merging the separate scattering operators via transfer operators, and removing common boundaries. We have validated the LEGO approach for both 2D and 3D configurations. In the field of electromagnetic bandgap (EBG) structures we have demonstrated that a cascade of embedding steps can be employed to form electromagnetically large complex composite blocks. LEGO is a modular method, in that previously combined blocks may be stored in a database for possible reuse in subsequent LEGO building step. Besides scattering operators that account for the exterior scattered field, we also use interior field operators by which the field may be reproduced within (sub)domains that have been combined at an earlier stage. Only the subdomains of interest are stored and updated to account for the presence of additional domains added in subsequent steps. We have also shown how the scattering operator can be utilized to compute the band diagram of EBG structures. Two alternative methods have been proposed to solve the pertaining eigenvalue problem. We have validated the results via a comparison with results from a plane-wave method for 2D EBG structures. In addition, we have demonstrated that our method also applies to unit cells containing scattering objects that are perfectly conducting or extend across the boundary of the unit cell. The optimization stage of a design process often involves tuning local medium properties. In LEGO we accommodated for this through a transfer of the equivalent sources on the boundary of a large scattering operator to the boundary of a relatively small designated domain in which local structure variations are to be tested. As a result, subsequent LEGO steps can be carried out with great efficiency. As demonstrators, we have locally tuned the transmission properties at the Y-junction of both a power splitter and a mode splitter in EBG waveguide technology. In these design examples the computational advantageous of the LEGO approach become clearly manifest, as computation times reduce from hours to minutes. This efficient optimization stage of the LEGO method may also be integrated with existing software packages as an additional design tool. In addition to the acceleration of the computations, the reusability of the composite building constitute an important advantage. The Green’s operators are expressed in terms of equivalent boundary currents. These operators have been obtained using integral equations. In the numerical implementation of the LEGO method we have discretized the operators via the method of moments with a flat-facetted mesh using local test and expansion functions for the fields and currents, respectively. In the 2D case we have investigated the influence of using piecewise constant and piecewise linear functions. For the 3D implementation, we have applied the Rao-Wilton-Glisson (RWG) functions in combination with rotated RWG functions. After discretization, operators and operator compositions are matrices and matrix multiplications, respectively. Since the matrix multiplications in a LEGO step dominate the computational costs, we aim at a maximum accuracy of the field for a minimum mesh density. For LEGO with SEP, we have determined the unknown currents through inverse field propagators, whereas with LEP, the currents are directly obtained from the tangential field components via inverse Gram matrices. After a careful assessment of the computational costs of the LEGO method, it turns out that owing to the removal of common boundaries and the reusability of scattering domains, the most efficient application of LEGO involves a closely-packed configuration of identical blocks. In terms of the number of array elements, N, the complexity of a sequence of LEGO steps for 2D and 3D applications increases as O(N1.5) and O(N2), respectively. We have discussed possible improvements that can be expected from "marching on in anything" or multi-level fast-multipole algorithms. From an evaluation of the resulting scattered field, it turns out that LEGO with SEP is more accurate than with LEP. However, the spurious interior resonance effect common to SEP in the construction of composite building blocks can not simply be avoided through a combined field integral equation. By contrast, LEGO based on LEP is robust. Further, we have demonstrated that additional errors due to the choice of domain shape or building sequence, or the accumulation of errors due to long LEGO sequences are negligible. Further, we have investigated integral equations for the scattering from 2D and 3D perfectly conducting and dielectric objects. The discretized integral operators directly apply to the LEGO method. For scattering objects that are not canonical, these integral equations are used in the construction of the elementary LEGO blocks. Since we aim at a maximum accuracy of the field for a minimum mesh density, the regular test and expansion integral parts are primarily determined through adaptive quadrature rules, while analytic expressions are used for the singular integral parts. It turns out that the convergence of the scattered field is a direct measure for the accuracy of the scattered field computed with LEGO based on SEP or LEP. As an alternative to the PMCHW and the M¨uller integral equations, we have proposed an new integral equation formulation, which leads to cubic convergence in the 2D case, irrespective of the mesh density and object shape. In case of scattering object with a regular boundary domain scaling may be used to improve the convergence rate of the scattered field