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1
Boyle, Cameron. "A Closed-Form Dynamic Model of the Compliant Constant-Force Mechanism Using the Pseudo-Rigid-Body Model." BYU ScholarsArchive, 2003. https://scholarsarchive.byu.edu/etd/53.
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A mathematical dynamic model is derived for the compliant constant-force mechanism, based on the pseudo-rigid-body model simplification of the device. The compliant constant-force mechanism is a slider mechanism incorporating large-deflection beams, which outputs near-constant-force across the range of its designed deflection. The equation of motion is successfully validated with empirical data from five separate mechanisms, comprising two configurations of compliant constant-force mechanism. The dynamic model is cast in generalized form to represent all possible configurations of compliant constant-force mechanism. Deriving the dynamic equation from the pseudo-rigid-body model is useful because every configuration is represented by the same model, so a separate treatment is not required for each configuration. An unexpected dynamic trait of the constant-force mechanism is discovered: there exists a range of frequencies for which the output force of the mechanism accords nearer to constant-force than does the output force at static levels.
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Griffith, Daniel Todd. "New methods for estimation, modeling and validation of dynamical systems using automatic differentiation." Texas A&M University, 2004. http://hdl.handle.net/1969.1/1408.
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The main objective of this work is to demonstrate some new computational methods
for estimation, optimization and modeling of dynamical systems that use automatic
differentiation. Particular focus will be upon dynamical systems arising in Aerospace
Engineering. Automatic differentiation is a recursive computational algorithm, which
enables computation of analytically rigorous partial derivatives of any user-specified
function. All associated computations occur, in the background without user
intervention, as the name implies. The computational methods of this dissertation are
enabled by a new automatic differentiation tool, OCEA (Object oriented Coordinate
Embedding Method). OCEA has been recently developed and makes possible efficient
computation and evaluation of partial derivatives with minimal user coding. The key
results in this dissertation details the use of OCEA through a number of computational
studies in estimation and dynamical modeling.
Several prototype problems are studied in order to evaluate judicious ways to use
OCEA. Additionally, new solution methods are introduced in order to ascertain the
extended capability of this new computational tool. Computational tradeoffs are studied
in detail by looking at a number of different applications in the areas of estimation,
dynamical system modeling, and validation of solution accuracy for complex dynamical
systems. The results of these computational studies provide new insights and indicate
the future potential of OCEA in its further development.
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Meznik, Ivan. "On Economic Interpretation of Lagrange Multipliers." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-82883.
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Nilsson, Ruben, and Simon Velander. "Simulering av mekaniska system med Lagranges metod." Thesis, KTH, Mekanik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-133459.
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Mekaniska system har länge varit av intresse för vetenskapen och vår förmåga att matematiskt beskriva dess dynamik är mycket god. Att effektivt kunna härleda de nödvändiga ekvationerna är dock inte trivialt och uttrycken som bildas är ofta icke-linjära differentialekvationer som ej leder till explicita lägesbeskrivningar av de rörliga komponenterna. Idag finns kraftfulla matematiska metoder och datorverktyg som möjliggör simulering av relativt komplicerade mekaniska system vilket denna rapport ägnats åt att undersöka med hjälp av exempelsystem. Två utvalda mekaniska systems beteenden med varierande begynnelsevillkor har undersökts med hjälp av datorsimuleringar. Det första systemet har bestått av två pendlar med en fjäder fastspänd mellan pendeländarna. Det andra systemet har bestått av en fritt rullande cylinder på horisontellt underlag med två pendlar fastspända på änden. Både konservativa och dissipativa system har modellerats. De konservativa systemens beteenden har genomgått enkel analys. Den matematiska metoden som använts är Lagranges metod [2] som utnyttjar systemets totala energi för att härleda rörelseekvationerna. Modellering, numerisk integrering, och grafisk simulering med animation har gjorts i programmet Maple, med tilläggspaketet Sophia [1]. Systemen har visualiserats framgångsrikt och analys av beteenden visade att båda systemen kan uppvisa periodiskt såväl som kaotiskt rörelsemönster beroende på energinivån i systemet.
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Greer, Neil. "The optimised Schwarz method and the two-Lagrange multiplier method for heterogeneous problems." Thesis, Heriot-Watt University, 2017. http://hdl.handle.net/10399/3266.
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In modern science and engineering there exist many heterogeneous problems, in which the material under consideration has non-uniform properties. For example when considering seepage under a dam, water will flow at vastly different rates through sand and stone. Mathematically this can be represented as an elliptic boundary value problem that has a large jump in coefficients between subdomains. The optimised Schwarz method and the related two-Lagrange multiplier method are non-overlapping domain decomposition methods that can be used to numerically solve such boundary value problems. These methods work by solving local Robin problems on each subdomain in parallel, which then piece together to give an approximate solution to the global boundary value problem. It is known that with a careful choice of Robin parameter the convergence of these methods can be sped up. In this thesis we first review the known results for the optimised Schwarz method, deriving optimised Robin parameters and studying the asymptotic performance of the method as the mesh parameter of the discretisation is refined and the jump in coefficients becomes large. Next we formulate the two-Lagrange multiplier method for a model two subdomain problem and show its equivalence to the optimised Schwarz method under suitable conditions. The two-Lagrange multiplier method results in a non-symmetric linear system which is usually solved with a Krylov subspace method such as GMRES. The convergence of the GMRES method can be estimated by constructing a conformal map from the exterior of the field of values of the system matrix to the interior of the unit disc. We approximate the field of values of the two-Lagrange multiplier system matrix by a rectangle and calculate optimised Robin parameters that ensure the rectangle is “well conditioned” in the sense that GMRES converges quickly. We derive convergence estimates for GMRES and consider the behaviour asymptotically as the mesh size is refined and the jump in coefficients becomes large. The final part of the thesis is concerned with the case of heterogeneous problems with many subdomains and cross points, where three or more subdomains coincide. We formulate the two-Lagrange multiplier method for such problems and consider known preconditioners that are needed to improve convergence as the number of subdomains increases. Throughout the thesis numerical experiments are performed to verify the theoretical results.
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Rees, M. D. "Moving point, particle and free-Lagrange methods." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235079.
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COUSSEMENT, GREGORY. "Equations d'euler-lagrange d'une methode d'optimisation et d'adaptation de maillages et unification avec d'autres methodes." Paris 11, 1996. http://www.theses.fr/1996PA112063.
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Cette these a pour objet de contribuer a l'evolution des techniques de construction de maillages par l'etude et la mise en uvre des equations d'euler-lagrange tridimensionnelles d'une methode variationnelle d'optimisation et d'adaptation de maillages structures par sous-domaines ainsi que par l'unification de la methode avec d'autres methodes populaires variationnelles et elliptiques. L'etude generalisee des fondements de la methode d'optimisation et d'adaptation consideree met en evidence les hypotheses utilisees initialement par jacquotte pour mesurer la deformation directe du maillage vis a vis d'un maillage de reference. L'analyse de la formulation euler-lagrange realisee pour les points situes a l'interieur et situes sur les bords des sous-domaines permet un traitement general de tous les points y compris de ceux soumis a des conditions de raccord multidomaine et/ou des conditions aux limites de nuds libres, fixes ou glissant sur des courbes ou des surfaces. Au travers de la double formulation variationnelle et euler-lagrange, l'unification avec d'autres methodes populaires montre que toutes ces methodes peuvent s'interpreter comme des procedures de construction de maillages qui minimisent une mesure de la deformation appreciee par le biais de proprietes controlant les changements de longueur, d'aire, de volume et/ou d'orthogonalite. Sur base du logiciel optim3d developpe a l'onera pour l'optimisation et l'adaptation de maillages multidomaines structures, la forme euler-lagrange du principe a ete mis en uvre avec succes. Pour permettre la construction de maillages, le systeme complexe d'equations differentielles couplees est linearise et est discretise par des differences finies. Le systeme algebrique resultant est resolu avec un procede hybride qui conjugue une technique de relaxation quasi-optimale de type gauss-seidel symetrique pour les points interieurs aux sous-domaines et une technique de relaxation de type jacobi pour les points de bords soumis aux conditions aux limites et aux raccords multi-domaines. La construction de maillages tridimensionnels pour des cas didactiques et des cas industriels complexes demontre la generalite des developpements realises ainsi que la robustesse de l'algorithme qui s'accommode de mauvaise initialisation, meme aleatoire, du maillage
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MOLINA, NORBERTO EDUARDO. "LAGRANGEAN METHOD TO SOLVE LAMINAR FLOW PERPENDICULAR TO AN INFINITE CYLINDER." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1990. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=20444@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
Este trabalho tem por objetivo simular numericamente o escoamento externo de uma corrente laminar incompressível, em regime permanente, para baixos números de Reynolds, em torno de um corpo sólido de forma cilíndrica. A solução do problema em estudo, é obtida resolvendo-se as equações de conservação de massa e quantidade de movimento bi-dimensionais. O método numérico selecionado para resolver as equações de conservação é uma combinação do método lagrangeano das características, com o método de volumes finitos. Adota-se um sistema de coordenadas curvilíneas que se adapta ao corpo, definido a partir da solução do escoamento potencial em torno do cilindro. Uma vez completado o procedimento numérico, o campo de velocidades, a distribuição de pressões e a tensão cizalhante em torno do cilindro, são analisados. A determinação do coeficiente de arraste proveniente da pressão dinâmica e da tensão viscosa contra a superfície sólida do cilindro também é realizada. Os resultados locais e médios são comparados com resultados experimentais e numéricos disponíveis, apresentando boa concordância.
This work intends to simulate numerically the external flow of incompressible laminar stream at steady state for low Reynolds numbers around a cilindrical body. The solution of the present problem is obtained by means of the resolution of the equations of conservation of mass and momentum. The present numerical method to solve the equations of conservation is a combination of the lagrangian method of the characteristics, and the method of finite volumes. A curvilinear system of coordinates is selected to adapt to the body geometry. The mesh is generated based on the potential flow solution around the cylinder. Once performed the numerical computation, the velocity profile, the pressure and shear stress distribuitions around the cylinder are analysed. The determination of the drag from the data on dynamic pressure and viscosity effects around the cylinder is also done. The local and average results are compared with the experimental and numerical results available, with a reasonable agreement.
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Priestley, A. "Lagrange and characteristic Galerkin methods for evolutionary problems." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376942.
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Ware, Antony Frank. "A spectral Lagrange-Galerkin method for convection-dominated diffusion equations." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302896.
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English, Russell Gary. "Lagrange multiplier method for contact and friction : implementation and theory." Thesis, University of Liverpool, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357426.
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Gagnon, Michael Anthony. "An adaptive mixed finite element method using the Lagrange multiplier technique." Worcester, Mass. : Worcester Polytechnic Institute, 2009. http://www.wpi.edu/Pubs/ETD/Available/etd-050409-115850/.
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Thesis (M.S.)--Worcester Polytechnic Institute.Keywords: a posteriori error estimate; adaptive; mesh refinement; lagrange multiplier; finite element method. Includes bibliographical references (leaf 26).
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Wysocki, Stefan. "Joint Euler-Lagrange method for moving surfaces in large-eddy simulation." Thesis, Imperial College London, 2012. http://hdl.handle.net/10044/1/10214.
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Continuous growth of computing power strongly encourages engineers to rely more on computational fluid dynamics for the design and testing of new technological solutions. The fast development of these new tools goes along with the increasing availability of high-performance computers, which are necessary to simulate realistic industrial applications. The presented immersed boundary (IB) method is applicable to simple and complex geometries with static and moving boundaries, where fluids interact with the solid structures. The formulation of the method is based on the Eulerian and Lagrangian principles and its key characteristics are its simple formulation and computational efficiency. Furthermore the nature of the method allows the simulations of flows in complex geometries without having to generate complex meshes. The spatial discretization is based on a fixed Cartesian mesh for the Eulerian variables and boundary movements are tracked with Lagrangian particles. Large- Eddy simulations of flows in simple and complex geometries demonstrate the performance of the applied immersed boundary method. Simple cases include the simulation of an isothermal pipe flow and the flow around a sphere. In the first instance, the fluid flows around a static sphere. In the second case the sphere moves relative to the grid for identical flow conditions. Simulations of complex geometries include the investigation of an isothermal and reactive opposed jet flow with perforated and fractal grids. The simulations require cell sizes near the resolution of direct numerical simulations. The injection phase of a piston-cylinder arrangement, assuming constant pressure, is also investigated with the proposed IB method. Good statistical results for first and second moments are achieved for all investigated cases, although the applied grids have to be fine enough to accurately resolve the wall shear stresses. In addition, the concept of using Lagrangian particles has been applied to immiscible flows. Particles are used to improve the accuracy of scalar transport and initial results of simple, two-dimensional test cases are presented.
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Stoffel, Joshua David. "Lagrange-Chebyshev Based Single Step Methods for Solving Differential Equations." University of Akron / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=akron1335299082.
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Wiedemann, Sebastian. "Adaptive finite elements for a contact problem in elastoplasticity with Lagrange techniques." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2013. http://dx.doi.org/10.18452/16695.
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Das Thema dieser Dissertation ist die Herleitung und numerische Analyse von finiten Elementen für ein Problem in der Elastoplastizität mit Kontaktbedingungen. Die hergeleiteten finite Elemente Verfahren basieren auf einer Formulierung als Sattelpunktproblem und der Nutzung von Polynomen höherer Ordnung. Die Analyse der vorgestellten Verfahren beginnt mit dem Zeigen der Wohldefiniertheit und der Konvergenz. Im nächsten Schritt werden a priori Abschätzungen der Konvergenzraten gezeigt. Weiterhin führt die Einführung von Lagrange Multiplikatoren zu einem einheitlichen Ansatz zur a posteriori Abschätzung des Diskretisierungfehlers unter der Verwendung von Elementen höherer Ordnung. Zusätzlich ermöglicht es der Zugang über Lagrange Multiplikatoren die Äquivalenz der Diskretisierungsfehler in den Spannungen und in den Energien für finite Elemente niederer Ordnung zu zeigen, was insbesondere neu für Viereckselemente ist. Diese Äquivalenz wiederum erlaubt nun den Beweis der Konvergenz von adaptiven finiten Elementen niederer Ordnung. Für Dreieckselemente wird sogar die optimale Konvergenz bewiesen. Die theoretischen Erkenntnisse werden durch numerische Experimente bestätigt.The topic of this thesis is the derivation and analysis of some finite element schemes for a contact problem in elastoplasticity. These schemes are based on the formulation of the models as saddle point problems and use finite element spaces of arbitrary polynomial degrees. In this thesis, these new approaches with higher-order finite elements are shown to be well defined and convergent. Moreover, some a~priori estimates on the rates of convergences are proven. The use of Lagrange multipliers in the saddle point formulation yields a coherent approach to reliable a~posteriori error estimates for the proposed higher-order schemes. Additionally, the Lagrange multipliers are used to show the equivalence of the errors of the stresses and the energies, for low order finite elements using triangular or quadrilateral cells. For the first time, this allows for a proof of convergence for quadrilateral-based adaptive finite elements. Furthermore, the approach based on triangular cells is shown to be of optimal convergence. The theoretical findings are confirmed by numerical experiments.
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Karangelis, Anastasios. "Analysis and massively parallel implementation of the 2-Lagrange multiplier methods and optimized Schwarz methods." Thesis, Heriot-Watt University, 2016. http://hdl.handle.net/10399/3102.
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Baker, M. D. "A spectral Lagrange-Galerkin method for periodic/non-periodic convection-dominated diffusion problems." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240539.
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Cardoso, OnÃzimo Carlos Viana. "Partitioned analysis of Offshore wind turbines using the Lagrange Localized Methods." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=13241.
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FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgicoAmong the new-found data about the availability of fossil fuels, which affirms that oil and natural gas sources will be almost depleted in the next century and the coal in the following two centuries. There is a global pursuit about new ways to produce energy. Another important fact that ratify this quest, lies at rise of the environment imbalance arouse from the burn of fossil fuels which, through the greenhouse effect, leads, for instance, to melting glaciers and increasing the temperature in the earth. The wind power, already used to move ships since antiquity is a relevant alternative way to produce energy, since it dispose of, at least, two great advantages, namely, it is endless and produce low negative consequences to environment. A place is considered to be good to receive the wind power engines called wind turbines, which convert the wind kinetic energy in electricity, if it is a ground plane with little amount of barriers. The sea, especially the regions far from the coast, satisfy the two latter requirement, and, furthermore, it is a place in which there are less obstructions about the noise pollution from the offshore wind turbines and there is not concern about deceases arouse in people who leave near of wind farms. In order to install the wind turbines in those spots away from the seashore, is required that its towers must be attached at the sea floor or must be develop a system that allow the turbine to float. Therefore the objective of the present work is to develop a structural modelling of the Monopile, TLP (Tension Leg Platform) and Spar type wind turbines subject using Finite Element Methods with the coupling method accomplished by Localized Lagrange Multipliers, jointly with the software SolidWorks and Autocad (drawing creation), ANSYS (mesh development) and Matlab (solver). The obtained results are relevant since such models are those which are most commonly used in offshore wind power plants. Lastly, due to the use of the latter coupling method, there is not the requisition to develop the study using meshes that agree each other. On the contrary, the analysis can be performed with non match meshes adjusting them with the Zero Moment Rule described in this present study.
Diante dos mais recentes dados com respeito a quantidade de combustÃveis fÃsseis ainda disponÃveis na natureza, os quais atestam que nÃo hà mais nem um sÃculo sequer para que o petrÃleo e o gÃs natural sejam praticamente extintos e que as reservas de carvÃo mineral suprirÃo somente mais 2 sÃculos de consumo, levando em conta o gasto atual. A preocupaÃÃo quanto a novas formas de extraÃÃo de energia se tornam necessÃrias e urgentes. Outro importante fator que ratifica o imediatismo de se buscar diferentes fontes de energia em detrimento de combustÃvel fÃssil, à o fato de que as emissÃes intrÃnsecas à sua queima estÃo gerando desequilÃbrio no clima global pela intensificaÃÃo do efeito estufa, apontado como um dos principais contribuidores do derretimento de geleiras e aquecimento da temperatura da terra. A energia eÃlica, jà utilizada desde a antiguidade para auxÃlio de locomoÃÃo de embarcaÃÃes e em moinhos de vento, se mostra uma alternativa de extrema relevÃncia, jà que, ela nÃo à portadora dos dois problemas crÃticos citados anteriormente. A saber, ela à infindÃvel e tem baixa consequÃncia negativa ao meio ambiente. Quanto aos locais que oferecem maior rendimento e produÃÃo para instalaÃÃo dos aerogeradores, responsÃveis pela conversÃo da energia cinÃtica do vento em energia elÃtrica, sÃo os que dispÃem de terreno mais plano e ausente de barreiras que impeÃam a continuidade do fluxo de vento. O mar, sobretudo as regiÃes mais distantes da costa, satisfazem Ãs duas necessidades citadas anteriormente, e, ainda se tratam de um local no qual nÃo hà a preocupaÃÃo quanto a poluiÃÃo sonora gerada pelos aerogeradores e nem com distÃrbios e doenÃas que possam ser desencadeadas em pessoas que residam pertos de grandes parques Ãolicos. A utilizaÃÃo de aerogeradores no mar (offshore) distantes da costa, e por conseguinte, em grandes profundidades, requer torres de sustentaÃÃo fixadas ao solo ou um sistema que proporcione que a turbina flutue. Diante do exposto, o trabalho em questÃo tem por objetivo realizar a modelagem estrutural do aerogerador flutuante (Spar), do portador de torre de tripà e do modelo monopile, sujeitos a carregamentos decorrentes de situaÃÃes normais e extremas, utilizando os mÃtodos dos Elementos Finitos juntamente com o MÃtodo de Acoplamento por Multiplicadores de Lagrange Localizados, atrelados aos softwares SolidWorks e Autocad (criaÃÃo do desenho), ANSYS (malha) e Matlab (solver). E, em decorrÃncia do fato da utilizaÃÃo do mÃtodo de acoplamento, nÃo hà necessidade de que as malhas dos subdomÃnios envolvidos sejam coincidentes. Pelo contrÃrio, pode-se utilizar malhas nÃo encaixantes para discretizar o sistema e, nas regiÃes onde hà contato entre malhas que nÃo coicidem, aplica-se a Regra do Momento Zero, descrita no presente trabalho. Nesse tipo de abordagem, pode haver uma separaÃÃo dos cÃdigos computacionais utilizados para o fluido e para a estrutura, os quais sÃo inicialmente tratados como entidades individuais e sà apÃs terem sido discretizados à que a informaÃÃo sobre suas malhas à recebida pela parte do cÃdigo responsÃvel por realizar o acoplamento dos subdomÃnios. Problemas de malhas que nÃo se encaixam podem surgir por diversos motivos, dentre eles, o fato de um subdomÃnio requerer uma malha mais refinada do que outros para que dele resultem resultados acurados. Pesquisadores de diferentes Ãreas podem gerar malhas separadas de distintos subdomÃnios e desejarem unÃ-los pelo mÃtodo abordado nesse trabalho em uma simulaÃÃo, ou a conformidade das malhas pode requerer muito tempo dispendido devido ao grande esforÃo computacional para a geraÃÃo de malhas conformes. Por fim, a aplicaÃÃo do mÃtodo produz resultados de grande relevÃncia, visto que, os modelos a que dizem respeito sÃo os mais comumente utilizados em projetos de aproveitamento de energia eÃlica offshore.
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Tröltzsch, Fredi. "On the Lagrange-Newton-SQP Method for the Optimal Control of Semilinear Parabolic Equations." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800995.
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A class of Lagrange-Newton-SQP methods is investigated for optimal control problems
governed by semilinear parabolic initial- boundary value problems. Distributed and boundary
controls are given, restricted by pointwise upper and lower bounds. The convergence of the method
is discussed in appropriate Banach spaces. Based on a weak second order sufficient optimality condition
for the reference solution, local quadratic convergence is proved. The proof is based on the
theory of Newton methods for generalized equations in Banach spaces.
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Klingler, Markus. "Die Methode der finiten Massen in der astrophysikalischen Hydrodynamik." Tübingen, Kelternstr. 19 : M. Klingler, 2003. http://deposit.d-nb.de/cgi-bin/dokserv?idn=969738749.
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CAMALET, EUGENE. "Methodes de couplage euler-lagrange pour les equations d'euler-poisson." Paris 6, 1995. http://www.theses.fr/1995PA066276.
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Nous etudions dans une premiere partie la modelisation d'un plasma froid par les equations d'euler-poisson sans pression. La description lagrangienne des equations de convection permet de prendre en compte les phenomenes de deferlement (vitesses multivoques) apparaissant dans ce type de plasma. Les instabilites dues a la methode particule/maille sont resorbees par l'introduction d'une pression numerique. La seconde partie est consacree a la simulation de dispositifs semiconducteurs de type mesfet et diode par un modele hydrodynamique isotherme. Les collisions sont modelisees par un terme de relaxation en temps. On utilise la methode numerique developpee dans la premiere partie. Enfin on etudie un modele sans pression ou la vitesse derive d'un potentiel couple a l'equation de poisson. Dans le cadre gravitationnel on montre que les solutions sont caracterisees par un principe de minimisation de l'energie. Si la densite est bornee on montre que les vitesses gagnent en regularite dans le cadre electrostatique et gravitationnel
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Claewplodtook, Pana. "Optimization of nonlinear dynamic systems without Lagrange multipliers." Ohio : Ohio University, 1996. http://www.ohiolink.edu/etd/view.cgi?ohiou1178654973.
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Bispo, Rafael Santana. "Simulação harmônica particionada usando um método baseado em multiplicadores de Lagrange." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/265157.
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Orientador: Renato PavanelloDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica
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Resumo: Atualmente, existe uma grande tendência no incremento da produção de energia elétrica através de fontes renováveis. Em especial, a geração de energia elétrica produzida através de parques eólicos tem sido bastante adotada. O projeto desses equipamentos envolve a modelagem dinâmica acoplada solo-fluido-estrutura que pode ser estudada usando-se a formulação particionada, onde o problema da interação entre os meios é tratado de maneira iterativa. Nesse tipo de técnica, é possível que modelos fisicamente heterogêneos, chamados de partições, possam utilizar diferentes técnicas de discretização, como por exemplo o domínio do fluido ser baseado em uma formulação de Elementos de Contorno e o domínio estrutura baseado em uma formulação em Elementos Finitos. Neste trabalho, é realizado um estudo dinâmico de turbinas eólicas, utilizando tratamento particionado e Multiplicadores de Lagrange afim de se obter as frequências características e as curvas de resposta em frequência do sistema em análise. A discretização do problema é realizada através do Método dos Elementos Finitos (FEM) utilizando elemento de pórtico e quadrilateral de Wilson. Desta forma, a resolução de problemas de interação, utilizando a formulação particionada, é estudada com a finalidade de avaliar a convergência e a viabilidade da técnica em problemas harmônicos estruturais
Abstract: Currently, there is a great tendency in increasing the production of electricity through renewable sources. In this context, the generation of electric energy produced by wind farms has been widely adopted. The design of these devices involves the dynamic modeling of coupling fluid-structure-soil that can be studied using the partitioned formulation, where the problem of interaction between the parties is iterative manner. In this type of technique, it is possible that physically heterogeneous models, called partitions, can use different discretization techniques, such as the domain of fluid is based on a formulation of boundary element or based on a finite element formulation. In this paper a harmonic simulation of wind turbines, using partitioned treatment and Lagrange multipliers is studied in order to obtain the characteristic frequencies and frequency response function of the system under analysis. The discretization of the problem is performed using the Finite Element Method (FEM), as well as beam elements and the quadrilateral Wilson element. Thus, the resolution of elastodynamics problems, using the partitioned formulation is studied with the aim of assessing the feasibility and convergence of this technique, applied to dynamic harmonic analysis
Mestrado
Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica
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小山, 悟史, Satoshi KOYAMA, 秀幸 畔上, and Hideyuki AZEGAMI. "形状最適化問題の解法における多制約の取り扱い." 日本機械学会, 2003. http://hdl.handle.net/2237/12171.
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Lamichhane, Bishnu P. "Higher order mortar finite elements with dual Lagrange multiplier spaces and applications." [S.l. : s.n.], 2006. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-26215.
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DeVries, Mark R. "Vibration of a cantilever beam that slides axially in a rigid frictionless hole." Thesis, Monterey, California : Naval Postgraduate School, 1990. http://handle.dtic.mil/100.2/ADA241352.
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Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, September 1990.Thesis Advisor(s): Salinas, David. "September 1990." Description based on title screen as viewed on December 17, 2009. DTIC Identifier(s): Vibration, sliding friction, guns barrels, cantilever beams, Euler equations, finite element analysis, transformations (mathematics), theses, frictionless holes, holes (openings), recoil. Author(s) subject terms: Cantilever beam, finite element method, axial motion, vibration, transient behavior. Includes bibliographical references (p. 110). Also available in print.
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HAMDI, ABDELOUAHED. "Methode de lagrangiens augmentes en programmation convexe et non convexe. Et applications a la decomposition." Clermont-Ferrand 2, 1997. http://www.theses.fr/1997CLF21921.
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Le travail effectue dans cette these est compose principalement de trois parties. La premiere partie est consacree a une analyse detaillee de la litterature concernant les methodes de penalisation, les methodes lagrangiennes, les methodes de lagrangiens augmentes, les methodes proximales et leurs relations avec la dualite. Une premiere contribution de cette partie se trouve dans une extension de l'analyse de convergence de la methode des multiplicateurs avec elimination partielle des contraintes, due a d. Bertsekas, dans le cadre d'un probleme d'optimisation non necessairement convexe avec des contraintes mixtes. Notre deuxieme contribution se situe dans l'amelioration des resultats de convergence locale de l'algorithme proximal des multiplicateurs, dans le cas d'un probleme non convexe. L'amelioration consiste en l'abandon des hypotheses d'optimalite du second ordre. La deuxieme partie de la these propose une nouvelle approche de la separabilite des lagrangiens augmentes. Cela est rendu possible grace a des transformations simples de l'ecriture du modele. Cet algorithme (appele sala) peut etre vu comme une application de la methode de decomposition par les prix, suivie de l'application de la methode des multiplicateurs. Des resultats de convergence de (sala) sont etablis, en outres un resultat sur l'ordre de convergence lineaire est donne. Dans cette partie, on montre aussi que sala represente une generalisation de la methode de decomposition proximale pour des problemes non convexes differentiables. Plusieurs nouveaux algorithmes de type (sala) sont proposes et etudies, particulierement l'algorithme diagonal (dsala) du premier et second ordre. Avec l'appui des etudes mathematiques, la troisieme partie est consacree a des experiences numeriques, pour tester les algorithmes, utilisant matlab sur une station ibm risc 6000, biprocesseur powerpc 604e. Les resultats obtenus sont satisfaisants et encourageants et illustrent bien les performances et le bon comportement des algorithmes developpes.
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Temitayo, Emmanuel Olaosebikan [Verfasser]. "Application of the Euler-Lagrange-Method for solving optimal control problems : Research Work / Olaosebikan Temitayo Emmanuel." München : GRIN Verlag, 2019. http://d-nb.info/1199542520/34.
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Houston, Paul D. "Lagrange-Galerkin methods for unsteady convection-diffusion problems : a posteriori error analysis and adaptivity." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.337607.
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Feng, Aichun. "Numerical simulation of nonlinear wave-body problem based on desingularized Rankine source and mixed Euler-Lagrange method." Thesis, University of Southampton, 2014. https://eprints.soton.ac.uk/366540/.
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Rankine source method coupled with Mixed Euler-Lagrange (MEL) algorithm is developed to investigate wave-body problems. Under Euler specification a boundary-value problem is solved by placing fundamental singularities outside the computational domain and satisfying the boundary conditions at prescribed control points. At every time step, Lagrangian frame is applied to update the control points position during regridding process. A space increment method for source points distribution incorporating horizontal free surface source arrangement and vertical desingularized distance is developed and this method connects free surface panel to body panel size. By reducing the number of source points, this method significantly increases the computational efficiency. A single node scheme is implemented to treat intersection points. This scheme regards intersection points only as body panel ending points. The first source points on the free surface are placed away from the intersection points and generated wave is started from these source points rather than intersection points. During regridding process, body panel number keeps constant and panel size varies to match the variation of wetted body surface. In the process of repanelling the free surface, panels slide horizontally due to the variation of wetted body surface pushing them back and forth. After their horizontal positions are fixed, the source points follow the wave elevation and are located on the updated wave surface in the vertical direction. A least square based smoothing technique is developed to eliminate the "sawtooth" phenomenon occurred in the free surface updating for two-dimensional fully nonlinear problem. Both two- and three-dimensional forced body oscillatory motion problems are studied and extensive comparisons show a good agreement with published results. The methods developed are proved to be accurate, efficient and robust for wave-body problems.
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Bermejo, Rodolfo. "Analysis of a Galerkin-Characteristic algorithm for the potential vorticity-stream function equations." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/30561.
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In this thesis we develop and analyze a
Galerkin-Characteristic method to integrate the potential
vorticity equations of a baroclinic ocean. The method proposed
is a two stage inductive algorithm. In the first stage the
material derivative of the potential vorticity is approximated
by combining Galerkin-Characteristic and Particle methods.
This yield a computationally efficient algorithm for this
stage. Such an algorithm consists of updating the dependent
variable at the grid points by cubic spline interpolation at
the foot of the characteristic curves of the advective
component of the equations. The algorithm is unconditionally
stable and conservative for Δt = O(h). The error analysis with respect to L² -norm shows that the algorithm converges with
order O(h); however, in the maximum norm it is proved that for
sufficiently smooth functions the foot of the characteristic
curves are superconvergent points of order O(h⁴ /Δt).
The second stage of the algorithm is a projection of
the Lagrangian representation of the flow onto the Cartesian
space-time Eularian representation coordinated with
Crank-Nicholson Finite Elements. The error analysis for this
stage with respect to L²-norm shows that the approximation
component of the global error is O(h²) for the free-slip boundary condition, and O(h) for the no-slip boundary condition. These estimates represent an improvement with respect to other estimates for the vorticity previously
reported in the literature. The evolutionary component of the
global error is equal to K(Δt² + h), where K is a constant that depends on the derivatives of the advective quantity along the Characteristic. Since the potential vorticity is a quasi-conservative quantitiy, one can conclude that K is in general small. Numerical experiments illustrate our theoretical results for both stages of the method.Science, Faculty of
Mathematics, Department of
Graduate
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Bessette, Gregory Carl. "Modeling of impact problems using an H-adaptive, explicit Lagrangian finite element method in three dimensions /." Full text (PDF) from UMI/Dissertation Abstracts International, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p3004213.
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Böttner, Carl-Uwe. "Über den Einfluss der elektrostatischen Feldkraft auf turbulente Zweiphasenströmungen numerische Modellierung mit der Euler-Lagrange-Methode /." [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=967401593.
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FALLAH, ABDELMJID. "Une analyse de la methode des domaines fictifs avec multiplicateurs de lagrange pour quelques problemes elliptiques." Nice, 1996. http://www.theses.fr/1996NICE4963.
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Ce travail presente l'etude de la methode des domaines fictifs avec multiplicateur de lagrange. Cette methode, qui peut etre consideree comme une methode generale pour resoudre une equation ou un systeme d'equations aux derivees partielles, consiste a remplacer le probleme initial par un autre pose sur un domaine de geometrie plus simple dont l'avantage est de permettre de travailler sur des maillages reguliers. La difficulte est de satisfaire les conditions aux limites prescrites sur le domaine initial. On traite, respectivement, les deux problemes de poisson et de stokes, en se basant sur la theorie des formulations mixtes pour verifier la condition de brezzi et babuska pour chacun de ces problemes. Les resultats d'existance et d'unicite de la solution de chacun des problemes sont etablis. La methode de multiplicateur de lagrange est connue d'etre en general stable et convergente sous certaine condition. Son principe est de choisir deux sous espaces, un a l'interieur du domaine et un autre sur une courbe fermee situee a l'interieur de ce domaine, puis essayer de combiner ces deux espaces avec le principe variationnel du point selle. La stabilite et l'ordre de convergence sont assures par une condition qui lie les pas de discretisation des deux sous espaces
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Oliveira, Anabela Pacheco de Pacheco de Oliveira Anabela De Oliveira Anabela Pacheco. "A comparison of Eulerian-Lagrangian methods for the solution of the transport equation /." Full text open access at:, 1994. http://content.ohsu.edu/u?/etd,208.
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Diniz, dos Santos Nuno Miguel. "Numerical methods for fluid-structure interaction problems with valves." Paris 6, 2007. http://www.theses.fr/2007PA066683.
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Cette thèse est motivée par la modélisation et la simulation numérique des phénomènes d’interaction fluide-structure autour de valves cardiaques. L’interaction avec la paroi des vaisseaux est traitée avec une formulation Arbitraire Lagrange Euler (ALE), tandis que l’interaction avec les valves est traitée à l’aide de multiplicateurs de Lagrange, dans une formulation de type Domaines Fictifs (FD). Après une présentation de synthèse des di- verses méthodes utilisées en interaction fluide-structure dans les écoulements sanguins, nous décrivons une méthode permettant de simuler la dynamique d’une valve immergée dans un écoulement visqueux incompressible. L’algori- thme de couplage est partionné, ce qui permet de conserver des solveurs fluides et structures indépendants. Le maillage du fluide est mobile pour suivre la paroi des vaisseaux, mais indépendant du maillage des valves. Ceci autorise des très grands déplacements sans nécessiter de remaillage. Nous proposons une stratégie pour gérer le contact entre plusieurs valves. L’algorithme est totalement indépendant des solveurs de structures et est bien adapté au couplage fluide-structure partionné. Enfin, nous proposons un schéma de couplage semi-implicite permettant de méler efficacement les formulations ALE et FD. Toutes les méthodes considérées sont accom- pagnées de nombreux tests numériques en 2D et 3DThis thesis is motivated by the modelling and the simulation of fluid-structure interaction phenomena in the vicinity of heart valves. On the one hand, the interaction of the vessel wall is dealt with an Arbitrary Lagrangian Eule- rian (ALE) formulation. On the other hand the interaction of the valves is treated with the help of Lagrange multipliers in a Fictitious Domains-like (FD) formulation. After a synthetic presentation of the several methods available for the fluid-structure interaction in blood flows, we describe a method that permits capture the dynamics of a valve immersed in an in- compressible fluid. The coupling algorithm is partitioned which allows the fluid and structure solvers to remain independent. In order to follow the ves- sel walls, the fluid mesh is mobile, but it remains none the less independent of the valve mesh. In this way we allow large displacements without the need to perform remeshing. We propose a strategy to manage contact between several immersed structures. The algorithm is completely independent of the structure solver and is well adapted to the partitioned fluid-structure coupling. Lastly we propose a semi-implicit coupling scheme allowing to mix, effectively, the ALE and FD formulations. The methods considered are followed with several numerical tests in 2D and 3D
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Kuhn, Claus. "Methode zur Auslegung mikrofluidischer Bauteile für beadbasierte Analysesysteme in der medizinischen Diagnostik." [S.l. : s.n.], 2005. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-25158.
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Kunle, Matthias. "Entwicklung und Untersuchung von Moving Least Square Verfahren zur numerischen Simulation hydrodynamischer Gleichungen." [S.l. : s.n.], 2001. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB9986261.
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Reschke, Christian. "Integrated flight loads modelling and analysis for flexible transport aircraft." [S.l. : s.n.], 2006. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-27974.
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Hartmann, Stefan. "Kontaktanalyse dünnwandiger Strukturen bei großen Deformationen." [S.l. : s.n.], 2007. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-31093.
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Pérez, Cesar Augusto Conopoima. "Mortar finite element method for cell response to applied electric field." Universidade Federal de Juiz de Fora (UFJF), 2017. https://repositorio.ufjf.br/jspui/handle/ufjf/6037.
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A resposta passiva e ativa de uma célula biológica a um campo elétrico é estudada aplicando um Método de Elementos Finitos Mortar MEFM. A resposta de uma célula é um processo com duas escalas temporais, o primeiro na escala de microsegundos para a polarização da célula e o segundo na escala de milisegundos para a resposta ativa devido a dinâmica complexa das correntes nos canais iônicos da membrana celular. O modelo matemático para descrever a dinâmica da resposta celular é baseado na lei de conservação de corrente elétrica em um meio condutor. Introduzindo uma variável adicional conhecida como multiplicador de Lagrange definido na interface da célula, o problema de valor de fronteira associado a conservação de corrente elétrica é desacoplado do problema de valor inicial associado a responta passiva e ativa da célula. O método proposto permite resolver o problema da distribuição de potencial elétrico em um arranjo geométrico arbitrário de células. Com o objetivo de validar a metodologia apresentada, a convergência espacial do método é numericamente investigada e a solução aproxima e exata que descreve a polarização de uma célula, são comparadas. Finalmente, para demonstrar a efetividade do método, a resposta ativa a um campo elétrico aplicado num arranjo de células de geometria arbitraria é investigada.
The response of passive and active biological cell to applied electric field is investigated with a Mortar Finite Element Method MFEM. Cells response is a process with two different time scales, one in microseconds for the cell polarization and the other in milliseconds for the active response of the cell due to the complex dynamics of the ion-channel current on the cell membrane. The mathematical model to describe the dynamics of the cell response is based on the conservation law of electric current in a conductive medium. By introducing an additional variable known as Lagrange multiplier defined on the cell interface, the boundary value problem associated to the conservation of electric current is decoupled from the initial value problem associated to the passive and active response of the cell. The proposed method allows to solve electric potential distribution in arbitrary cell geometry and arrangements. In order to validate the presented methodology, the h-convergence order of the MFEM is numerically investigated. The numerical and exact solutions describing cell polarization are also compared. Finally, to demonstrate the effectiveness of the method, the active response to an applied electric field in cells clusters and cells with arbitrary geometry are investigated.
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Altintan, Derya. "An Extension To The Variational Iteration Method For Systems And Higher-order Differential Equations." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613864/index.pdf.
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It is obvious that differential equations can be used to model real-life problems. Although it is possible to obtain analytical solutions of some of them, it is in general
difficult to find closed form solutions of differential equations. Finding thus approximate solutions has been the subject of many researchers from different areas.
In this thesis, we propose a new approach to Variational Iteration Method (VIM) to obtain the solutions of systems of first-order differential equations. The main
contribution of the thesis to VIM is that proposed approach uses restricted variations only for the nonlinear terms and builds up a matrix-valued Lagrange multiplier that leads to the extension of the method (EVIM).
Close relation between the matrix-valued Lagrange multipliers and fundamental solutions of the differential equations highlights the relation between the extended version of the variational iteration method and the classical variation of parameters formula.
It has been proved that the exact solution of the initial value problems for (nonhomogenous) linear differential equations can be obtained by such a generalisation using
only a single variational step.
Since higher-order equations can be reduced to first-order systems, the proposed approach is capable of solving such equations tooindeed, without such a reduction, variational iteration method is also extended to higher-order scalar equations. Further, the close connection with the associated first-order systems is presented. Such extension of the method to higher-order equations is then applied to solve boundary value problems: linear and nonlinear ones. Although the corresponding Lagrange multiplier resembles the Green&rsquo
s function, without the need of the latter, the extended approach to the variational iteration method is systematically applied to solve boundary value problems, surely in the nonlinear case as well. In order to show the applicability of the method, we have applied the EVIM to various real-life problems: the classical Sturm-Liouville eigenvalue problems, Brusselator reaction-diffusion, and chemical master equations. Results show that the method is simple, but powerful and effective.
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Maury, Bertrand. "Resolution numerique des equations de navier-stokes 2d et 3d avec surface libre par une methode euler-lagrange arbitraire." Paris 6, 1995. http://www.theses.fr/1995PA066773.
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Dans le cadre general de l'approche euler-lagrange arbitraire, une methode complete de resolution des equations de navier-stokes avec surface libre par elements finis est presentee. La prise en compte du terme d'inertie et la convection de la surface libre sont bases sur la methode des caracteristiques. Des proprietes de consistance et de conservation de la masse et de l'energie pour le schema propose sont demontrees. Diverses applications 2d et 3d confirment la validite et la stabilite de la methode
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Vazquez, Thais Godoy. "Funções de interpolação e regras de integração tensorizaveis para o metodo de elementos finitos de alta ordem." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/263500.
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Orientador: Marco Lucio BittencourtTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
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Resumo: Este trabalho tem por objetivo principal o desenvolvimento de funções de interpolaçao e regras de integraçao tensorizaveis para o Metodo dos Elementos Finitos (MEF) de alta ordem hp, considerando os sistemas de referencias locais dos elementos. Para isso, primeiramente, determinam-se ponderaçoes especficas para as bases de funçoes de triangulos e tetraedros, formada pelo produto tensorial de polinomios de Jacobi, de forma a se obter melhor esparsidade e condicionamento das matrizes de massa e rigidez dos elementos. Alem disso, procuram-se novas funçoes de base para tornar as matrizes de massa e rigidez mais esparsas possiveis. Em seguida, escolhe-se os pontos de integraçao que otimizam o custo do calculo dos coeficientes das matrizes de massa e rigidez usando as regras de quadratura de Gauss-Jacobi, Gauss-Radau-Jacobi e Gauss-Lobatto-Jacobi. Por fim, mostra-se a construçao de uma base unidimensional nodal que permite obter uma matriz de rigidez praticamente diagonal para problemas de Poisson unidimensionais. Discute-se ainda extensoes para elementos bi e tridimensionais
Abstract: The main purpose of this work is the development of tensor-based interpolation functions and integration rules for the hp High-order Finite Element Method (FEM), considering the local reference systems of the elements. We first determine specific weights for the shape functions of triangles and tetrahedra, constructed by the tensorial product of Jacobi polynomials, aiming to obtain better sparsity and numerical conditioning for the mass and stiffness matrices of the elements. Moreover, new shape functions are proposed to obtain more sparse mass and stiffness matrices. After that, integration points are chosen that optimize the cost for the calculation of the coefficients of the mass and stiffness matrices using the rules of quadrature of Gauss-Jacobi, Gauss-Radau-Jacobi and Gauss-Lobatto-Jacobi. Finally, we construct an one-dimensional nodal shape function that obtains an almost diagonal stiffness matrix for the 1D Poisson problem. Extensions to two and three-dimensional elements are discussed.
Doutorado
Mecanica dos Sólidos e Projeto Mecanico
Doutor em Engenharia Mecânica
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Tanseng, Pornpot. "Implementation of hypoplasticity for fast Lagrangian simulations." Berlin Logos-Verl, 2005. http://deposit.ddb.de/cgi-bin/dokserv?id=2704430&prov=M&dok_var=1&dok_ext=htm.
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Vo-Van, Claudine. "Analyse de données pharmacocinétiques fragmentaires : intégration dans le développement de nouvelles molécules." Paris 5, 1994. http://www.theses.fr/1994PA05P044.
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Plášil, Pavel. "Interakce konstrukce ocelové nádrže a kapaliny při seizmické události." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2013. http://www.nusl.cz/ntk/nusl-226475.
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Construction of structural computational model of the tank with fluid using program package ANSYS based on the Finite Element Method. Solve eigen-vibration of the tank with or without effects of fluid. Application of Euler and Lagrange method for modeling fluid. Solve seismic response using response spectra. Verify of the tank in accordance to EC 3 and EC8.
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Gath, Peter Friedrich. "CAMTOS - a software suite combining direct and indirect trajectory optimization methods /." [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10361094.
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Wang, Tian Bo. "Synthèse et étude élasto-dynamique d'une chaine fermée de solides articulés." Besançon, 1989. http://www.theses.fr/1989BESA2003.
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Etude des mecanismes articules caracteristiques des manipulateurs et de la robotique. Synthese des mecanismes. Cas de mecanismes deformables. Etude elastodynamique. Etude des vibrations. Calculs par elements finis
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Mendonça, Luziane Ferreira de. "Aceleração quase-Newton para problemas de minimização com restrições." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306668.
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Orientadores: Vera Lucia da Rocha Lopes, Jose Mario MartinezTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Sistemas de Otimalidade (ou Sistemas KKT) são sistemas formados pelas condições primais-duais estacionárias para a solução de problemas de otimização. Sob hipóteses adequadas (condições de qualificação), os minimizadores locais de um problema de minimização satisfarão as equações e inequações KKT; entretanto, infelizmente, muitos outros pontos estacionários (incluindo maximizadores) também são soluções desse sistema não linear. Por essa razão, os métodos destinados à resolução de problemas de programação não-linear fazem uso constante da estrutura de minimização, e o uso simples de métodos destinados à resolução de sistemas não-lineares podem gerar soluções espúrias. Todavia, caso o método destinado à resolução do sistema KKT tenha um ponto inicial situado na região de atração para um minimizador, esse método pode vir a ser muito eficiente. Neste trabalho, os métodos quase-Newton para a resolução de sistemas não-lineares são usados como aceleradores de algoritmos de programação não-linear (Lagrangiano Aumentado) com restrições de igualdade, desigualdade e caixa. Utilizamos como acelerador o método simétrico inverso de correção de posto um (ISR1), o qual realiza reínicios periódicos e faz uso das estruturas esparsas das matrizes para armazenamento. São demonstrados resultados de convergência e são realizados vários experimentos numéricos que comprovam a eficiência desta estratégia para problemas de minimização com restrições de igualdade, e indicam outros caminhos para problemas de minimização com restrições gerais (igualdade, desigualdade e caixa)
Abstract: Optimality (or KKT) systems arise as primal-dual stationarity conditions for constrained optimization problems. Under suitable constraint qualifications, local minimizers satisfy KKT equations but, unfortunately, many other stationary points (including, perhaps, maximizers) may solve these nonlinear systems too. For this reason, nonlinear-programming solvers make strong use of the minimization structure and the naive use of nonlinear-system solvers in optimization may lead to spurious solutions. Nevertheless, in the basin of attraction of a minimizer, nonlinear-system solvers may be quite efficient. In this work quasi-Newton methods for solving nonlinear systems are used as accelerators of nonlinear-programming (augmented Lagrangian) algorithms. A periodically-restarted memoryless symmetric rank-one (SRI) correction method is introduced for that purpose. Convergence results are given. For problems with only equality constraints, numerical experiments that confirm that the acceleration is effective are presented. A bunch of problems with equalities, inequalities and box constraints is tested and several comments and suggestions for further work are presented
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Doutor em Matemática Aplicada