La Méthode de la Trajectoire Adiabatique Contrainte est développée dans le but de résoudre globalementl’équation de Schrödinger. Cette méthode utilise le formalisme de Floquet et une décomposition de Fourier pourdécrire les dépendances temporelles. Elle transforme ainsi un problème dynamique en un problème aux valeurspropres partiel dans un espace de Hilbert étendu au temps. Cette manipulation requiert l’application decontraintes sur les conditions initiales de l’état propre de Floquet recherché. Les contraintes sont appliquées parl’intermédiaire d’un opérateur absorbant artificiel. Cet algorithme est adapté à la description de systèmes dirigéspar des hamiltoniens dépendant explicitement du temps. Il ne souffre pas de l’accumulation d’erreurs au cours dutemps puisqu’il fournit une solution globale ; les erreurs éventuelles proviennent de la non-complétude des basesfinies utilisées pour la description moléculaire ou temporelle et de l’imperfection du potentiel absorbant dépendantdu temps nécessaire pour fixer les conditions initiales. Une forme générale de potentiel absorbant a étédéveloppée pour être en mesure d’intégrer un problème avec une condition initiale quelconque. Des argumentsrelatifs au suivi adiabatique dans le cas de Hamiltoniens non-hermitiens sont également présentés. Nous insistonssur le rôle des facteurs de phase géométrique. Les méthodes développées sont appliquées à des systèmesatomiques ou moléculaires soumis à des impulsions laser intenses, en relation avec la problématique du contrôlemoléculaire. Nous considérons plusieurs exemples : modèles d’atomes à deux ou trois niveaux, ion moléculairehydrogène et molécules froides de sodium. / The Constrained Adiabatic Trajectory Method (CATM) allows us to compute global solutions of the time-dependent Schrödinger equation using the Floquet formalism and Fourier decomposition. The dynamical problem is thustransformed into a “static” problem, in the sense that the time will be included in an extended Hilbert space. Thisapproach requires that suitable constraints are applied to the initial conditions for the relevant Floquet eigenstate.The CATM is well suited to the description of systems driven by Hamiltonians with explicit and complicated timevariations. This method does not have cumulative errors and the only error sources are the non-completeness ofthe finite molecular and temporal basis sets used, and the imperfection of the time-dependent absorbing potentialwhich is essential to impose the correct initial conditions. A general form is derived for the absorbing potential,which can reproduce any dispersed boundary conditions. Arguments on adiabatic tracking in the case of nonhermitianHamiltonians are also presented. We insist on the role of geometric phase factors. The methods areapplied to atomic and molecular systems illuminated by intense laser pulses, in connection with molecular controlproblems. We study several examples : two or three-level atomic models, hydrogen molecular ion, cold sodiummolecules.

La thèse se base sur la recherche des possibilités de caractérisation du son aérien de sources sonores arbitraires. A cette fin, une approche particulière est étudiée à l’endroit où la caractérisation de la source est faite via une surface d’interface qui enveloppe totalement ou partiellement la source physique. Deux descripteurs qui dépendent de la fréquence sont definis au travers d’une telle surface: la pression sonore bloquée et l’impédance de la source. Le précédent représente la pression sonore créée par le système d’exploitation source qui agit sur la surface enveloppante quand elle est rendue immobile. Cette dernière représente le rapport des amplitudes de réponse de pression et les amplitudes de vitesse d’excitation normales au travers de la surface. La surface enveloppante définit un volume d’air qui contient la source physique appelée l’espace source. Les deux descripteurs définis sur l’espace source, la pression bloquée et l’impédance de la source sont montrés comme étant intrinsèques à la source, c’est-à-dire indépendants de l’espace acoustique environnant. Une fois définis, ces descripteurs permettent de trouver la pression sonore et la vitesse particulaire normale à la surface de l’interface quand l’espace source est couplé à un espace récepteur arbitraire, c’est-à-dire une pièce. Cela permet alors la prédiction du son dans l’espace récepteur. Les conditions de couplage nécessitent que l’espace récepteur soit caractérisé en utilisant la même surface enveloppante telle que l’espace source. En acceptant de garder à l’esprit la simplicité de la mesure, la surface enveloppante a été conçue vu qu’elle comporte une ou plusieurs surfaces rectangulaires planes. Le défi de la recherche était alors d’obtenir une impédance significative de la surface au travers de la surface plane rectangulaire (continue) ainsi que celle de la pression bloquée compatible avec la formulation de l’impédance. Cela a conduit à une décomposition dans l’espace de la pression sonore et de la vitesse des particules au sein du nombre fini des composants, chacun défini par une amplitude complexe et une distribution dans l’espace particulière. De cette façon, la pression bloquée se réduit à un vecteur d’amplitude de pression complexe, tandis que l’impédance devient une matrice de pression et des rapports d’amplitudes complexes de la vitesse de défauts de de décompositions ont été recherchés dans le détail: la méthode harmonique de surface et la méthode du patch. Le premier se rapproche de la pression de surface et de la vitesse normale par des combinaisons de fonctions de surface trigonométriques en 2D tandis que ce dernier partage la surface en petites parcelles et intervient sur chaque parcelle de façon discrète en utilisant les valeurs moyennes du patch. / The thesis investigates possibilities of air-borne sound characterisation of arbitrary sound sources. To this end a particular approach is studied where the source characterisation is done via an interface surface which fully or partially envelopes the physical source. Two frequency dependent descriptors are defined across such a surface: the blocked sound pressure and the source impedance. The former represents the sound pressure created by the operating source which acts on the enveloping surface when this is made immobile. The latter represents the ratio of pressure response amplitudes and normal velocity excitation amplitudes across the surface. The enveloping surface defines an air volume containing the physical source, called the source space. The two source descriptors defined on the source space, the blocked pressure and the source impedance, are shown to be intrinsic to the source, i.e. independent of the surrounding acoustical space. Once defined, these descriptors allow one to find the sound pressure and normal particle velocity at the interface surface when the source space is coupled to an arbitrary receiver space, i.e. a room. This in turn allows for sound prediction in the receiver space. The coupling conditions require that the receiver space is characterised using the same enveloping surface as the source space. Bearing the measurement simplicity in mind, the enveloping surface has been conceived as consisting of one or several rectangular plane surfaces. The research challenge was then to obtain meaningful surface impedance across a (continuous) rectangular plane surface as well as the blocked pressure compatible with impedance formulation. This has led to a spatial decomposition of sound pressure and particle velocity into finite number of components, each defined by a complex amplitude and a particular spatial distribution. In this way the blocked pressure reduces to a vector of complex pressure amplitudes while the impedance becomes a matrix of pressure and velocity complex amplitude ratios. Two decomposition methods have been investigated in detail: the surface harmonic method and the patch method. The former approximates the surface pressure and normal velocity by combinations of 2D trigonometric surface functions while the latter splits the surface into small patches and treats each patch in a discrete way, using patch-averaged values.

Descargas atmosféricas representam uma das principais causas de interrupção no fornecimento de energia para os consumidores, e embora tenham efeitos mais intensos quando incidem diretamente nas redes elétricas, é o caso das descargas indiretas que chama mais atenção, já que elas ocorrem com maior frequência. Tanto as primeiras descargas que geralmente ocorrem com maior intensidade de corrente, quanto as descargas subsequentes que têm menor tempo de frente associado, irradiam campos eletromagnéticos que ao se acoplarem com as redes elétricas geram surtos que podem causar tanto a interrupção do fornecimento de energia quanto danos a equipamentos. A presença de edifícios na região de incidência da descarga atmosférica afeta a propagação das ondas irradiadas, criando diferentes padrões de campos resultantes, os quais são responsáveis por sobretensões induzidas. Embora tanto a descarga atmosférica em si quanto a caracterização do ambiente ao seu redor sejam de natureza complexa para sua representação, ferramentas computacionais bem estruturadas podem representar o fenômeno de forma satisfatória, como é o caso da ferramenta computacional desenvolvida neste trabalho utilizando o método das diferenças finitas no domínio do tempo. O presente trabalho apresenta dois estudos para verificação da influência de edificações na propagação de campo irradiado por descargas atmosféricas. O primeiro estudo avaliou o comportamento das componentes do campo elétrico e do campo magnético irradiados, comparando resultados obtidos com e sem a presença de edificações numa pequena região. Tanto os parâmetros geométricos dos três edifícios considerados neste estudo, como a permissividade e a condutividade elétrica do solo e dos edifícios, foram variados para identificar a sua influência nos campos irradiados. Os resultados mostraram diferentes comportamentos das componentes dos campos resultantes em função da variação desses parâmetros, observando-se inversão de polaridade, oscilações na forma de onda e tanto redução quanto aumento do valor de campo. O segundo estudo avaliou um caso mais geral em que a componente vertical de campo elétrico foi tomada em nove pontos diferentes de uma região tipicamente urbana, com a presença de 102 edifícios. Os valores de campo avaliados em cada ponto, dez metros acima do solo, consideraram a incidência aleatória de 28 descargas atmosféricas distintas, cada uma atingindo o topo de um dado edifício. Os resultados desse segundo estudo mostraram que exceto nos casos em que a descarga atmosférica ocorre próximo do ponto analisado, há reduções significativas do campo elétrico vertical. Desta forma é possível perceber que não apenas a existência de edifícios, mas a sua concentração com diferentes características elétricas e geométricas, podem influenciar significativamente a propagação de campo irradiado. Os valores calculados a partir da ferramenta desenvolvida podem ser usados em conjunto com modelos de acoplamento, para o cálculo de sobretensões induzidas em redes elétricas, em situações realistas com configurações mais complexas. / Atmospheric discharges represent one of the main causes of interruption in power supply to consumers, and although they have more intense effects when direct impact on energy lines, are the case of indirect discharges that draws more attention, since they occur more frequently. Both the first discharges, occurring generally with greater intensity of current, as subsequent discharges that have shorter front time associated, radiate electromagnetic fields which engage with the electrical networks generating surges that can cause so much disruption of power supply as damage to the equipment. The presence of buildings in the lightning incident area affects the propagation of the radiated waves, creating different patterns of resultant fields, which are responsible for induced overvoltages. Although both the lightning itself and characterization of the surrounding environment are of a complex nature for its representation, structured computational tools can represent satisfactorily the phenomenon, such as the software tool developed here using the finite difference time domain method. This work presents two studies to verify the influence of buildings in the propagation of lightning irradiated field. The first study assessed the behavior of the components of the electric field and magnetic field irradiated, by comparing results obtained with and without the presence of buildings in a small region. Both the geometric parameters of the three buildings considered in this study, as the permittivity and electrical conductivity of the soil and buildings, were changed to identify their influence on radiated fields. The results showed different behaviors of the components of the resulting field due to the variation of these parameters, observing polarity inversion, oscillations in the waveform and either a reduction or increase of the field value. The second study evaluated a more general case where the vertical component of the electric field was taken at nine different points of a typical urban area, in the presence of 102 buildings. The field values evaluated at each point, ten meters above the ground, considered the effect of 28 different random lightning, which hit the top of a given building. The results of this second study showed that except in cases where atmospheric discharge occurs near the analyzed point, there are significant reductions of the vertical electric field. Thus it can be seen that not only the existence of buildings, but its concentration with different electrical and geometrical characteristics, can significantly influence the propagation of irradiated field. The values calculated from the developed tool can be used in conjunction with coupling models for calculating induced overvoltages on power lines, in realistic situations with complex configurations.

Considera-se neste trabalho o projeto de estruturas de concreto para edifícios de múltiplos andares, com fundação profunda, levando-se em conta a interação solo-estrutura. Essa interação é analisada por meio de um método numérico em que a superestrutura (lajes, vigas e pilares) e os elementos estruturais de fundação (blocos e estacas) são considerados uma estrutura única, modelada pelo método dos elementos finitos e implementada no código computacional PEISE (Pórtico Espacial com Interação Solo-Estrutura), desenvolvido nesta pesquisa. O maciço de solos é representado por um modelo geotécnico proposto por Aoki e Lopes, em 1975, que utiliza a solução de Mindlin para o cálculo de deslocamentos em meio semi-infinito, elástico, contínuo e isótropo, e que considera a existência de uma superfície indeslocável, abaixo da qual as deformações do maciço podem ser desprezadas. A resposta elástica da interação solo-estrutura é subordinada a valores limites, observados em ensaios de capacidade de carga das estacas. Como forma de validar o programa e mostrar sua aplicação em problemas práticos de engenharia, resultados de exemplos foram comparados com os obtidos por outras metodologias presentes na literatura. Também, acompanhou-se o desempenho estrutural de um edifício de 26 pavimentos, com fundação em estaca hélice contínua, em sua fase construtiva, com o monitoramento de recalques e a medida de deformações em pilares, para obtenção indireta de suas solicitações normais. Os recalques foram obtidos por meio de nivelamento ótico de precisão, e as solicitações normais nos pilares foram avaliadas indiretamente, pela variação de seu comprimento, utilizando-se extensômetro mecânico removível e considerando-se as variações dos fatores ambientais e a reologia do concreto. / Design of concrete structures for multi-story buildings with deep foundation is considered in this work, taking in account the soil-structure interaction. This interaction is analysed with a numerical method where the superstructure (slabs, beams, and columns), and the foundation structural elements (blocks and piles) are considered a unique structure, modeled by the finite element method and implemented in the PEISE (soil-structure interaction in spatial frame), software that was developed in this search. The geo-technical model proposed by Aoki and Lopes (1975) represents the soil, where Mindlin\'s solution is used to calculate displacements in a semi-infinite, elastic, continuous, and isotropic environment. This solution also considers the existence of an unmovable surface, under which the soil deformations shall be neglected. The elastic response of soil-structure interaction is subordinated to limit values observed in \"in situ\" loading capacity piles tests. The examples elaboration proves the developed formulation validity through results comparison with others methodologies. Also the structural performance of a 26 story building with augercast piles was observed during the construction by measurement of settlements and columns length variation. Settlements were measured by means of optical level. Loads over columns were indirectly evaluated through column length variation, using a demountable mechanical extensometer and considering corrections due to the variation of environmental conditions and to the concrete\'s rheology.

Avec l’essor de l’électronique embarquée, les câbles électriques constituentune part importante des pièces automobiles tandis que l’espace à bord n’a cessé de diminuer. Leur flexibilité requiert la prédiction de leur déformation durant leur montage afin d’éviter le contact avec d’autres pièces du véhicule et leur endommagement. Les outils actuels ne permettent pas une prédiction assez réaliste et précise de leur comportement, nécessaire dans un volume de travail très restreint. Les étapes de montage sont donc validées via la réalisation de maquettes réelles coûteuses. Cette thèsea pour but d’améliorer la simulation numérique de ces pièces souples. Nous proposonsici un code de simulation 3D basé sur un modèle de poutre géométriquement exact résolu par la méthode des éléments finis. Son originalité tient dans le couplage des quaternions pour modéliser les rotations 3D et de la méthode asymptotique numérique pour la continuation du système non linéaire qui lui confère une grande robustesse. Un banc d’essai permettant l’identification des paramètres homogénéisés nécessaires au modèle numérique et sa validation par comparaison de la géométrie finale et du chemin d’équilibre est présenté. Combinés à des développements analytiques sur les modèles de poutres avec cisaillement, les essais mènent à une évaluation critique du modèle deTimoshenko 3D pour la représentation des torons de câbles. / With on-board electronics expansion, electrical cables are an essential partof automotive pieces and the space on board has plummeted. Their flexibility requires to predict their deformation during vehicle assembly in order to avoid the contact with other pieces and damaging. Current numerical tools do not allow a realistic and accurate prediction, which is necessary in the obstructed car space. Assembly steps thus are validated on costly physical mock-ups. This thesis aims at improving numerical simulation of these flexible pieces. We herein propose a 3D algorithm based on a geometrically exact beam model solved by the finite element method. This work’s originality stands in coupling quaternions as rotational parameters and the asymptotic numerical method as nonlinear solver which results in a very robust algorithm. A test bench designed to identify the homogenized beam parameters of the numerical model and to validate it by offering a comparison on the final geometry and the equilibrium path is presented. Analytical developments on shear beams and the results of these experimental tests lead to a critical evaluation of the 3D Timoshenko model for representing stranded cables.

Descargas atmosféricas representam uma das principais causas de interrupção no fornecimento de energia para os consumidores, e embora tenham efeitos mais intensos quando incidem diretamente nas redes elétricas, é o caso das descargas indiretas que chama mais atenção, já que elas ocorrem com maior frequência. Tanto as primeiras descargas que geralmente ocorrem com maior intensidade de corrente, quanto as descargas subsequentes que têm menor tempo de frente associado, irradiam campos eletromagnéticos que ao se acoplarem com as redes elétricas geram surtos que podem causar tanto a interrupção do fornecimento de energia quanto danos a equipamentos. A presença de edifícios na região de incidência da descarga atmosférica afeta a propagação das ondas irradiadas, criando diferentes padrões de campos resultantes, os quais são responsáveis por sobretensões induzidas. Embora tanto a descarga atmosférica em si quanto a caracterização do ambiente ao seu redor sejam de natureza complexa para sua representação, ferramentas computacionais bem estruturadas podem representar o fenômeno de forma satisfatória, como é o caso da ferramenta computacional desenvolvida neste trabalho utilizando o método das diferenças finitas no domínio do tempo. O presente trabalho apresenta dois estudos para verificação da influência de edificações na propagação de campo irradiado por descargas atmosféricas. O primeiro estudo avaliou o comportamento das componentes do campo elétrico e do campo magnético irradiados, comparando resultados obtidos com e sem a presença de edificações numa pequena região. Tanto os parâmetros geométricos dos três edifícios considerados neste estudo, como a permissividade e a condutividade elétrica do solo e dos edifícios, foram variados para identificar a sua influência nos campos irradiados. Os resultados mostraram diferentes comportamentos das componentes dos campos resultantes em função da variação desses parâmetros, observando-se inversão de polaridade, oscilações na forma de onda e tanto redução quanto aumento do valor de campo. O segundo estudo avaliou um caso mais geral em que a componente vertical de campo elétrico foi tomada em nove pontos diferentes de uma região tipicamente urbana, com a presença de 102 edifícios. Os valores de campo avaliados em cada ponto, dez metros acima do solo, consideraram a incidência aleatória de 28 descargas atmosféricas distintas, cada uma atingindo o topo de um dado edifício. Os resultados desse segundo estudo mostraram que exceto nos casos em que a descarga atmosférica ocorre próximo do ponto analisado, há reduções significativas do campo elétrico vertical. Desta forma é possível perceber que não apenas a existência de edifícios, mas a sua concentração com diferentes características elétricas e geométricas, podem influenciar significativamente a propagação de campo irradiado. Os valores calculados a partir da ferramenta desenvolvida podem ser usados em conjunto com modelos de acoplamento, para o cálculo de sobretensões induzidas em redes elétricas, em situações realistas com configurações mais complexas. / Atmospheric discharges represent one of the main causes of interruption in power supply to consumers, and although they have more intense effects when direct impact on energy lines, are the case of indirect discharges that draws more attention, since they occur more frequently. Both the first discharges, occurring generally with greater intensity of current, as subsequent discharges that have shorter front time associated, radiate electromagnetic fields which engage with the electrical networks generating surges that can cause so much disruption of power supply as damage to the equipment. The presence of buildings in the lightning incident area affects the propagation of the radiated waves, creating different patterns of resultant fields, which are responsible for induced overvoltages. Although both the lightning itself and characterization of the surrounding environment are of a complex nature for its representation, structured computational tools can represent satisfactorily the phenomenon, such as the software tool developed here using the finite difference time domain method. This work presents two studies to verify the influence of buildings in the propagation of lightning irradiated field. The first study assessed the behavior of the components of the electric field and magnetic field irradiated, by comparing results obtained with and without the presence of buildings in a small region. Both the geometric parameters of the three buildings considered in this study, as the permittivity and electrical conductivity of the soil and buildings, were changed to identify their influence on radiated fields. The results showed different behaviors of the components of the resulting field due to the variation of these parameters, observing polarity inversion, oscillations in the waveform and either a reduction or increase of the field value. The second study evaluated a more general case where the vertical component of the electric field was taken at nine different points of a typical urban area, in the presence of 102 buildings. The field values evaluated at each point, ten meters above the ground, considered the effect of 28 different random lightning, which hit the top of a given building. The results of this second study showed that except in cases where atmospheric discharge occurs near the analyzed point, there are significant reductions of the vertical electric field. Thus it can be seen that not only the existence of buildings, but its concentration with different electrical and geometrical characteristics, can significantly influence the propagation of irradiated field. The values calculated from the developed tool can be used in conjunction with coupling models for calculating induced overvoltages on power lines, in realistic situations with complex configurations.

The reliability of modern gas turbine engines is largely due to careful damage tolerant design a method of structural design based on the assumption that flaws (cracks) exist in any structure and will continue to grow with usage. With proper monitoring, largely in the form of periodic inspections at conservative intervals reliability and safety is maintained. These methods while reliable can lead to the early retirement of some components and unforeseen failure if design assumptions fail to reflect reality. With improvements to sensor and computing technology there is a growing interest in a system that could continuously monitor the health of structural aircraft as well as forecast future damage accumulation in real-time. Through the use of two-dimensional and three-dimensional numerical modeling the initial goals and findings for this continued work include: (a) establishing measurable parameters directly linked to the health of the blade and (b) the feasibility of detecting accumulated damage to the structural material and thermal barrier coating as well as the onset of damage causing structural failure.

The reliability of modern gas turbine engines is largely due to careful damage tolerant design a method of structural design based on the assumption that flaws (cracks) exist in any structure and will continue to grow with usage. With proper monitoring, largely in the form of periodic inspections at conservative intervals reliability and safety is maintained. These methods while reliable can lead to the early retirement of some components and unforeseen failure if design assumptions fail to reflect reality. With improvements to sensor and computing technology there is a growing interest in a system that could continuously monitor the health of structural aircraft as well as forecast future damage accumulation in real-time. Through the use of two-dimensional and three-dimensional numerical modeling the initial goals and findings for this continued work include: (a) establishing measurable parameters directly linked to the health of the blade and (b) the feasibility of detecting accumulated damage to the structural material and thermal barrier coating as well as the onset of damage causing structural failure.

The reliability of modern gas turbine engines is largely due to careful damage tolerant design a method of structural design based on the assumption that flaws (cracks) exist in any structure and will continue to grow with usage. With proper monitoring, largely in the form of periodic inspections at conservative intervals reliability and safety is maintained. These methods while reliable can lead to the early retirement of some components and unforeseen failure if design assumptions fail to reflect reality. With improvements to sensor and computing technology there is a growing interest in a system that could continuously monitor the health of structural aircraft as well as forecast future damage accumulation in real-time. Through the use of two-dimensional and three-dimensional numerical modeling the initial goals and findings for this continued work include: (a) establishing measurable parameters directly linked to the health of the blade and (b) the feasibility of detecting accumulated damage to the structural material and thermal barrier coating as well as the onset of damage causing structural failure.

Ce travail porte sur le développement d'algorithmes et l'application de méthodes numériques pour la résolution des problèmes inverses d'estimation de paramètres, d'identification de conditions aux limites et d'identification de sources dans un milieu poreux. Ces outils seront d'une grande utilité pour l'aide à la gestion des ressources en eaux souterraines et à leur préservation quant aux dégradations. L'objectif de cette thèse est de résoudre ces problèmes inverses en se basant sur différentes approches : Une résolution basée sur l'optimisation de forme topologique qui est la recherche de la géométrie d'un objet qui soit optimale vis à vis d'un critère donné, et ce sans aucun a priori sur sa topologie, c'est-à-dire sur le nombre de "trous" qu'il peut contenir. Sachant que ces trous représentent les puits recherchés. Pour ce faire, nous avons adopté la méthode du gradient topologique, qui consiste à étudier le comportement d'une fonction objectif lors de la création d'un petit trou à l'intérieur du domaine. Une résolution basée sur la minimisation d'une fonctionnelle d'erreur en énergie en utilisant des données surabondantes sur une partie de la frontière du domaine afin de compléter les données sur toute la frontière du domaine et de déterminer les positions, les débits et le nombre de puits existants à l'intérieur du domaine. Une résolution par le couplage de la méthode de paramétrisation adaptative qui a l'avantage de minimiser le nombre des inconnus de paramètres permettant d'interpréter au mieux les données disponibles et la méthode du gradient topologique. Ce couplage nous permet à la fois d'identifier les zones géologiques, de déterminer les valeurs de la transmissivité hydraulique dans chaque zone et de localiser les positions des puits. / This work deals with the development of algorithms and application of numerical methods for solving inverse problems of parameters estimation, identification of boundary conditions and localisation of sources in porous media. These tools will be usefull in the management of groundwater resources and their preservation as to damage. The objective of this thesis is to solve the inverse problem based on different approaches: A resolution based on topological shape optimization is to find an optimal design without any priori assumption about its topology, that is, about the number of holes it may contain. Knowing that these holes represent the searched wells. To do this, we have adopted the method of topological gradient, which is to study the behavior of an objective function when creating a small hole inside the domain. A resolution based on the minimization of a constitutive law gap functional by using overspecified data on a part of the boundary of the domain to complete the data on all the boundary of the domain and determine the positions, the flows and the number of existing wells inside the domain. A resolution by the coupling of the adaptive parameterization method which has the advantage to minimize the number of the unknowns of parameters allowing to interpret at best the available data and the method of the topological gradient. This coupling allows us at the same time to identify the geological zones, to determine the values of the hydraulic transmissivity in every zone and to locate wells' positions.