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International audience; This paper proposes the application of the Finite Element Tearing and Interconnecting method (FETI-2LM) a Domain Decompositon Method (DDM) [1], [2] for the full-wave simulation of large antenna array (few thousands of radiating elements). The proposed methodology makes it possible to efficiently calculate in a post-processing step the antenna patterns for steering directions within the desired field of view while taking into account the active reflection coefficients. The methodology is based on an efficient extraction of the embedded radiating elements far field radiation patterns as well as the Generalized Scattering Matrix (GSM) [3] of the array by implementing massively parallel computers. The beauty of the GSM is its capability to handle the active S-parameters independently of the steering direction. This permits to generate the angular-dependent active reflection coefficients by post-processing. This implementation is a step forward to provide us with a tool that permits to evaluate by simulation large antenna array while taking into account all the phenomena and interactions that may degrade the key performances that are required at a higher level, to specify a global system before fabrication.

In a recent work (A. Jouade and A. Barka, “Massively parallel implementation of FETI-2LM methods for the simulation of the sparse receiving array evolution of the GRAVES radar system for space surveillance and tracking, IEEE Access , vol. 7, pp. 128968–128979, 2019), we have discussed our implementation of the finite-element tearing and interconnecting (FETI) method and the domain decomposition method (DDM) for the full-wave simulation of the large GRAVES sparse array (60 m diameter disk). Owing to the nonregular distribution of the antennas of the sparse array, such simulations in reasonable times are not accessible with existing FETI methods optimized for repetitive geometries, which do not benefit from an effective parallelization technique. A particularity of the preprocessing step of our DDM is that the complete sparse array mesh is not built upstream of the resolution of the electromagnetic problem. Each subdomain in our decomposition is equipped with its own local mesh, belonging to a limited set of unit-cell meshes, generated separately. Initially, a total of 13 692 subdomains were chosen among three types of subdomains, considering those corresponding to antennas (200), air subdomains (800), and ground plane subdomains (12 592). This simulation has required 13 692 Intel Xeon Broadwell E5-2680v4 processing cores equipped with 4 GB of memory, each handling one subdomain. A new strategy is shown, which requires only 2408 cores for the same simulation, leading to an 82.41% reduction in the required number of cores, as well as a 30% reduction in the simulation time.

International audience; Transmit-arrays (TAs) are a popular cost-effective solution for high-gain antennas at millimeter waves (mmW). The design of these antennas relies on the fine tuning of the sub-wavelength unit-cells that compose the aperture. The intricacy of the unit-cells increases as new features are implemented, such as dual-band operation and wide-angle beam steering, making this antenna even more computationally challenging. In this work, a high gain (25 dBi @ 20 GHz and 28 dBi @ 30 GHz) multi-scale Ka dual-band TA for beam-steering applications is analyzed using a massively parallel implementation on multicores clusters of the Finite Element Tearing and Interconnecting method, with a two Lagrange Multiplier (FETI-2LM) technique. The main contribution of this work is the implementation of 3D non-periodic grids with sub-domains of different scales, that is suitable for proper modelling of different regions of the antenna (horn feed, lens cells, air region). An automatic batch file procedure is proposed for the TA meshing, allowing the limited set of constitutive unit-cells of the TA to be meshed separately. Additionally, we are using a block-Krylov strategy to efficiently capture the TA beam-steering capability, without restarting from scratch the interface problem for each feed position. Since other Finite Element Method (FEM) results were not accessible due the size of the problem, the FETI-2LM numerical results provided in this work are compared with other MultiLevel Fast Multipole Method (MLFMM) [1] and Transmission Line Modeling Method (TLM) [2] of CST Microwave Studio solvers, as well as with the measured results of the corresponding Ka dual-band prototype. The computational infrastructure has been used only a fraction of its capacity. Therefore, a much higher gain design (40 dBi) can be assessed, opening a new realm of applicability of TAs in the space segment usually occupied by reflector-based solutions.

To solve multisource electromagnetic problems, a new way of using Krylov type iterative algorithms is presented to improve the finite-element tearing and interconnecting domain decomposition method with two Lagrange multipliers (FETI-2LMs). There are three main ingredients in the proposed algorithms: 1) a recycling Krylov method is used to solve the condensed interface problem introduced by the FETI-2LM method; 2) all the search direction vectors for all the successive sources are stored and used to build a projection, which decreases the number of iterations for the successive sequences of ORTHODIR Krylov iterations; and 3) successive problems are solved with a block technique preserving the numerical efficiency of the previous recycling Krylov strategy and greatly improving the parallel efficiency of the method. Performances and accuracy of the proposed block Krylov recycling strategy will be discussed based on the simulation of two engineering applications (monostatic radar cross section of large antenna array and radiating element coupling of an antenna array) and the comparison of the simulated results with measurements. For the most difficult configuration of linearly independent right hand-sides (TEM mode ports), a speedup of 11.7 is observed, while for linearly dependent right hand-sides (plane wave excitations), the speedup of 115 obtained by the proposed method outperforms those obtained with the existing recycling Krylov techniques already published and applied to FETI solved electromagnetic problems (speedup of 1.7).

International audience; Recently the performances of radar absorbing materials have been extended by designing new thin structures with wideband properties and large angles of incidence. In this paper, the design and performances of such ultrawideband microwave absorber of low thickness material developed within the framework of the SAFAS project (self-complementary surface with low signature) are confirmed with complementary quasi monostatic measurements and finite array simulations using Finite Element Tearing and Interconnecting domain decomposition methods (FETI).

National audience; Dans cet article, nous démontrons qu'il est possible de remplacer les couches diélectriques d'un absorbant à métamatériaux initialement conçu avec des matériaux RF par des matériaux composites structuraux, i.e. renforcés de fibres. Ces matériaux, compatibles avec les procédés de fabrication du domaine naval militaire ont été réalisés et mesurés. L'effet des différentes couches de l'absorbant sur la bande passante est détaillé. Après optimisation de l'épaisseur de chaque couche grâce à un modèle analytique, l'absorbant présente un coefficient de réflexion inférieur à-14 dB dans la bande 4.6 GHz-17.2 GHz en incidence normale, pour une épaisseur totale de 8.9 mm. Le comportement de l'absorbant en incidence oblique est aussi discuté.

International audience; Using structural composite materials for the fabrication of Radar Absorbing Materials (RAM) allows combining the strong load bearing capability with the radar absorbing functionality in a unique structure. This article shows the possibility to transpose an already existing metamaterial absorber to the domain of composite materials. The dielectric layers of the absorber initially designed with radio-frequency (RF) materials are replaced with fiber-reinforced composite materials and their thickness is optimized again. The working principle of the absorber is explained layer by layer on the Smith chart. The performances of the composite absorber are compared against the initial RF design and against other classical absorbers. The composite design has a total thickness of 8.9 mm and achieves a reflection coefficient below 14 dB within the band 4.6 GHz - 17.2 GHz at normal incidence. The reflection coefficient remains under -10 dB at oblique incidence up to 45°.; L'utilisation de matériaux composites structurels pour la fabrication de matériaux absorbants radar permet de combiner la capacité de charge élevée avec la fonctionnalité d'absorption radar dans une structure unique. Cet article montre la possibilité de transposer un méta matériaux absorbant déjà existant, dans le domaine des matériaux composites. Les couches diélectriques de l'absorbant initialement conçues avec des matériaux radiofréquences (RF) sont remplacées par des matériaux composites renforcés de fibres et leur épaisseur est à nouveau optimisée. Le principe de fonctionnement de l'absorbant est expliqué couche par couche sur la carte de Smith. Les performances de l'absorbant composite sont comparées à la conception RF initiale et à d'autres absorbants classiques. La conception composite a une épaisseur totale de 8,9 mm et atteint un coefficient de réflexion inférieur à -14 dB dans la bande 4,6 GHz - 17,2 GHz à incidence normale. Le coefficient de réflexion reste inférieur à -10 dB en incidence oblique jusqu'à 45 °.

International audience; In this paper, a wideband dual polarized self-complementary connected array antenna with low radar cross section (RCS) under normal and oblique incidence is presented. First, an analytical model of the multilayer structure is proposed in order to obtain a fast and reliable predimensioning tool providing an optimized design of the infinite array. The accuracy of this model is demonstrated thanks to comparative simulations with a full wave analysis software. RCS reduction compared to a perfectly conducting flat plate of at least 10 dB has been obtained over an ultrawide bandwidth of nearly 7:1 at normal incidence and 5:1 (3.8 to 19 GHz) at 60° in both polarizations. These performances are confirmed by finite element tearing and interconnecting computations of finite arrays of different sizes. Finally, the realization of a 28x28 cell prototype and measurement results are detailed.

International audience

In this paper, we present a new methodology for a nonoverlapping domain decomposition method using boundary integral equations and adaptive cross approximation in the frequency domain (IE-ACA-DDM). This paper proposes two main novelties. First, the IE-DDM condition number is improved with the development of a formulation based on electric field integral equation (EFIE) implementation over the entire subdomains and on a simplification of the magnetic field integral equation (MFIE) on the interfaces. As a consequence, the number of matrix–vector products is significantly reduced during the iterative resolution. Then, this paper proves that the ACA can be applied and efficiently implemented in IE-DDM methods. Moreover, a hierarchical LU (HLU) decomposition is proposed to accelerate the ACA solver. The IE-ACA-DDM is very suitable for the resolution of multiple excitations and to bypass the low-frequency breakdown. The flexibility, accuracy, and efficiency of IE-ACA-DDM are demonstrated by comparing with reference integral equation solutions and scaled mock-up measurements.

This paper is presenting Finite Element Tearing and Interconnecting (FETI) simulation results of large scale Ka-band lens transmit-arrays obtained on massively parallel clusters. The computation times observed with the FETI method allow us to consider using it in the optimization phase of such transmit-arrays.

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National audience

In order to extend the performance of radar absorbing materials, it is necessary to design new structures with wideband properties and large angles of incidence which are also as thin as possible. The objective of this work, realized within the framework of the SAFAS project (self-complementary surface with low signature) is, then, the development of an ultra-wideband microwave absorber of low thickness. The design of such material requires a multilayered structure composed with dielectric layers, metasurfaces, and wide-angle impedance matching layers. This solution has been realized with on-the-shelf materials, and measured to validate the concept. At normal incidence, the bandwidth ratio, defined for a magnitude of the reflection coefficient below &minus, 10 dB, is 4.7:1 for an absorber with a total thickness of 11.5 mm, which corresponds to &lambda, /7 at the lowest operating frequency. For an incidence of 60&deg, this bandwidth ratio is reduced to 3.8:1, but the device remains ultra-wideband.

An original method is proposed which associates rigorous 3D finite element methods (FEM) with Floquet modes through FACTOPO multidomain formalism for computing the radar cross section (RCS) of large array antennas. The most original aspect of the method is the fact that the source unit cell is characterized by a generalized scattering matrix (GSM) which does not depend on the plane wave incidence impinging the structure. Consequently, the factorization step of the FEM matrix, which is the main computational effort, is performed only once. The assembling procedure consists then in expressing the FEM GSM matrix in the Floquet mode basis for each incidence and to solve a linear system giving the complex amplitude of the Floquet modes on the array/cell interface. Associated with this formalism, lateral and back structure effects can be treated using physical optics (PO) combined with the equivalent current method (ECM) to improve the accuracy for far broadside incidence.

In this article, we describe a sub-domain method for electromagnetic computations based on boundary element method. The benefits of the sub-domain method are that the computation can be split between several companies for collaborative studies; also the computation time can be reduced by one or more orders of magnitude especially in the context of parametric studies. The accuracy and efficiency of this technique is assessed by RCS computations on an aircraft air intake with duct and rotating engine mock-up called CHANNEL. Collaborative results, obtained by combining two sets of sub-domains computed by two companies, are compared with measurements on the CHANNEL mock-up. The comparisons are made for several angular positions of the engine to show the benefits of the method for parametric studies. We also discuss the accuracy of two formulations of the sub-domain connecting scheme using edge based or modal field expansion. To cite this article: P. Soudais, A. Barka, C. R. Physique 7 (2006).

National audience

This paper presents the scalability of finite element tearing and interconnecting (FETI-2LM) methods for solving challenging electromagnetic frequency domain problems encountered in the design of low RCS antenna arrays. The scalability of the FETI-2LM method working on Nehalem X5560 cluster will be presented for antenna mock-up.

We present the first part of a study supported by the French Ministry of Defense, entitled SAFAS, which aims at developing a low profile self-complementary radiating surface with low signature. This surface concept is intended to be used for antenna and absorber designs. We show some preliminary results for an antenna array required to work for incidences up to 60° over an ultra-wide frequency band with ratio 5:1.

In this paper, we present a non-overlapping domain decomposition method using integral equations in the frequency domain for the resolution of wave scattering from metallic objects. The objective is to use multi-domain modelling to process multi-scale structures. This method is flexible thanks to an independance between sub-domains and relying on the local resolution of these sub-domains. Moreover, the convergence is improved compared to a classical resolution. This method is achieved for predicting radar cross-sections, studying antenna sitting on large platforms and EMC applications.

In this paper, we present a multidomain and multi-method coupling scheme called FACTOPO, based on generalized scattering matrix computations on three-dimensional (3-D) subdomains. The global target /spl Omega/ is split in N/sub V/ subdomains (V/sub i/)(i=1, N/sub V/), separated by N/sub I/ fictitious surfaces (/spl Gamma//sub j/)(j=1,N/sub I/). We use a modal representation of the tangent fields on the interfaces. In each domain, the generalized scattering matrix S/sub i/ is computed with different methods such as the 3-D finite-element method (FEM) or the electric field integral equation (EFIE). This coupling scheme leads to an important reduction in computational resources, especially for cavities with one dimension much larger than the other two. The advantages of this formulation for parametric studies is illustrated by two cases: computing the RCS of an air-intake terminated with a flat PEC or a fan (CHANNEL) and of an antenna structure coupled to an electronic feed with a varying parameter (DENEB). Numerical as well as experimental results are presented.

The design of array antennas including nonlinear devices requires specific simulation tools. These tools should combine the electromagnetic modeling of passive components with an appropriate description of nonlinearities potentially induced by the active circuitry. An iterative approach is proposed here for the simulation of transmitting arrays, including power amplifiers, taking into account distortion and varying antenna loads induced by coupling effects. Our approach predicts, for the first time at our knowledge, a significant effect of nonlinearity on the sidelobe levels of the active array antennas.

We present here a Finite Element Method devoted to the simulation of 3D periodic structures of arbitrary geometry. The numerical method based on ARPACK and PARDISO libraries, is discussed with the aim of extracting the eigenmodes of periodical structures and thus establishing their frequency band gaps. Simulation parameters and the computational optimization are the focus. Resolution will be used to characterize EBG (Electromagnetic Band Gap) structures, such as plasma rods and metallic cubes.

National audience

We discuss in this paper the design, fabrication and test of transmitting and receiving horn antennas based on elliptical apertures. Two prototype antennas have been fabricated, simulated and measured in the S and X band demonstrating the capability of this concept to provide low side lobe levels and good insulation levels.

Design of artificial materials or radiating element mock-up need a specific effort for full wave modeling. Due to the heterogeneity of the structure, Finite Element Method is chosen. A high performance solver based on FETI Method is developed and applied to an X band EBG material.

This paper presents the implementation of finite element tearing and interconnecting (FETI) methods on parallel MPI machines for solving electromagnetic frequency domain problems encountered in the design of electromagnetic band gap (EBG) materials and antenna arrays.

Domain Decomposition Methods have demonstrated efficiency and accuracy during the resolution of Maxwell Equations in the frequency domain for both RCS applications and Antenna structures interactions [1], [6]. In the domain of Finite Element Methods, and for the resolution of acoustic Helmoltz equations, efficient sub-domain connecting techniques have been applied and called « Dual-Primal Finite Element Tearing and Interconnecting » [2][3]. These techniques are known under the acronym FETI-DP and have been adapted to electromagnetic (FETI-DPEM) for the calculation of antenna arrays and metamaterial periodic structures [4][5]. In this paper we describe the implementation of an algebraic parallel FETI solver developed at ONERA for both acoustic and electromagnetic applications. It has been called as a library in the FEM module of the FACTOPO tool developed for both Antenna and RCS applications.

Phase error computations of direction finding C band array antennas mounted on a motor glider are presented in this paper. The robustness of the proposed array to phase errors will be assessed in on going studies.

In active transmitting arrays, high-power amplifiers (HPA) are conveniently used to provide microwave power at the input of each radiating element. They are generally connected to the radiating elements through isolators, designed to reduce the influence of the surroundings on the amplifiers load. Load-pull effects may indeed affect the transfer characteristics of HPAs and even destroy them above excessive Voltage Standing Wave Ratios (VSWRs). Still, isolators are generally bulky and lossy devices, and advantages could be obtained by downsizing these stages. In the perspective of reducing isolation, the impact of load variations must be predicted for a safe design of array antennas. In this paper, an original iterative approach is proposed for the simulation of transmitting arrays, supplied by HPAs driven into distorsion, taking into account varying antenna loads induced by coupling effects (see Fig. 1). The global description of the array antenna is achieved in the frequency domain through a Domain Decomposition Method (DDM). It allows to describe circuit components and antenna components altogether in highly modular schemes.

This paper presents a new way of modelling very large planar array antennas included in tridimensional structure. The aim is to match a rigorous method to a Floquet mode expansion. The first method is in fact a multi domain one (a domain decomposition method) based on electrical field integral equation -EFIE- and partial differential equation -FEM-. It describes electromagnetic behaviour of a single radiating element of the array. The description requires the use of generalised scattering matrices. Fields in radiation space are expressed by an Floquet modes combination with usual hypothesis. The array's environment is finally taken into account by asymptotic methods (PO and PTD) or rigorous method (EFIE). The accuracy and efficiency of our technique is illustrated by RCS diagram of a patch antenna placed in a canonical metallic box.

In this paper, we describe a sub-domain method for electromagnetic computations based on boundary element method. The benefits of the sub-domain method are the following: (1) the computation can be split between several companies for collaborative studies; (2) the computation time can be reduced by one or more orders of magnitude especially in the context of parametric studies. The accuracy and efficiency of this technique is assessed by directivity computations of monopole antennas mounted on a Fokker 100 aircraft. Multidomain results obtained by combining two sets of sub-domains are compared with direct boundary element methods. The computations are made in the VHF band for several positions of the monopoles, several generator loads and several engine faces to show the benefits of the multidomain method for parametric studies.

An original method is proposed which associates rigorous method (electrical field integral equation-EFIE and partial differential equation-FEM) with Floquet modes through multidomain formalism. Large array antennas can then be accurately analysed.

The electromagnetic scattering from the interior of a complex jet engine inlet contributes significantly to the overall radar cross section (RCS) of a modern jet aircraft. Previously we have presented a general multi-domain and multi-method coupling scheme, based on generalized scattering matrices computations of three-dimensional inlet subdomains. This method is really suitable in a context of parametric investigations (local inlet engine modifications). In this paper we discuss a new algorithm providing the radar modulation due to a set of rotating blades computed with only one solution for any blade position. A validation of this method is presented on a simplified rotating structure connected with an evolutive inlet.

International audience

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International audience

National audience

Cette contribution présente la réalisation et la mesure d’un absorbant à métamatériaux initialement conçu avec des matériaux RF et remplacés par des matériaux composites structuraux, i.e. renforcés de fibres. L’absorbant présente un module du coefficient de réflexion mesuré en incidence normale inférieur à - 13.2 dB de 5.2 GHz à 18 GHz, pour une épaisseur totale de 8.9 mm. Le module de coefficient de réflexion mesuré est inférieur à -10 dB jusqu’à 45° d’incidence quelle que soit la polarisation entre 4.9 et 18 GHz.

This thesis is about the electromagnetic simulation of large scale problems as the wave scattering from aircrafts and the airborne antennas radiation. It consists in the development of a method combining domain decomposition and hierarchical compression of the surface integral equations. First, we remind the principles of the boundary element method and the hierarchical representation of the surface integral equations with the Adaptive Cross Approximation algorithm. Then, we present the IE-DDM formulation obtained from a sub-domain integral representation. The matrices resulting of the discretization of the formulation are stored in the H-matrix format. A solver especially fitted with the hierarchical representation of the IE-DDM formulation has been developed. This study highlights the efficiency of the sub-domain decomposition as a preconditioner of the integral equations. Moreover, the method is fast for the resolution of multiple incidences and the resolution of low frequencies problems., Cette étude s’inscrit dans le domaine de la simulation électromagnétique des problèmes de grande taille tels que la diffraction d’ondes planes par de larges plateformes et le rayonnement d’antennes aéroportées. Elle consiste à développer une méthode combinant décomposition en sous-domaines et compression hiérarchique des équations intégrales de frontière. Pour cela, nous rappelons dans un premier temps les points importants de la méthode des équations intégrales de frontière et de leur compression hiérarchique par l’algorithme ACA (Adaptive Cross Approximation). Ensuite, nous présentons la formulation IE-DDM (Integral Equations – Domain Decomposition Method ) obtenue à partir d’une représentation intégrale des sous-domaines. Les matrices résultant de la discrétisation de cette formulation sont stockées au format H-matrice (matrice hiérarchique). Un solveur spécialement adapté à la résolution de la formulation IE-DDM et à sa représentation hiérarchique a été conçu. Cette étude met en évidence l’efficacité de la décomposition en sous- domaines en tant que préconditionneur des équations intégrales. De plus, la méthode développée est rapide pour la résolution des problèmes à incidences multiples ainsi que la résolution des problèmes basses fréquences.

Electromagnetic periodic structures are of great interest. These structures act as frequency filters and allow the manufacturing of meta-materials which appear to be composite and artificial. They exhibit electromagnetic properties that are unusual to natural materials such as band gaps. This allows new devices to guide, focus or stop the propagation. This is for example useful to avoid coupling between various radiating elements via the characterization of the surface waves which propagate at the interface between air and the periodic structure. This thesis provides a description of the finite element method dedicated to the characterization of periodic structures. Numerical modelling results in eigenvalue problems of large sizes. It involves solving linear systems compounds of sparse matrices. A method is therefore discussed for solving this type of problem, optimizing and combining different algorithms. Before discussing the different aspects of the developed method, we establish an exhaustive list of all the existing methods by stating their advantages and drawbacks. We note that the finite element method can handle a wide range of periodic structures in three dimensions without limitation on their shape. We present different formulations of this method. Then the algorithmic aspects of the method are detailed. We show that an analysis of the resolution settings can impact the physical interpretations of the results. Finally we show the performance of our tool on classical validation results from the bibliography and we discuss the characterization of surface waves. Therefore, the study of a patch antenna array included in metal cavities is conducted. To conclude we can say that the studies conducted in this thesis have resulted in the production of a code used in an environment calculation initially present at ONERA.; En électromagnétisme les structures périodiques suscitent un grand intérêt. Ces structures agissent ainsi comme des filtres fréquentiels et permettent la fabrication de méta-matériaux, composites et artificiels. Elles présentent des propriétés électromagnétiques inédites pour les matériaux naturels telles que des bandes interdites. On a ainsi pu fabriquer de nouveaux dispositifs permettant de guider, de focaliser ou de stopper la propagation. C'est par exemple utile pour éviter le couplage entre différents éléments rayonnants notamment via la caractérisation des ondes de surface qui se propagent à l'interface entre l'air et la structure périodique. Ce travail de thèse s'inscrit dans ce contexte et propose une description de la méthode des éléments finis dédiée à la caractérisation des structures périodiques. La modélisation numérique aboutit à des problèmes de valeurs propres de grandes tailles. Elle implique la résolution de systèmes linéaires composés de matrices creuses. Une méthode est abordée pour résoudre ce type de problème, en optimisant et combinant différents algorithmes. Avant d'aborder les différents aspects de la méthode développée, nous établissons une liste exhaustive de l'ensemble des méthodes qui existent en énonçant leurs avantages et leurs inconvénients. Nous constatons notamment que la méthode des éléments finis permet de traiter un large éventail de structures périodiques en trois dimensions sans limitation sur leur forme géométrique. Nous présentons alors les différentes formulations de cette méthode. Ensuite les aspects algorithmiques de la méthode sont détaillés. Nous montrons notamment qu'une analyse des paramètres de résolution permet de préciser les interprétations physiques des résultats obtenus. Finalement nous présentons les performances de notre outil sur des cas d'applications issus de la littérature et nous abordons la caractérisation des ondes de surface. Pour cela, l'étude d'un réseau d'antennes patchs insérées dans des cavités métalliques est conduite. Notons pour conclure que les études conduites au cours de cette thèse ont abouti à la production d'un code utilisable dans un environnement de calcul initialement présent à l'ONERA.