La méthode PEEC est connue comme une bonne méthode pour la modélisation des interconnexions électriques dans les domaines de l’électronique de puissance et l’électrotechnique. Elle s'applique à une large gamme de dispositifs : circuits imprimés, bus-barres, conducteurs massifs. Elle est particulièrement bien adaptée pour la modélisation de régions conductrices du type filaire. Cependant, elle est requise d’un maillage structuré(discrétisation des géométries en quadrangles) et l’approche est limitée en fréquence (grande épaisseur de peau). Enfin, il semble actuellement difficile d’envisager la modélisation de conducteurs volumiques dans une formulation PEEC standard.Cette thèse développe des formulations intégrales en utilisant des éléments de facette afin d’lever des verrous de la méthode PEEC standard évoqués ci-dessus. Elle constitue de fait une généralisation de la méthode PEEC standard par la prise en compte de maillages non structurés (volumique et surfacique) et la prise en compte de notion de régions minces à faible épaisseur de peau.Les applications visées sont la modélisation de systèmes de conducteurs complexes (des régions non simplement connexes) en prenant en compte des connexions entre des régions (volumique/filaire, surfacique/filaire,volumique/surfacique et surfacique/surfacique). / The PEEC method is known as a good method for modeling electrical connections in the domains of powerelectronics and electrical engineering. It applies to a wide range of devices: printed circuits, bus-bars, solidconductors. It is particularly well adapted for modeling the wire type conductive regions. However, it is requireda structured mesh (discretization geometries quadrangles) and this approach is limited in frequency (high skindepth). Finally, it now seems difficult to envisage modeling of the volume conductors in standard PEECformulation.This thesis develops integrals formulations using facet elements to improve the above mentioned limitations ofthe standard PEEC method. It is in fact a generalization of the standard PEEC method by taking into accountunstructured meshes (volume and surface) and taking into account the notion of thin region with a small skindepth.The applications are the modeling of complex systems of conductors (non-simply connected regions) taking intoaccount the connections between regions (volume / wireframe, surface / wired volume / surface and surface /surface).

The master’s thesis deals with the piezoelectric coefficients, the resonance frequency and especially the piezoelectric constants verification. With the assistance of several devices, for instance LCR-meter HIOKI 3532, impedance analyzer Agilent 4294A and LCR-meter Agilent E4980A, the resonance and the anti-resonance frequencies as well as impedance and capacitance of samples are measured. The paper opens with the theory of the piezoelectric phenomenon and the difference between direct and indirect piezoelectric phenomenon, it also describes the basic behaviour of a piezoelectric ceramic element during mechanical straining or applied voltage. Further, the paper concerns the description of various piezoelectric constants and their calculations. Subsequent part of the paper is devoted to the temperature dependence of the main piezoelectric parameters of PZT ceramics. The materials coefficients are delineated as a function of temperature of the piezoelectric charge coefficients dij, relative permittivity r, electromechanical coupling factor kij and frequency constants Ni. One of the chapters also determines the piezoelectric charge constant d33 of PZT ceramics by laser interferometer and compares it with the value measured by resonance methods. The surface displacement was measured by a single-beam interferometer Polytec OFV-5000. The results of measurements of piezoelectric charge coefficients d33 acquired by the first and the second method are identical. The last section of the paper is focused on different methods of experimental studies on the characteristics of heat transfer by diffusing heat through conduction between the silver-plated surface of cylinder made of PZT ceramics. The effect on the resonance and the anti-resonance frequencies is monitored. There after, the real heat, determined by thermo camera and the physical model of heat transfer created in program COMSOL Multiphysics, is analysed.