Les travaux présentés dans ce mémoire s'inscrivent dans la thématique de la transmission d'énergie sans fil, appliquée à l'alimentation à distance de capteurs, de réseaux de capteurs et d'actionneurs à faible consommation. Cette étude porte sur la conception, la caractérisation, et la mesure d'un circuit Rectenna (Rectifying antenna) à double polarisation circulaire à 2.45 GHz, compact et à rendement de conversion RF-DC optimisé. Un outil d'analyse globale basé sur la méthode itérative a été développé et exploité pour valider la faisabilité de cette analyse. La diode Schottky a été modélisée en utilisant une impédance de surface. La rectenna à double polarisation circulaire, réalisée en technologie micro-ruban, a été validée expérimentalement. Elle est caractérisée par la rejection de la 2ème harmonique et une possibilité de recevoir les deux sens de polarisation LHCP et RHCP par l'intermédiaire de 2 accès. Le rendement mesuré avec une densité de puissance de 0.525 mW/cm² est de l'ordre de 63%, tandis que la tension DC obtenue aux bornes d'une charge optimale de 1.6 kohm est de 2.82 V / The work presented in this thesis is within the subject of wireless power transmission, power applied to the remote sensors, networks of sensors and actuators with low power consumption. This study focuses on the design, characterization, and measurement of a rectenna circuit (rectifying antenna) with dual circular polarization at 2.45 GHz, and optimisation of the conversion efficiency. A global analysis tool, based on the iterative method was developed and used to validate the feasibility of this concept by this method. The Schottky diode was modeled using surface impedance. The dual circular polarization rectenna with microstrip technology has been optimized and characterized experimentally operating at 2.45 GHz. It includes the property of harmonic rejections. Two accesses can receive either direction LHCP or RHCP sense. The conversion efficiency of 63% has been measured with a power density of 0.525 mW/cm². A DC voltage of 2.82V was measured across an optimum load of 1.6 kohm

A necessidade de obter solução de grandes sistemas lineares resultantes de processos de discretização de equações diferenciais parciais provenientes da modelagem de diferentes fenômenos físicos conduz à busca de técnicas numéricas escaláveis. Métodos multigrid são classificados como algoritmos escaláveis.Um estimador de erros deve estar associado à solução numérica do problema discreto de modo a propiciar a adequada avaliação da solução obtida pelo processo de aproximação. Nesse contexto, a presente tese caracteriza-se pela proposta de reutilização das estruturas matriciais hierárquicas de operadores de transferência e restrição dos métodos multigrid algébricos para acelerar o tempo de solução dos sistemas lineares associados à equação do transporte de contaminantes em meio poroso saturado. Adicionalmente, caracteriza-se pela implementação das estimativas residuais para os problemas que envolvem dados constantes ou não constantes, os regimes de pequena ou grande advecção e pela proposta de utilização das estimativas residuais associadas ao termo de fonte e à condição inicial para construir procedimentos adaptativos para os dados do problema. O desenvolvimento dos códigos do método de elementos finitos, do estimador residual e dos procedimentos adaptativos foram baseados no projeto FEniCS, utilizando a linguagem de programação PYTHONR e desenvolvidos na plataforma Eclipse. A implementação dos métodos multigrid algébricos com reutilização considera a biblioteca PyAMG. Baseado na reutilização das estruturas hierárquicas, os métodos multigrid com reutilização com parâmetro fixo e automática são propostos, e esses conceitos são estendidos para os métodos iterativos não-estacionários tais como GMRES e BICGSTAB. Os resultados numéricos mostraram que o estimador residual captura o comportamento do erro real da solução numérica, e fornece algoritmos adaptativos para os dados cuja malha retornada produz uma solução numérica similar à uma malha uniforme com mais elementos. Adicionalmente, os métodos com reutilização são mais rápidos que os métodos que não empregam o processo de reutilização de estruturas. Além disso, a eficiência dos métodos com reutilização também pode ser observada na solução do problema auxiliar, o qual é necessário para obtenção das estimativas residuais para o regime de grande advecção. Esses resultados englobam tanto os métodos multigrid algébricos do tipo SA quanto os métodos pré-condicionados por métodos multigrid algébrico SA, e envolvem o transporte de contaminantes em regime de pequena e grande advecção, malhas estruturadas e não estruturadas, problemas bidimensionais, problemas tridimensionais e domínios com diferentes escalas. / The need for solving large linear systems arising from the discretization of partial differential equations modelling physical phenomena motivates the search for scalable numerical techniques. Multigrid algorithms are instances of such techniques.In order to provide a suitable assessment of the solution obtained by such algorithms, an error estimator must be associated to the numerical solution of the discretized problem. In this context, this thesis proposes the reutilization of the hierarchical matrix structures of transfer operators and the restriction to algebraic multigrid methods to speed up the process of solving the linear systems associated with the contaminant transport equation in saturated porous media. In addition, it features the implementation of residual estimates for problems involving constant or non-constant data, the regimes of small- or large-scale advection and the proposal of employing the residual estimates associated to the source term and to the initial condition to build adaptive procedures for the problem data. The development of the computer codes of the finite element method, residual estimator and adaptive procedures were based on the FEniCS project, using the programming language PYTHONR and developed on the Eclipse platform. The implementation of the algebraic methods with reutilization relied upon the libray PyAMG. Grounding on the idea of reutilizing the hierarchical structures, fixed and automatic parameters multigrid methods were proposed and extended to non-stationary iterative methods such as GMRES and BICGSTAB. The numerical results demonstrate that the residual estimator captures the behavior of the real error of the numerical solution, and provide adaptive algorithms for the data whose output mesh yields a numerical solution alike to that obtained from a uniform mesh with more elements. Moreover, the methods with reutilization are faster than those that do not reuse the structures. Besides, the efficiency of such methods can also be observed in the solution of an auxiliary problem, which is necessary for deriving the residual estimates in the regime of large-scale advection. These results encompass both the type SA algebraic multigrid method and those pre-conditioned by them. Moreover, they involve the transport of contaminants in regime of small- and large-scale advection, structured and non-structured meshes, bi- and tridimensional problems and domains with different scales.

A necessidade de obter solução de grandes sistemas lineares resultantes de processos de discretização de equações diferenciais parciais provenientes da modelagem de diferentes fenômenos físicos conduz à busca de técnicas numéricas escaláveis. Métodos multigrid são classificados como algoritmos escaláveis.Um estimador de erros deve estar associado à solução numérica do problema discreto de modo a propiciar a adequada avaliação da solução obtida pelo processo de aproximação. Nesse contexto, a presente tese caracteriza-se pela proposta de reutilização das estruturas matriciais hierárquicas de operadores de transferência e restrição dos métodos multigrid algébricos para acelerar o tempo de solução dos sistemas lineares associados à equação do transporte de contaminantes em meio poroso saturado. Adicionalmente, caracteriza-se pela implementação das estimativas residuais para os problemas que envolvem dados constantes ou não constantes, os regimes de pequena ou grande advecção e pela proposta de utilização das estimativas residuais associadas ao termo de fonte e à condição inicial para construir procedimentos adaptativos para os dados do problema. O desenvolvimento dos códigos do método de elementos finitos, do estimador residual e dos procedimentos adaptativos foram baseados no projeto FEniCS, utilizando a linguagem de programação PYTHONR e desenvolvidos na plataforma Eclipse. A implementação dos métodos multigrid algébricos com reutilização considera a biblioteca PyAMG. Baseado na reutilização das estruturas hierárquicas, os métodos multigrid com reutilização com parâmetro fixo e automática são propostos, e esses conceitos são estendidos para os métodos iterativos não-estacionários tais como GMRES e BICGSTAB. Os resultados numéricos mostraram que o estimador residual captura o comportamento do erro real da solução numérica, e fornece algoritmos adaptativos para os dados cuja malha retornada produz uma solução numérica similar à uma malha uniforme com mais elementos. Adicionalmente, os métodos com reutilização são mais rápidos que os métodos que não empregam o processo de reutilização de estruturas. Além disso, a eficiência dos métodos com reutilização também pode ser observada na solução do problema auxiliar, o qual é necessário para obtenção das estimativas residuais para o regime de grande advecção. Esses resultados englobam tanto os métodos multigrid algébricos do tipo SA quanto os métodos pré-condicionados por métodos multigrid algébrico SA, e envolvem o transporte de contaminantes em regime de pequena e grande advecção, malhas estruturadas e não estruturadas, problemas bidimensionais, problemas tridimensionais e domínios com diferentes escalas. / The need for solving large linear systems arising from the discretization of partial differential equations modelling physical phenomena motivates the search for scalable numerical techniques. Multigrid algorithms are instances of such techniques.In order to provide a suitable assessment of the solution obtained by such algorithms, an error estimator must be associated to the numerical solution of the discretized problem. In this context, this thesis proposes the reutilization of the hierarchical matrix structures of transfer operators and the restriction to algebraic multigrid methods to speed up the process of solving the linear systems associated with the contaminant transport equation in saturated porous media. In addition, it features the implementation of residual estimates for problems involving constant or non-constant data, the regimes of small- or large-scale advection and the proposal of employing the residual estimates associated to the source term and to the initial condition to build adaptive procedures for the problem data. The development of the computer codes of the finite element method, residual estimator and adaptive procedures were based on the FEniCS project, using the programming language PYTHONR and developed on the Eclipse platform. The implementation of the algebraic methods with reutilization relied upon the libray PyAMG. Grounding on the idea of reutilizing the hierarchical structures, fixed and automatic parameters multigrid methods were proposed and extended to non-stationary iterative methods such as GMRES and BICGSTAB. The numerical results demonstrate that the residual estimator captures the behavior of the real error of the numerical solution, and provide adaptive algorithms for the data whose output mesh yields a numerical solution alike to that obtained from a uniform mesh with more elements. Moreover, the methods with reutilization are faster than those that do not reuse the structures. Besides, the efficiency of such methods can also be observed in the solution of an auxiliary problem, which is necessary for deriving the residual estimates in the regime of large-scale advection. These results encompass both the type SA algebraic multigrid method and those pre-conditioned by them. Moreover, they involve the transport of contaminants in regime of small- and large-scale advection, structured and non-structured meshes, bi- and tridimensional problems and domains with different scales.

There are several algorithms for solving the linear system of equations that arise from the finite element method with linear or near-linear computational complexity. One way is to find an approximation of the stiffness matrix that is such that it can be used in a preconditioned conjugate residual method, that is, a preconditioner to the stiffness matrix. We have studied two preconditioners for the conjugate residual method, both based on writing the stiffness matrix in block form, factorising it and then approximating the Schur complement block to get a preconditioner. We have studied the stationary reaction-diffusion-advection equation in two dimensions. The mesh is refined adaptively, giving a hierarchy of meshes. In the first method the Schur complement is approximated by the stiffness matrix at one coarser level of the mesh, in the second method it is approximated as the assembly of local Schur complements corresponding to macro triangles. For two levels the theoretical bound of the condition number is 1/(1-C²) for either method, where C is the Cauchy-Bunyakovsky-Schwarz constant. For multiple levels there is less theory. For the first method it is known that the condition number of the preconditioned stiffness matrix is O(l²), where l is the number of levels of the preconditioner, or, equivalently, the number mesh refinements. For the second method the asymptotic behaviour is not known theoretically. In neither case is the dependency of the condition number of C known. We have tested both methods on several problems and found the first method to always give a better condition number, except for very few levels. For all tested problems, using the first method it seems that the condition number is O(l), in fact it is typically not larger than Cl. For the second method the growth seems to be superlinear.

Content of this thesis is theoretic introduction to the steady state of network, theoretic analysis of methods, which serves for calculation of steady state of network such as Gauss Seidel iterative method or Newton Raphson modified method and economy in the energetics, concretely fixation of costs of the power line and calculation of the optimal time of building up the recuperative power line. This thesis includes calculation of steady state of requested network with normal trouble-free network and for criterion (n-1), their analysis and design of recuperative precaution.

The master’s thesis deals with a calculation of steady state and short-circuit conditions in a 110 kV system during a bridge operation of transformers in a Sokolnice substation. The theoretical part of the thesis deals with a calculation of steady state of a system using Newton’s iterative method, it investigates short-circuits – their timing, distinctive values and a method of their calculation. In the practical part the 100 kV grid supplied from Sokolnice substation is described. The main goal of the thesis is a comparation of two basic wirings: bridge operation of T202 and T203 transformers (contemporarily in service) and bridge operation of T402 and T403 (in service after 2017). These two wirings were controlled even during one state of emergency during which the Sokolnice substation will be affected by an outage of one busbar. Voltage conditions, loading of power line and transformers and overall power balance were controlled. Short-circuit conditions were also calculated and short-circuit resistance of particular substations was inspected. In the conclusion technical measures needed to ensure smooth bridge operation of convertors T402 and T403.

<p>The linear complementarity problems (LCP) arise from linear or quadratic programming, or from a variety of other particular application problems, like boundary problems, network equilibrium problems,contact problems, market equilibria problems, bimatrix games etc. Recently, many people have focused on the solver of LCP with a matrix having some kind of special property, for example, when this matrix is an H+-matrix, since this property is a sufficient condition for the existence and uniqueness of the soluition of LCP. Generally speaking, solving LCP can be approached from two essentially different perspectives. One of them includes the use of so-called direct methods, in the literature also known under the name pivoting methods. The other, and from our perspective - more interesting one, which we actually focus on in this thesis,<br />is the iterative approach. Among the vast collection of iterative solvers,our choice was one particular class of modulus based iterative methods.Since the subclass of modulus based-methods is again diverse in some sense, it can be specialized even further, by the introduction and the use of matrix splittings. The main goal of this thesis is to use the theory of H -matrices for proving convergence of the modulus-based multisplit-ting methods, and to use this new technique to analyze some important properties of iterative methods once the convergence has been guaranteed.</p> / <p>Problemi linearne komplementarnosti (LCP) se javljaju kod problema linearnog i kvadratnog programiranja i kod mnogih drugih problema iz prakse, kao &scaron;to su, na&nbsp; primer, problemi sa graničnim slojem, problemi mrežnih ekvilibrijuma, kontaktni problemi, problemi određivanja trži&scaron;ne ravnoteže, problemi bimatričnih igara i mnogi drugi. Ne tako davno, veliki broj autora se bavio razvijanjem postupaka za re&scaron;avanje LCP sa matricom koja ispunjava neko specijalno svojstvo, na primer, da pripada klasi H+-matrica, budući da je dobro poznato da je ovaj uslov dovoljan da obezbedi egzistenciju i jedinstvenost re&scaron;enja LCP. Uop&scaron;teno govoreći, re&scaron;avanju LCP moguce&nbsp; je pristupiti dvojako. Prvi pristup podrazumeva upotrebu takozvanih direktnih metoda, koje su u literaturi poznate i pod nazivom metode pivota. Drugoj kategoriji, koja je i sa stanovi&scaron;ta ove teze interesantna, pripadaju iterativni postupci. S obzirom da je ova kategorija izuzetno bogata, mi smo se opredelili za jednu od najznačajnijih varijanti, a&nbsp; to je modulski iterativni postupak. Međutim, ni ova odrednica nije dovoljno adekvatna, budući da modulski postupci obuhvataju nekolicinu različitih pravaca. Zato smo se odlučili da posmatramo postupke koji se zasnivaju na razlaganjima ali i vi&scaron;estrukim razlaganjima matrice. Glavni cilj ove doktorske disertacije jeste upotreba teorije H -matrica u teoremama o konvergenciji modulskih metoda zasnovanih na multisplitinzima matrice i kori&scaron;ćenje ove nove tehnike, sa ciljem analize bitnih osobina, nakon &scaron;to je konvergencija postupka zagarantovana.</p>

The work describes techniques for solving systems of linear and differential equations. It explains the definition of conversion from system of linear to system of differential equations. The method of the elementary transmission and the transform algorithm are presented. Both of methods are demonstrated on simply examples and properties of conversion are shown. The work compares fast and accurate solutions of methods and algorithm. For computing examples and solving experiments following programs were used: TKSL and TKSL/C. The program TKSL/C was enriched with the graphic user interface which makes the conversion of systems and computing results easier.

本論文係研究和發展平行疊代法（PARALLEL ITERATIVE METHOD ）以解決數學規劃（ MATHEMATICAL PROGRAMMING）中之互補問題（COMPLEMENTA-RITY PROBLEM）。互補問 題源自解決國防軍事、工程經濟及管理科學等領域之應用，而由於近年來各種超級或 平行電腦不斷地創新，使得發展平行演算法以充分並有效地應用超級或平行電腦來解 決大型科學計算的問題日趨重要。 在本篇論文中，我們分別探討線性互補問題以及非線性互補問題。首先我們發展出一 半非同步（SEMI-ASYNCHRONOUS ）法來解決線性互補問題，此法之特性在於其能大幅 地減低因同步法所造成處理機閒置（IDLING）之冗額成本（OVERHEAD）；同時，也放 寬了非同步法對問題所加諸之限制，因而擴大了半非同步法所能應用之範圍。我們也 建立了有關該法收斂性（CONVERGENCE ）之理論根據。此外，線性互補問題之探討， 實為進一步研究非線性互補問題之基礎。 其次，我們提出一個整體性之架構，探討平行牛頓法（NEWTON METHOD ）及其各種變 型（VARIATIONS）來解決各種非線性互補問題，比較並研究各種方法的特性、限制及 執行效率。 然後，針對上述各種演算法，我們在教育部電算中心之IBM ３０９０上發展並模擬各 該法之平行運算，經由廣泛地實驗測試，以獲得具體之數值結果，來檢驗其效率，並 比較研究各法之適用性與優劣。最後，我們也提出一些相關之問題，以供未來後續研 究之參考。

Dizertační práce se věnuje funkcionálním diferenciálním rovnicím smíšeného typu. Poskytuje kritéria pro existenci globálních a semi-globálních řešení diferenciálních systémů smíšeného typu. Metody použité v teto práci spočívají v sestavení vhodných operátorů pro diferenciální rovnice a prokázání existence jejich pevných bodů. Tyto pevné body jsou potom použity ke konstrukci řešení rovnic s předcházením a zpožděním. V důkazech tvrzení jsou použity monotónní iterační metoda a Schauderovy-Tychonovovy věty o existenci pevného bodu. V obou případech jsou uvedeny také odhady řešení. Pokud je použita iterační metoda, lze tyto odhady zlepšit iterováním. Kromě toho jsou odvozena kritéria pro lineární rovnice a systémy a je uvedena řada přikladů. Dosažené výsledky lze aplikovat také pro obyčejné diferenciální rovnice nebo diferenciální rovnice se zpožděním či s předcházením argumentu.