Academic literature on the topic 'MINRES method'

Many methods for computing eigenvalues of a large sparse matrix involve shift-invert transformations which require the solution of a shifted linear system at each step. This thesis deals with shift-invert iterative techniques for solving eigenvalue problems where the arising linear systems are solved inexactly using a second iterative technique. This approach leads to an inner-outer type algorithm. We provide convergence results for the outer iterative eigenvalue computation as well as techniques for efficient inner solves. In particular eigenvalue computations using inexact inverse iteration, the Jacobi-Davidson method without subspace expansion and the shift-invert Arnoldi method as a subspace method are investigated in detail. A general convergence result for inexact inverse iteration for the non-Hermitian generalised eigenvalue problem is given, using only minimal assumptions. This convergence result is obtained in two different ways; on the one hand, we use an equivalence result between inexact inverse iteration applied to the generalised eigenproblem and modified Newton's method; on the other hand, a splitting method is used which generalises the idea of orthogonal decomposition. Both approaches also include an analysis for the convergence theory of a version of inexact Jacobi-Davidson method, where equivalences between Newton's method, inverse iteration and the Jacobi-Davidson method are exploited. To improve the efficiency of the inner iterative solves we introduce a new tuning strategy which can be applied to any standard preconditioner. We give a detailed analysis on this new preconditioning idea and show how the number of iterations for the inner iterative method and hence the total number of iterations can be reduced significantly by the application of this tuning strategy. The analysis of the tuned preconditioner is carried out for both Hermitian and non-Hermitian eigenproblems. We show how the preconditioner can be implemented efficiently and illustrate its performance using various numerical examples. An equivalence result between the preconditioned simplified Jacobi-Davidson method and inexact inverse iteration with the tuned preconditioner is given. Finally, we discuss the shift-invert Arnoldi method both in the standard and restarted fashion. First, existing relaxation strategies for the outer iterative solves are extended to implicitly restarted Arnoldi's method. Second, we apply the idea of tuning the preconditioner to the inner iterative solve. As for inexact inverse iteration the tuned preconditioner for inexact Arnoldi's method is shown to provide significant savings in the number of inner solves. The theory in this thesis is supported by many numerical examples.

The central theme of this thesis is the design of optimal balanced black-box stopping criteria in iterative solvers of symmetric positive-definite, symmetric indefinite, and nonsymmetric linear systems arising from finite element approximation of stochastic (parametric) partial differential equations. For a given stochastic and spatial approximation, it is known that iteratively solving the corresponding linear(ized) system(s) of equations to too tight algebraic error tolerance results in a wastage of computational resources without decreasing the usually unknown approximation error. In order to stop optimally-by avoiding unnecessary computations and premature stopping-algebraic error and a posteriori approximation error estimate must be balanced at the optimal stopping iteration. Efficient and reliable a posteriori error estimators do exist for close estimation of the approximation error in a finite element setting. But the algebraic error is generally unknown since the exact algebraic solution is not usually available. Obtaining tractable upper and lower bounds on the algebraic error in terms of a readily computable and monotonically decreasing quantity (if any) of the chosen iterative solver is the distinctive feature of the designed optimal balanced stopping strategy. Moreover, this work states the exact constants, that is, there are no user-defined parameters in the optimal balanced stopping tests. Hence, an iterative solver incorporating the optimal balanced stopping methodology that is presented here will be a black-box iterative solver. Typically, employing such a stopping methodology would lead to huge computational savings and in any case would definitely rule out premature stopping. The constants in the devised optimal balanced black-box stopping tests in MINRES solver for solving symmetric positive-definite and symmetric indefinite linear systems can be estimated cheaply on-the- fly. The contribution of this thesis goes one step further for the nonsymmetric case in the sense that it not only provides an optimal balanced black-box stopping test in a memory-expensive Krylov solver like GMRES but it also presents an optimal balanced black-box stopping test in memory-inexpensive Krylov solvers such as BICGSTAB(L), TFQMR etc. Currently, little convergence theory exists for the memory-inexpensive Krylov solvers and hence devising stopping criteria for them is an active field of research. Also, an optimal balanced black-box stopping criterion is proposed for nonlinear (Picard or Newton) iterative method that is used for solving the finite dimensional Navier-Stokes equations. The optimal balanced black-box stopping methodology presented in this thesis can be generalized for any iterative solver of a linear(ized) system arising from numerical approximation of a partial differential equation. The only prerequisites for this purpose are the existence of a cheap and tight a posteriori error estimator for the approximation error along with cheap and tractable bounds on the algebraic error.

Un montage par excitation des plasmons de surface est mis au point pour etudier les interfaces et les couches minces. Cette technique est appliquee a l'etude des films solides deposes par la methode langmuir blodgett et a l'etude de l'interface liquide/solide

Developpement d'dune methode de mesure de resistance thermique de contact dans des doubles tubes metalliques minces destines a la fabrication de condenseurs pour des installations nucleaire. La methode, qui fonctionne en regime instationnaire, est basee sur l'analyse de la reponse de l'echantillon a une sollicitation thermique du type echelon temperature

La premiere partie de cette these est consacree a l'etude asymptotique de problemes elliptiques du second ordre, dans une structure reticulee periodique dependant de deux parametres, avec differentes conditions sur la frontiere des trous de la structure. La deuxieme partie de cette these a pour objet l'obtention d'un modele de jonction des poutres et l'application de ce modele a l'etude d'une grue

<p>Landminor är ett stort problem både under och efter krigstid. De metoder som används för att detektera minor har inte ändrats mycket sedan 1940-talet. Forskning med mål att utvärdera olika elektro-optiska sensorer och metoder som skulle kunna användas för att skapa mer effektiv min-detektion genomförs på FOI. Försök som har gjorts med data från bland annat laser-radar och IR-sensorer har gett intressanta resultat.</p><p>I det här examensarbetet utvärderades olika fenomen och egenskaper i laser-radar- och IR-data. De testade egenskaperna var intensitet, IR, ytlikhet och höjd.</p><p>En metod som segmenterar intressanta objekt och bakgrundsdata utformades och implementerades. Metoden använde sig av expectation-maximization-skattning och ett minimum message length-kriterium. Ett scatter separability-kriterium användes för att bestämma kvalitén på de olika egenskaperna och på den resulterande segmenteringen.</p><p>Data insamlad under en mätkampanj av FOI användes för att testa metoden. Resultatet visade bland annat att ytlikhetsmåttet gav en bra segmentering för stora objekt med släta ytor, men var sämre för små objekt med skrovliga ytor. Vid jämförelse med en manuellt skapad mål-mask visade det sig att metoden klarade av att välja ut egenskaper som i många fall gav en godkänd segmentering.</p><br><p>Land mines are a huge problem in conflict time and after. Methods used to detect mines have not changed much since the 1940's. Research aiming to evaluate output from different electro-optical sensors and develop methods for more efficient mine detection is performed at FOI. Early experiments with laser radar sensors show promising results, as do analysis of data from infrared sensors.</p><p>In this thesis, an evaluation is made of features found in laser radar- and in infrared -sensor data. The tested features are intensity, infrared, a surfaceness feature extracted from the laser radar data and height above an estimated ground plane.</p><p>A method for segmenting interesting objects from background data using theexpectation-maximization algorithm and a minimum message length criterion is designed and implemented. A scatter separability criterion is utilized to determine the quality of the features and the resulting segmentation.</p><p>The method is tested on real data from a field trial performed by FOI. The results show that the surfaceness feature supports the segmentation of larger object with smooth surfaces but gives no contribution to small object with irregular surfaces. The method produces a decent result of selecting contributing features for different neighbourhoods of a scene. A comparison with a manually created target mask of the neighbourhood and the segmented components show that in most cases a high percentage separation of mine data and background data is possible.</p>

Le plissement est généralement observé dans les structures minces ayant un comportement de type membrane. Ces structures minces ne supportent pas d'effort de flexion et sont donc sollicitées en traction. Dans cette thèse, nous avons développé une technique de réduction de modèle pour la modélisation du plissement des membranes minces. Cette technique, basée sur les séries de Fourier à double échelle, permet de déduire d'un modèle complet de membrane, un modèle réduit capable de prendre en compte les instabilités globales et locales. Les valeurs critiques de charge et longueur d'onde sont déterminées analytiquement puis numériquement. Des exemples numériques nous ont permis de valider le modèle numérique par rapport au modèle analytique. Les modèles numériques étudiés prennent en compte le modèle complet et le modèle réduit de la membrane. Le modèle complet est simulé dans Abaqus et résolu numériquement à l'aide de la méthode de la longueur d'arc et le modèle réduit est implémenté dans Matlab et résolu numériquement à l'aide de la méthode asymptotique numérique. Nous avons étudié le comportement de la membrane sous sollicitation mécanique, thermique et thermo-mécanique. Les résultats obtenus montrent que le modèle réduit est capable de se substituer au modèle complet dans la détermination des contraintes critiques et longueurs d'onde correspondantes. Le gain en temps de calcul obtenu est important, ceci grâce à la très faible densité de maillage requis par le modèle réduit. Le modèle réduit est très sensible aux conditions aux bords de la membrane et requiert d'avoir une longueur d'onde des plis quasiment constante dans la largeur de la membrane<br>Wrinkling is an instability phenomenon generally observed in thin structures with membrane's behavior. Those thin structures have no rigidity to flexion and are therefore used in traction. In this thesis, we developed a reduction model's technique for the modeling of wrinkling phenomenon in thin membranes. This technique, based on the double scale Fourier series, allow us to deduce from a full membrane model, a reduced membrane model that is able to take into account the global and local instability of the structure. The critical load and critical wavelength are determined analytically on one side, then numerically on the other side. Numerical exemples are conducted to validate the numerical model towards the analytical one. Numerical models studied take into account both full and reduce membrane models. The full model is simulated in Abaqus and solved numerically using the arc length method and the reduced model is implemented in Matlab and solved numerically using the asymptotic numerical method. We studied the membrane behavior under mechanical, thermal and thermo-mechanical loading. The results obtained show that the full membrane model can be replaced by the reduced one in determining critical loads and corresponding wavelengths. The gain in computation time obtained is important, due to the coarse mesh required by the reduced model. The reduced model is very sensitive to membrane's boundaries conditions and requires to have a quasi constant wavelength along the membrane width

The intensity of use of a mineral is traditionally defined as the consumption (production plus net imports) of the mineral divided by gross national product. It has been proposed that this ratio of raw material input to gross economic output is a predictable function of per capita income and that the relationship is based on economic theory. Though the theory has never been clearly defined, the intensity of use method has been used to make long term forecasts. This dissertation formulates a theoretical model of the consumption of minerals and the resulting intensity of use which is used to test the validity of the traditional intensity of use measure and its forecasting ability. Previous justifications of the intensity of use hypothesis state that changes in technical efficiency, substitution rates among inputs, and demands are explained by per capita income, which, as it grows, produces a regular intensity of use pattern. The model developed in this research shows that the life of the goods in use, foreign trade of raw and final goods, prices, consumer preferences, technical innovations, as well as the above factors fully explain economic use, which is not simply a function of per capita income. The complete model is used to restate the traditional theory of intensity of use and to examine the sensitivity of traditional measures to changes in the explanatory variables which are commonly omitted. The full model demonstrates the parameters that must be examined when making a long term forecast. Regular intensity of use patterns are observed for many minerals in many nations. Setting aside the theoretical questions, the intensity of use method is often used to make long term projections based on these trends in intensity of use as well as the trends in population and gross national product. This dissertation examines the forecasting ability of the traditional intensity of use method and finds that it is not necessarily an improvement over naive consumption time trend forecasts. Furthermore, it is unstable for very long term projections.

Thesis (M.S.) -- University of Maryland, College Park, 2007.<br>Thesis research directed by: Dept. of Mechanical Engineering. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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