The dissertation thesis deals with Evolution optimization of control algorithms. The first part of the thesis describes the principles and partial methods of evolution optimization methods especially those used in two-level transplant evolution method. Later the grammatical evolution method is described, which modified algorithm became impulse for creation of transplant evolution method. The transplant evolution method and its two-level modification are new evolutionary algorithms proposed in this work, which were used for optimization of structure and parameters of general controllers control algorithms. The transplant evolution algorithm and its extended two-level modification are described in detail in next chapters. The proper settings of evolutionary algorithms are important for minimization the time of optimization and for finds results approaching the global optimum. For proper setting the parameters of differential evolution was created meta-evolution algorithm that is described in chapter named meta-evolution. The basic concepts of control, chosen methods of system identification and controller parameters settings are described in next part. This part describes algorithms of digital controllers and some specific methods uses in digital control. The demonstrations of control algorithm optimizations of various types of controllers are showed in experimental part. The optimized algorithms of general controllers are compared with various types of PSD controllers which were set by various algebraic methods or differential evolution for various models of systems. In the conclusion of this work is stated a recommendation for further development of evolutionary optimization of controllers are focusing on parallel and distributed computing.

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This thesis theoretically and experimentally studies the characteristics of integrated microresonators (MRs) built by passive (no gain) and non-magnetic materials and characterized by both Hermitian and non-Hermitian Hamiltonians. In particular, I have studied three different microresonators: a typical Microring Resonator (MR), a Taiji Microresonator (TJMR), which consists of a microresonator with an embedded S-shaped waveguide, and a new geometry called the Infinity-Loop Microresonator (ILMR), which is characterized by a microresonator shaped like the infinity symbol coupled at two points to the bus waveguide. To get an accurate picture of the three devices, they were modeled using both the transfer matrix method and the temporal coupled mode theory. Neglecting propagation losses, the MR is described by a Hermitian Hamiltonian, while the TJMR and the ILMR are described by a non-Hermitian one. An important difference between Hermitian and non-Hermitian systems concerns their degeneracies. Hermitian degeneracies are called Diabolic Points (DPs) and are characterized by coincident eigenvalues and mutually orthogonal eigenvectors. In contrast, non-Hermitian degeneracies are called Exceptional Points (EPs). At the EP, both the eigenvalues and the eigenvectors coalesce. The MR is at a DP instead, and the TJMR and the ILMR are at an EP. Since the TJMR and ILMR are at an EP, they have interesting features such as the possibility of being unidirectional reflectors. Here, it is shown experimentally how in the case of the TJMR this degeneracy can also be used to break Lorentz reciprocity in the nonlinear regime (high incident laser powers), discussing the effect of the Fabry-Perot of the bus waveguide facets. The effect of backscattering, mainly due to the waveguide surface-wall roughness, on the microresonators is also studied. This phenomenon induces simultaneous excitation of the clockwise and counterclockwise modes, leading to eigenvalue splitting. This splitting makes the use of typical quality factor estimation methods unfeasible. To overcome this problem and mitigate the negative effects of backscattering, a new experimental technique called interferometric excitation is introduced. This technique involves coherent excitation of the microresonator from both sides of the bus waveguide, allowing selective excitation of a single supermode. By adjusting the relative phase and amplitude between the excitation fields, the splitting in the transmission spectrum can be eliminated, resulting in improved quality factors and eigenvalue measurements. It is shown that this interferometric technique can be exploited under both stationary and dynamic conditions of time evolution. The thesis also investigates the sensing performance of the three microresonators as a function of a backscattering perturbation, which could be caused, for example, by the presence of a molecule or particle near the microresonator waveguide. It is shown that the ILMR has better performance in terms of responsivity and sensitivity than the other two microresonators. In fact, it has both the enhanced sensitivity due to the square root dependence of the splitting on the perturbation (characteristic of EPs) and the ability to completely eliminate the region of insensitivity as the backscattering perturbation approaches zero, which is present in both the other two microresonators. To validate the models used, they were compared with experimental measurements both in the linear regime and, for TJMR, also in the nonlinear regime, with excellent agreement.

In high-power electric drives, multilevel inverters are generally deployed to address issues such as electromagnetic interference, switch voltage stress and harmonic distortion. The switching frequency of the inverter is always kept low, of the order of 1KHz or even less to reduce switching losses and synchronous pulse width modulation (PWM) is used to avoid the problem of sub-harmonics and beat frequencies. This is particularly important if the switching frequency is very low. The synchronous PWM is getting popularity as its realization is very easy with digital controllers compared to analog controllers. Neutral-point-clamped (NPC) inverters, cascaded H-bridge, and flying-capacitor multilevel inverters are some of the popular schemes used for high-power applications. Hybrids of these multilevel inverters have also been proposed recently to take advantage of the basic configurations. Multilevel inverters can also be realized by feeding the induction motor from both ends (open-end winding) using conventional inverter structures. For controlling the output voltage of these inverters, various PWM techniques are used. Chapter-1 of this thesis provides an over view of the various multilevel inverter schemes preceded by a discussion on basic two-level VSI topology. The inverters used in motor drive applications have to be operated in over-modulation range in order to extract the maximum fundamental output voltage that is possible from the dc-link. Operation in this high modulation range is required to meet temporary overloads or to have maximum power operation in the high speed range (flux weakened region). This, however, introduces a substantial amount of low order harmonics in the Motor phase voltages. Due to these low-order harmonic frequencies, the dynamic performance of the drive is lost and the current control schemes are severely affected especially due to 5th and 7th harmonic components. Further, due to these low-order harmonics and non-linear PWM operation in over-modulation region, frequent over-current fault conditions occur and reliability of the drive is jeopardized. The twelve sided-polygonal space vector diagram (dodecagonal space vectors) can be used to overcome the problem of low order 5th and 7th harmonics and to give more range for linear modulation while keeping the switching frequency at a minimum compared to conventional hexagonal space vector based inverters. Thus, the dodecagonal space-vector switching can be viewed as an engineering compromise between low switching frequency and quality load current waveform. Most of the previous works of dodecagonal space-vector generation schemes are based on NPC inverters. However, sophisticated charge control schemes are required in NPC inverters to deal with the neutral-point voltage fluctuation and the neutral-point voltage shifting issues. The losses in the clamping diodes are another major concern. In the second chapter, a multilevel dodecagonal space-vector generation scheme based on flying capacitor topology, utilizing an open end winding induction motor is presented. The neutral point charge-balancing problem reported in the previous works is not present in this scheme, the clamping diodes are eliminated and the number of power supplies required has been reduced. The capacitors have inherent charge balancing capability, and the charge control is done once in every switching cycle, which gives tight voltage control for the capacitors. For the speed control of induction motors, the space-vector PWM scheme is more advantageous than the sine-triangle PWM as it gives a more linear range of operation and improved harmonic performance. One major disadvantage with the conventional space-vector PWM is that the trigonometric operations demand formidable computational efforts and look-up tables. Carrier based, common-mode injected PWM schemes have been proposed to simplify the PWM process. However, the freedom of selecting the PWM switching sequences is limited here. Another way of obtaining SVPWM is using the reference voltage samples and the nearest vector information to switch appropriate devices for proper time intervals, realizing the reference vector in an average sense. In-formation regarding the sector and nearest vectors can be easily obtained by comparing the instantaneous amplitudes of the reference voltages. This PWM approach is pro-posed for the speed control of the motor in this thesis. The trigonometric operations and the requirement of large look-up tables in the conventional SVPWM are avoided in this method. It has the additional advantage that the switching sequences can be decided at will, which is helpful in reducing further, the harmonic distortion in certain frequency ranges. In this way, this method tries to combine the advantages of vector based methods (conventional SVPWM) and scalar methods (carrier-based methods). The open-end winding schemes allowed the required phase voltage levels to be generated quite easily by feeding from both ends of the windings. Thus, most of the multilevel inverters based on dodecagonal space-vector structures relied on induction motors with open-end windings. The main disadvantage of open-end winding induction motor is that six wires are to be run from the inverter to the motor, which may be unacceptable in certain applications. Apart from the inconvenience of laying six wires, the voltage reflections in the wires can lead to over voltages at the motor terminals, causing insulation failures. Where as the topology presented in chapter-2 of this thesis uses open-end winding motor with flying-capacitor inverters for the generation of dodecagonal space-vectors, the topology presented in chapter-3 utilizes a cascade connection of flying-capacitors and floating H-bridge cells to generate the same set of voltage space-vectors, thus allowing any standard induction motor as the load. Of the methods used for the speed control of induction motors, namely sine-triangle PWM and space vector PWM, the latter that provides extra modulation range is naturally preferred. It is a well-understood fact that the way in which the PWM switching sequences are applied has a significant influence on the harmonic performance of the drive. However, this topic has not been addressed properly for dodecagonal voltage space-vector based multilevel inverter drives. In chapter-4 of the thesis, this aspect is taken into ac-count and the notion of “harmonic flux trajectories” and “stator flux ripple” are used to analyze the harmonic performance of the various PWM switching schemes. Although the PWM method used in this study is similar to that in chapter-2, the modification in the PWM switching sequence in the PWM algorithm yields significant improvements in harmonic performance. The proposed topologies and PWM schemes are extensively simulated and experimentally verified. The control scheme was implemented using a DSP processor running at a clock frequency 150MHz and a four-pole, 3.7kW, 50Hz, 415V three-phase induction motor was used as the load. Since the PWM ports are limited in a DSP, a field-programmable gate array (FPGA) was used to decode the PWM signals from the DSP to generate timing information required for PWM sequencing for all the power devices. The same FPGA was used to generate the dead-time signals for the power devices also.

Multilevel converters have become the direct accepted solution for high power converter applications. They are used in wide variety of power electronic applications like power transmission and distribution, electric motor drives, battery management and renewable energy management to name a few. For medium and high voltage motor drives, especially induction motor drives, the use of multilevel voltage source inverters have become indispensible. A high voltage multilevel inverter could be realized using low voltage switching devices which are easily available and are of low cost. A multilevel inverter generates voltage waveforms of very low harmonic distortion by switching between voltage levels of reasonably small amplitude differences. Thus the dv/dt of the output voltage waveform is small and hence the electromagnetic interference generated is less. Because of better quality output generation, the switching frequency of the multilevel inverters could be reduced to control the losses. Thus, a multilevel converter stands definitely a class apart in terms of performance from a conventional two-level inverter. Many multilevel inverter topologies for induction motor drives are available in the literature. The basic multilevel topologies are the neutral point clamped (NPC) inverter, flying capacitor (FC) inverter and the cascaded H-bridge (CHB) inverter. Various other hybrid multilevel topologies have been proposed by using the basic multilevel inverter topologies. It is also possible to obtain multilevel output by using conventional two-level inverters feeding an open-end winding induction motor from both sides. All the conventional multilevel voltage source inverters generate hexagonal (6 sided polygons) voltage space vector structures. When an inverter with hexagonal space vector structure is operated in the over modulation range, significant low order harmonics are generated in the phase voltage output. Over modulation operation is required for the full utilization of the available DC-link voltage and hence maximum power generation. Among the harmonics generated, the fifth and seventh harmonics are of significant magnitudes. These harmonics generate torque ripple in the motor output and are undesirable in high performance motor drive applications. The presence of these harmonics further creates problems in the closed loop current control of a motor, affecting the dynamic performance. Again, the harmonic currents generate losses in the stator windings. Therefore, in short, the presence of harmonic voltages in the inverter output is undesirable. Many methods have been proposed to eliminate or mitigate the effect of the harmonics. One solution is to operate the inverter at high switching frequency and thereby push the harmonics generated to high frequencies. The stator leakage inductance offers high impedance to the high frequency harmonics and thus the harmonic currents generated are negligible. But, high switching frequency brings switching losses and high electromagnetic interference generation in the drive system. And also, high switching frequency operation is effective only in the linear modulation range. Another solution is to use passive harmonic filters at the inverter output. For low order harmonics, the filter components would be bulky and costly. The loss created by the filters degrades the efficiency of the drive system as well. The presence of a filter also affects the dynamic performance of the drive system during closed loop operation. Special pulse width modulation (PWM) techniques like selective harmonic elimination (SHE) PWM can prevent the generation of a particular harmonic from the phase voltage output. The disadvantages of such schemes are limited modulation index, poor dynamic performance and extensive offline computations. An elegant harmonic elimination method is to generate a voltage space vector structure having more number of sides like a dodecagon (12 sided polygons) or an octadecagon (18 sided polygons) rather than a hexagon. Inverter topologies generating dodecagonal voltage space vector structure eliminate fifth and seventh order harmonics, represented as 6n 1; n = odd harmonics, from the phase voltages and hence from the motor phase currents, throughout the entire modulation range. The first harmonics appearing the phase voltage are the 11th and 13th harmonics. Another advantage is the increased linear modulation range of operation for a given DC-link voltage, because geometrically dodecagon is closer to circle than a hexagon. An octadecagonal structure eliminates the 11th and 13th harmonics as well from the phase voltage output. The harmonics present in the phase voltage are of the order 18n 1; n = 1; 2; 3; :::. Thus the total harmonics distortion (THD) of the phase voltage is further improved. The linear modulation range also gets enhanced compared to hexagonal and dodecagonal structures. Multilevel dodecagonal and octadecagonal space vector structures combines the advantages of both multilevel structure and dodecagonal and octadecagonal structure and hence are very attractive solutions for high performance induction motor drive schemes. Chapter 1 of this thesis introduces the multilevel in-verter topologies generating hexagonal, dodecagonal and octadecagonal voltage space vector structures. Inverter topologies generating multilevel dodecagonal and octadecago-nal voltage space vector structures have been proposed before but using multiple DC sources delivering active power. The presence of more than one DC source in the inverter topology makes the back to back operation (four-quadrant operation) of the drive system difficult. And also the drive system becomes more costly and bulky. This thesis proposes induction motor drive schemes generating multilevel dodecagonal and octadecagonal volt-age space vector structures using a single DC source. In Chapter 2, an induction motor drive scheme generating a six-concentric multilevel dodecagonal voltage space vector structure using a single DC source is proposed for an open-end winding induction motor. In the topology, two three-level inverters drive an open-end winding IM, one inverter from each side. DC-link of primary inverter is from a DC source (Vdc) which delivers the entire active power, whereas the secondary inverter DC-link is maintained by a capacitor at a voltage of 0:289Vdc, which is self-balanced during the inverter operation. The PWM scheme implemented ensures low switching frequency for primary inverter. Secondary inverter operates at a small DC-link voltage. Hence, switching losses are small for both primary and secondary inverters. An open-loop V/f scheme was used to test the topology and modulation scheme. In the work proposed in Chapter 3, the topology and modulation scheme used in the first work is modified for a star connected induction motor. Again, the scheme uses only a single DC source and generates a six-concentric multilevel space vector struc-ture. The power circuit topology is realized using a three-level flying capacitor (FC) inverter cascaded with an H-bridge (CHB). The capacitors in the CHB inverter are maintained at a voltage level of 0:1445Vdc. The FC inverter switches between volt-age levels of [Vdc; 0:5Vdc; 0] and the CHB inverter switches between voltage levels of [+01445Vdc; 0; 0:1445Vdc]. The PWM scheme generates a quasi-square waveform output from the FC inverter. This results in very few switchings of the FC inverter in a funda-mental cycle and hence the switching losses are controlled. The CHB inverter switches Ch. 0: at high frequency compared to the FC inverter and cancels the low order harmonics (6n 1; n = odd) generated by the FC inverter. Even though the CHB operates at higher switching frequency, the switchings are at low voltage thereby controlling the losses. The linear modulation range of operation is extended to 48:8Hz for a base frequency of 50Hz. An open-loop V/f scheme was used to test the topology and modulation scheme. In Chapter 4, a nine-concentric multilevel octadecagonal space vector structure is proposed for the first time, again using a single DC source. The circuit topology remains same as the work in Chapter 3, except that the CHB capacitor voltage is maintained at 0:1895Vdc. The 5th; 7th; 11th and 13th harmonics are eliminated from the phase voltage output. The linear modulation range is enhanced to 49:5Hz for a base speed of 50Hz. An open-loop V/f scheme and rotor field oriented control scheme were used to test the proposed drive system. All the proposed drive schemes have been extensively simulated and tested in hard-ware. Simulation was performed in MATLAB-SIMULINK environment. For implement-ing the inverter topology, SKM75GB12T4 IGBT modules were used. The control al-gorithms were implemented using a DSP (TI’s TMS320F28334) and an FPGA (Xilinx Spartan XC3S200). A 1kW , 415V , 4-pole induction motor was used for the experiment purpose. The above mentioned induction motor drive schemes generate phase voltage outputs in which the low order harmonics are absent. The linear modulation range is extended near to the base frequency of operation compared to hexagonal space vector structure. In the inverter topologies, the secondary inverters or the CHB inverters functions as harmonic filters and delivers zero active power. The primary inverter in the topologies switches at low frequency, reducing the power loss. Single DC source requirement brings down the cost of the system as well as permitting easy four-quadrant operation. This is also advantageous in battery operated systems like EV applications. With these features and advantages, the proposed drive schemes are suitable for high performance, medium voltage induction motor drive applications.

The falling cost of batteries, along with an increasing need to cut emissions, has spurred significant interest in the electrification of vehicles. In addition, as semiconductor devices have evolved, the research for electric vehicles with higher battery voltage has increased. The traction inverter is an important part of the electric power train and can account for a substantial portion of the drive train’s losses. This thesis therefore models, simulates, and studies the losses for a convectional Two-Level (2L) inverter and a Three-Level T-Type (3LT) inverter utilizing Silicon Carbide (SiC) MOSFETs and compares the two inverter topologies in terms of efficiency. The rated power of the inverters is 120 kW at a DC voltage of 800 V. The theoretical basis of SiC MOSFET and its reverse conduction, operation of 2L and 3LT inverter topologies, and Space Vector Pulse Width Modulation (SVPWM) technique are introduced in the initial part of the thesis. To estimate switching and conduction losses, Simulink is used to model and simulate an electric drive system. These estimated losses are then utilized to develop efficiency maps for both topologies over the complete speed-torque range. Based on the efficiency comparison, the 3LT topology outperforms the 2L topology for any requested torque in the medium to the high-speed range, which is typical of highway driving. In the low-speed, high-torque region, which is typical of city driving, the 2L topology is superior. The efficiency of each topology is affected by switching frequency, device junction temperature, and DC-link voltage. However, the comparison reveals that the maximum average difference in efficiency is 0.35%, with the 3LT topology being superior. Finally, the efficiency differences between the two inverter topologies are minimal. As a result, it may be concluded that the two topologies perform similarly. Thus, it can be inferred that comparing the efficiency of the two topologies should not be the sole criterion for selecting which topology should be used for the electric drive. / Den sjunkande kostnaden för batterier, tillsammans med ett ökande behov av att minska utsläppen, har lett till ett stort intresse för elektrifiering av fordon. Dessutom, har utvecklingen av halvledare lett till en ökning inom forskningen av elfordon med högre batterispänning. Traktionsomriktaren är en viktig del av den elektriska drivlinan och kan stå för en stor del av de totala förlusterna i drivlinan. I denna rapport modelleras, simuleras och studeras därför förlusterna i en konventionell omriktare med två nivåer (2L) och en T-typ omriktare med tre nivåer (3LT). Båda topologierna använder kiselkarbid (SiC) MOSFETs i jämförelsen av resultaten med avseende på verkningsgrad. Inverterarnas nominella effekt är 120 kW vid en likspänning på 800 V. Den teoretiska grunden för SiC MOSFET och hur de fungerar, hur 2L- och 3LT-inverterstopologierna fungerar samt tekniken för Space Vector Pulse Width Modulation (SVPWM) presenteras i rapporten. För att uppskatta switch- och ledningsförluster används Simulink för att modellera och simulera det elektriska drivsystemet. De uppskattade förlusterna används sedan för att utveckla verkningsgradskartor för de båda topologierna över hela det operativa området. Baserat på verkningsgradsjämförelsen mellan topologierna så presterar 3LT-topologin bättre än 2L-topologin i driftspunkter i medelhöga till höga hastigheter, vilket är typiskt för motorvägskörning. Vid låga hastigheter med högt vridmoment, vilket är typiskt för stadskörning, är 2L-topologin bättre. Verkningsgraden för de båda topologierna påverkas av switchfrekvensen, halvledarens temperatur samt DC-länkspänning. Jämförelsen visar dock att den största genomsnittliga skillnaden i verkningsgrad mellan de två topologierna är 0,35%, där 3LT-topologin är bättre. Sammanfattningsvis så är skillnaderna i verkningsgrad mellan de två topologierna minimala, vilket innebär att de båda topologierna har liknande prestanda med avseende på verkningsgrad. Man bör därför inte bara ha verkningsgrad som det enda kriteriet vid val av topologi för elektriska drivlinor.

[pt] O principal objetivo da dissertação é explicar a assinatura do Tratado sobre Reduções Ofensivas Estratégicas - o Tratado de Moscou – pelo presidente George W. Bush e a aprovação unânime, pelos senadores norte-americanos, da resolução de conselho e consentimento para a ratificação do tratado. Tais decisões são vistas como resultados de um jogo de negociação no qual se observam a interação e a influência recíproca entre os níveis internacional e doméstico. As hipóteses indicam que membros do Executivo e grande parte do Senado norte-americanos mostraram-se interessados no tratado – que estipula uma redução substancial do número agregado de ogivas nucleares estratégicas dos EUA e da Rússia, de modo a não exceder 1.700-2.200 para cada parte no fim de 2012 –, pois ele garante a autonomia para definir como a redução será implementada e para determinar a estrutura das forças ofensivas estratégicas em face das novas ameaças aos EUA e aos seus aliados. / [en] The main purpose of the dissertation is to explain the signature of the Strategic Offensive Reductions Treaty - known as the Treaty of Moscow - by president George W. Bush and the unanimous approval of the resolution of advice and consent to ratification of the treaty by the U.S. Senate. These decisions are seen as the results of a bargaining game in which the national and the international levels interact and influence each other. The hypotheses indicate that the members of the U.S. executive and a huge number of the U.S. senators were interested in the treaty - which stipulates that each party shall reduce substantially the aggregate number of U.S. and Russian strategic nuclear warheads, so that it does not exceed 1,700-2,200 for each side by the end of 2012 - because it preserves the ability to define how the reductions will be implemented and to determine for themselves the structure of their strategic offensive forces, in order to respond to the new threats to their country and its allies.

Les équations de Maxwell en régime harmonique comportent plusieurs difficultés lorsque la fréquence est élevée. On peut notamment citer le fait que leur formulation variationnelle n’est pas définie positive et l’effet de pollution qui oblige à utiliser des maillages très fins, ce qui rend problématique la construction de solveurs itératifs. Nous proposons une stratégie de solution précise et rapide, qui associe une discrétisation par des éléments finis d’ordre élevé à des préconditionneurs de type décomposition de domaine. La conception, l’implémentation et l’analyse des deux méthodes sont assez difficiles pour les équations de Maxwell. Les éléments finis adaptés à l’approximation du champ électrique sont les éléments finis H(rot)-conformes ou d’arête. Ici nous revisitons les degrés de liberté classiques définis par Nédélec, afin d’obtenir une expression plus pratique par rapport aux fonctions de base d’ordre élevé choisies. De plus, nous proposons une technique pour restaurer la dualité entre les fonctions de base et les degrés de liberté. Nous décrivons explicitement une stratégie d’implémentation qui a été appliquée dans le langage open source FreeFem++. Ensuite, nous nous concentrons sur les techniques de préconditionnement du système linéaire résultant de la discrétisation par éléments finis. Nous commençons par la validation numérique d’un préconditionneur à un niveau, de type Schwarz avec recouvrement, avec des conditions de transmission d’impédance entre les sous-domaines. Enfin, nous étudions comment des préconditionneurs à deux niveaux, analysés récemment pour l’équation de Helmholtz, se comportent pour les équations de Maxwell, des points de vue théorique et numérique. Nous appliquons ces méthodes à un problème à grande échelle qui découle de la modélisation d’un système d’imagerie micro-onde, pour la détection et le suivi des accidents vasculaires cérébraux. La précision et la vitesse de calcul sont essentielles dans cette application. / The time-harmonic Maxwell’s equations present several difficulties when the frequency is large, such as the sign-indefiniteness of the variational formulation, the pollution effect and the problematic construction of iterative solvers. We propose a precise and efficient solution strategy that couples high order finite element (FE) discretizations with domain decomposition (DD) preconditioners. High order FE methods make it possible for a given precision to reduce significantly the number of unknowns of the linear system to be solved. DD methods are then used as preconditioners for the iterative solver: the problem defined on the global domain is decomposed into smaller problems on subdomains, which can be solved concurrently and using robust direct solvers. The design, implementation and analysis of both these methods are particularly challenging for Maxwell’s equations. FEs suited for the approximation of the electric field are the curl-conforming or edge finite elements. Here, we revisit the classical degrees of freedom (dofs) defined by Nédélec to obtain a new more friendly expression in terms of the chosen high order basis functions. Moreover, we propose a general technique to restore duality between dofs and basis functions. We explicitly describe an implementation strategy, which we embedded in the open source language FreeFem++. Then we focus on the preconditioning of the linear system, starting with a numerical validation of a one-level overlapping Schwarz preconditioner, with impedance transmission conditions between subdomains. Finally, we investigate how two-level preconditioners recently analyzed for the Helmholtz equation work in the Maxwell case, both from the theoretical and numerical points of view. We apply these methods to the large scale problem arising from the modeling of a microwave imaging system, for the detection and monitoring of brain strokes. In this application accuracy and computing speed are indeed of paramount importance.