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Dissertations / Theses on the topic 'Schwarz methods'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Dubois, Olivier. "Optimized Schwarz methods for the advection-diffusion equation." Thesis, McGill University, 2003. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=19701.

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The optimized Schwarz methods were recently introduced to enhance the convergence of the classical Schwarz iteration, by replacing the Dirichlet transmission conditions with different conditions obtained through an optimization of the convergence rate. This is formulated as a min-max problem. These new methods are well-studied for elliptic second order symmetric equations. The purpose of this work is to compute optimized Robin transmission conditions for the advection-diffusion equation in two dimensions, by finding the solution of the min-max problem. The asymptotic expansion, for small mesh

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2

Tang, Wei-pai. "Schwarz splitting and template operators." Stanford, CA : Dept. of Computer Science, Stanford University, 1987. http://doi.library.cmu.edu/10.1184/OCLC/19643650.

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Thesis (Ph. D.)--Stanford University, 1987.<br>"June 1987." "Also numbered Classic-87-03"--Cover. "This research was supported by NASA Ames Consortium Agreement NASA NCA2-150 and Office of Naval Research Contracts N00014-86-K-0565, N00014-82-K-0335, N00014-75-C-1132"--P. vi. Includes bibliographical references (p. 125-129).

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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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4

Garay, Jose. "Asynchronous Optimized Schwarz Methods for Partial Differential Equations in Rectangular Domains." Diss., Temple University Libraries, 2018. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/510451.

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Mathematics<br>Ph.D.<br>Asynchronous iterative algorithms are parallel iterative algorithms in which communications and iterations are not synchronized among processors. Thus, as soon as a processing unit finishes its own calculations, it starts the next cycle with the latest data received during a previous cycle, without waiting for any other processing unit to complete its own calculation. These algorithms increase the number of updates in some processors (as compared to the synchronous case) but suppress most idle times. This usually results in a reduction of the (execution) time to achieve

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5

Fritz, Manuel [Verfasser], and Holger [Akademischer Betreuer] Schwarz. "Methods for enhanced exploratory clustering analyses / Manuel Fritz ; Betreuer: Holger Schwarz." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2021. http://d-nb.info/1237270723/34.

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Schwarz, Jolanda M. [Verfasser]. "Advanced Image Reconstruction Methods for Ultra-High Field MRI / Jolanda M. Schwarz." Bonn : Universitäts- und Landesbibliothek Bonn, 2020. http://d-nb.info/1218474947/34.

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7

Shakir, Noman [Verfasser], and Guido [Akademischer Betreuer] Kanschat. "Multilevel Schwarz Methods for Incompressible Flow Problems / Noman Shakir ; Betreuer: Guido Kanschat." Heidelberg : Universitätsbibliothek Heidelberg, 2017. http://d-nb.info/1180986784/34.

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8

Ovtchinnikov, Serguei. "Parallel implicit fully coupled Newton-Krylov-Schwarz methods for numerical simulations of magnetohydrodynamics." Diss., Connect to online resource, 2006. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3239463.

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9

Du, Xiuhong. "Additive Schwarz Preconditioned GMRES, Inexact Krylov Subspace Methods, and Applications of Inexact CG." Diss., Temple University Libraries, 2008. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/6474.

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Mathematics<br>Ph.D.<br>The GMRES method is a widely used iterative method for solving the linear systems, of the form Ax = b, especially for the solution of discretized partial differential equations. With an appropriate preconditioner, the solution of the linear system Ax = b can be achieved with less computational effort. Additive Schwarz Preconditioners have two good properties. First, they are easily parallelizable, since several smaller linear systems need to be solved: one system for each of the sub-domains, usually corresponding to the restriction of the differential operator to that s

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10

Terkhova, Karina. "Capacitance matrix preconditioning." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244593.

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11

Dubois, Olivier 1980. "Optimized Schwarz methods for the advection-diffusion equation and for problems with discontinuous coefficients." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103379.

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Optimized Schwarz methods are iterative domain decomposition procedures with greatly improved convergence properties, for solving second order elliptic boundary value problems. The enhanced convergence is obtained by replacing the Dirichlet transmission conditions in the classical Schwarz iteration with more general conditions that are optimized for performance. The convergence is optimized through the solution of a min-max problem. The theoretical study of the min-max problems gives explicit formulas or characterizations for the optimized transmission conditions for practical use, and it perm

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12

Lucero, Lorca José Pablo [Verfasser], and Guido [Akademischer Betreuer] Kanschat. "Multilevel Schwarz methods for multigroup radiation transport problems / Jose Pablo Lucero Lorca ; Betreuer: Guido Kanschat." Heidelberg : Universitätsbibliothek Heidelberg, 2018. http://d-nb.info/1177149095/34.

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13

Schwarz, Mathias [Verfasser], Vasilis [Akademischer Betreuer] [Gutachter] Ntziachristos, Friedrich [Gutachter] Simmel, and Norbert [Gutachter] Hanik. "Multispectral Optoacoustic Dermoscopy: Methods and Applications / Mathias Schwarz ; Gutachter: Vasilis Ntziachristos, Friedrich Simmel, Norbert Hanik ; Betreuer: Vasilis Ntziachristos." München : Universitätsbibliothek der TU München, 2017. http://d-nb.info/1145141307/34.

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14

Mukhamedov, Farukh. "High performance computing for the discontinuous Galerkin methods." Thesis, Brunel University, 2018. http://bura.brunel.ac.uk/handle/2438/16769.

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Discontinuous Galerkin methods form a class of numerical methods to find a solution of partial differential equations by combining features of finite element and finite volume methods. Methods are defined using a weak form of a particular model problem, allowing for discontinuities in the discrete trial and test spaces. Using a discontinuous discrete space mesh provides proper flexibility and a compact discretisation pattern, allowing a multidomain and multiphysics simulation. Discontinuous Galerkin methods with a higher approximation polynomial order, the socalled p-version, performs better i

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15

Dolean, Victorita. "Algorithmes par decomposition de domaine et méthodes de discrétisation d'ordre elevé pour la résolution des systèmes d'équations aux dérivées partielles. Application aux problèmes issus de la mécanique des fluides et de l'électromagnétisme." Habilitation à diriger des recherches, Université de Nice Sophia-Antipolis, 2009. http://tel.archives-ouvertes.fr/tel-00413574.

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My main research topic is about developing new domain decomposition algorithms for the solution of systems of partial differential equations. This was mainly applied to fluid dynamics problems (as compressible Euler or Stokes equations) and electromagnetics (time-harmonic and time-domain first order system of Maxwell's equations). Since the solution of large linear systems is strongly related to the application of a discretization method, I was also interested in developing and analyzing the application of high order methods (such as Discontinuos Galerkin methods) to Maxwell's equations (somet

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16

Jung, Michael, and Todor D. Todorov. "On the Convergence Factor in Multilevel Methods for Solving 3D Elasticity Problems." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601510.

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The constant gamma in the strengthened Cauchy-Bunyakowskii-Schwarz inequality is a basic tool for constructing of two-level and multilevel preconditioning matrices. Therefore many authors consider estimates or computations of this quantity. In this paper the bilinear form arising from 3D linear elasticity problems is considered on a polyhedron. The cosine of the abstract angle between multilevel finite element subspaces is computed by a spectral analysis of a general eigenvalue problem. Octasection and bisection approaches are used for refining the triangulations. Tetrahedron, pentahedron and

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17

Haferssas, Ryadh Mohamed. "Espaces grossiers pour les méthodes de décomposition de domaine avec conditions d'interface optimisées." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066450.

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L'objectif de cette thèse est la conception, l'analyse et l'implémentation d'une méthode de décomposition de domaine efficiente pour des problèmes de la mécanique des solides et des fluides. Pour cela les méthodes de Schwarz optimisée (OSM) sont considérées et révisées. Les méthodes de décomposition de domaine de Schwarz optimisées ont été introduites par P.L. Lions, elles apportent une amélioration aux méthodes de Schwarz classiques en substituant les conditions d'interface de Dirichlet par des conditions de type Robin et cela pour les méthodes avec ou sans recouvrement. Les conditions de Rob

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18

Szydlarski, Mikolaj. "Algebraic Domain Decomposition Methods for Darcy flow in heterogeneous media." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2010. http://tel.archives-ouvertes.fr/tel-00550728.

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Afin de répondre aux besoins de l'industrie pétrolière d'une description plus fine de la géométrie et des propriétés pétrophysiques des bassins et des réservoirs, la simulation numérique des écoulements en milieux poreux doit évoluer vers des algorithmes plus performants et plus robustes vis à vis de la taille des simulations, de la complexité des maillages et des hétérogénéités du milieu poreux. Les méthodes de décomposition de domaine constituent une alternative aux méthodes multigrilles et pourraient permettre de lever les difficultés précédentes en terme de robustesse et d'efficacité sur a

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19

Gu, Yaguang. "Nonlinear optimized Schwarz preconditioning for heterogeneous elliptic problems." HKBU Institutional Repository, 2019. https://repository.hkbu.edu.hk/etd_oa/637.

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In this thesis, we study problems with heterogeneities using the zeroth order optimized Schwarz preconditioning. There are three main parts in this thesis. In the first part, we propose an Optimized Restricted Additive Schwarz Preconditioned Exact Newton approach (ORASPEN) for nonlinear diffusion problems, where Robin transmission conditions are used to communicate subdomain errors. We find out that for the problems with large heterogeneities, the Robin parameter has a significant impact to the convergence behavior when subdomain boundaries cut through the discontinuities. Therefore, we perfor

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20

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 metho

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21

Bugel, Mathilde. "Couplage entre la dynamique moléculaire et la mécanique des milieux continus." Thesis, Bordeaux 1, 2009. http://www.theses.fr/2009BOR13849/document.

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A l'échelle macroscopique, la mécanique des milieux continus (MMC) rencontre parfois des difficultés à représenter correctement le comportement d'un système physique, du fait d'une modélisation insuffisante des phénomènes. Ces faiblesses sont particulièrement marquées dans les systèmes où les interfaces, qui font apparaître des échelles d'espace très différentes, jouent un rôle prépondérant : microfluidique, écoulements polyphasiques etc.. Or, dans de nombreux domaines, et notamment dans le milieu pétrolier, les modèles macroscopiques existants semblent insuffisants pour pouvoir traiter correc

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22

Banjai, Lehel. "Computation of conformal maps by fast multipole method accelerated Schwarz-Christoffel transformation." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.400550.

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23

Gustafsson, William. "Evaluating the Longstaff-Schwartz method for pricing of American options." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-254406.

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24

Schwartz, Alexandra [Verfasser], and Christian [Akademischer Betreuer] Kanzow. "Mathematical Programs with Complementarity Constraints : Theory, Methods and Applications / Alexandra Schwartz. Betreuer: Christian Kanzow." Würzburg : Universitätsbibliothek der Universität Würzburg, 2011. http://d-nb.info/1014891930/34.

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25

Schwarz, Daniela [Verfasser]. "Untersuchungen zur Entwicklung einer wassersparenden Methode für die streifenförmige Beregnung von Dammkulturen im Feldgemüsebau / Daniela Schwarz." Kassel : Universitätsbibliothek Kassel, 2019. http://d-nb.info/1193089816/34.

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26

Ramirez, Villalba Leidy catherine. "Towards an efficient modeling of Fluid-Structure Interaction." Thesis, Ecole centrale de Nantes, 2020. http://www.theses.fr/2020ECDN0029.

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Les applications industrielles FSI se caractérisent par des géométries et des matériaux complexes. Afin de prédire avec précision leur comportement, des coûts de calcul élevés sont associés, à la fois en temps et en ressources informatiques. Pour améliorer la qualité de la prédiction sans pénaliser le temps de calcul, et pour réduire le temps de calcul sans impacter la précision disponible aujourd'hui, deux axes principaux sont explorés dans ce travail. Le premier est l'étude d'un algorithme asynchrone qui pourrait permettre l'utilisation de modèles structurels complexes. Le second consiste à

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27

Siegl, Alexander. "Einzelzell-basierte Methoden zur Charakterisierung Schwamm-assoziierter Bakterien." kostenfrei, 2009. http://www.opus-bayern.de/uni-wuerzburg/volltexte/2009/3744/.

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Berthe, Paul-Marie. "Méthodes de décomposition de domaine de type relaxation d'ondes optimisées pour l'équation de convection-diffusion instationnaire discrétisée par volumes finis." Thesis, Paris 13, 2013. http://www.theses.fr/2013PA132055.

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Dans le contexte du stockage des déchets radioactifs en milieu poreux, nous considérons l’équation de convection-diffusion instationnaire et sa discrétisation par des méthodes numériques. La discontinuité des paramètres physiques et la variabilité des échelles d’espace et de temps conduisent à utiliser des discrétisations différentes en temps et en espace dans différentes régions du domaine. Nous choisissons dans cette thèse le schéma volumes finis en dualité discrète (DDFV) et le schéma de Galerkin Discontinu en temps couplés à une méthode de décomposition de domaine de Schwarz de type relaxa

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Wüger, Daniel. "Anwendbarkeit und Justiziabilität völkerrechtlicher Normen im schweizerischen Recht : Grundlagen, Methoden und Kriterien /." Bern : Stämpfli, 2005. http://www.gbv.de/dms/spk/sbb/recht/toc/48066322X.pdf.

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30

Kleindienst, Roman [Verfasser], Stefan [Akademischer Betreuer] Sinzinger, Ulrich [Gutachter] Schwarz, and Stefan [Gutachter] Altmeyer. "Innovative Methoden für die optische System- und Funtionsintegration / Roman Kleindienst ; Gutachter: Ulrich Schwarz, Stefan Altmeyer ; Betreuer: Stefan Sinzinger." Ilmenau : TU Ilmenau, 2018. http://d-nb.info/117813475X/34.

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31

Wang, Yanqiu. "Preconditioning for the mixed formulation of linear plane elasticity." Diss., Texas A&M University, 2004. http://hdl.handle.net/1969.1/2781.

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In this dissertation, we study the mixed ﬁnite element method for the linear plane elasticity problem and iterative solvers for the resulting discrete system. We use the Arnold-Winther Element in the mixed ﬁnite element discretization. An overlapping Schwarz preconditioner and a multigrid preconditioner for the discrete system are developed and analyzed. We start by introducing the mixed formulation (stress-displacement formulation) for the linear plane elasticity problem and its discretization. A detailed analysis of the Arnold-Winther Element is given. The ﬁnite element discretization of the

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32

Wittenbrink, Philipp Paul [Verfasser], Jürgen [Akademischer Betreuer] Schwarz, Jürgen [Gutachter] Schwarz, and Markus [Gutachter] Thewes. "Entwicklung eines Prozessmodells zur Produktivitätsoptimierung des maschinellen Tunnelvortriebs unter Anwendung von Lean Methoden / Philipp Paul Wittenbrink ; Gutachter: Jürgen Schwarz, Markus Thewes ; Akademischer Betreuer: Jürgen Schwarz ; Universität der Bundeswehr München, Fakultät für Bauingenieurwesen und Umweltwissenschaften." Neubiberg : Universitätsbibliothek der Universität der Bundeswehr München, 2019. http://d-nb.info/1193502306/34.

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Wittenbrink, Philipp Paul [Verfasser], Jürgen [Akademischer Betreuer] Schwarz, Jürgen Gutachter] Schwarz, and Markus [Gutachter] [Thewes. "Entwicklung eines Prozessmodells zur Produktivitätsoptimierung des maschinellen Tunnelvortriebs unter Anwendung von Lean Methoden / Philipp Paul Wittenbrink ; Gutachter: Jürgen Schwarz, Markus Thewes ; Akademischer Betreuer: Jürgen Schwarz ; Universität der Bundeswehr München, Fakultät für Bauingenieurwesen und Umweltwissenschaften." Neubiberg : Universitätsbibliothek der Universität der Bundeswehr München, 2019. http://nbn-resolving.de/urn:nbn:de:bvb:706-6179.

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34

Schwarz, Stephan [Verfasser], Jochen [Akademischer Betreuer] Fröhlich, and Thomas [Akademischer Betreuer] Boeck. "An immersed boundary method for particles and bubbles in magnetohydrodynamic flows / Stephan Schwarz. Gutachter: Jochen Fröhlich ; Thomas Boeck. Betreuer: Jochen Fröhlich." Dresden : Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://d-nb.info/1068446498/34.

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Bucher, Max [Verfasser], Alexandra [Akademischer Betreuer] Schwartz, and Christian [Akademischer Betreuer] Kanzow. "Optimality Conditions and Numerical Methods for a Continuous Reformulation of Cardinality Constrained Optimization Problems / Max Bucher ; Alexandra Schwartz, Christian Kanzow." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2018. http://d-nb.info/1167926323/34.

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Garbely, Karin Kieser Marita. "Mystery Shopping als Bewertungsmethode der Dienstleistungsqualität von wissenschaftlichen Bibliotheken." Chur : Hochschule für Technik und Wirtschaft HTW, Arbeitsbereich Informationswissenschaft, 2009. http://www.fh-htwchur.ch/uploads/media/CSI_31_Garbely_Kieser.pdf.

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37

Ilzig, Katrin. "Approximation stochastischer Charakteristiken von Funktionalen schwach korrelierter Prozesse." Doctoral thesis, Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201001000.

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In praktischen Aufgabenstellungen können zur Modellierung zufälliger Einflüsse, welche sich durch schwache Abhängigkeiten auszeichnen, schwach korrelierte zufällige Funktionen genutzt werden. Die nähere Untersuchung von Funktionalen schwach korrelierter zufälliger Funktionen ist durch die Gestalt der Lösungen von praktischen Fragestellungen motiviert. Die stochastischen Charakteristiken dieser Lösungen lassen sich im Allgemeinen nicht exakt bestimmen, so dass auf Approximationsverfahren zurückgegriffen werden muss. Diese stehen im Mittelpunkt der Dissertation. Zu Beginn werden Entwicklungen vo

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Storck, Johann. "Management of Intellectual Property in China A Framework for Complementary Protection Methods /." St. Gallen, 2006. http://www.biblio.unisg.ch/org/biblio/edoc.nsf/wwwDisplayIdentifier/01654573002/$FILE/01654573002.pdf.

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Schütze, Gregor [Verfasser], and Markus [Akademischer Betreuer] Schwarz. "Entwicklung, Validierung und Anwendung einer HPLC-MS/MS-Methode zur quantitativen Bestimmung von Tryptophan und seinen Metaboliten / Gregor Schütze. Betreuer: Markus Schwarz." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2014. http://d-nb.info/1060632519/34.

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Rüdisser, Michèle F. "Boards of directors at work : an integral analysis of nontransferable duties under Swiss company law from an economic perspective /." [S.l.] : [s.n.], 2009. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=018680407&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Superina, Marco. "Praxis der discounted cash flow-Bewertungsmethode in der Schweiz : unter besonderer Berücksichtigung /." Bern : P. Haupt, 2000. http://aleph.unisg.ch/hsgscan/hm00007143.pdf.

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Schwartz, Keike [Verfasser]. "Characterization of Vibrio spp. isolates from Germany by reference to human clinical isolates using phenotypic and WGS-assisted genotypic methods / Keike Schwartz." Berlin : Freie Universität Berlin, 2021. http://d-nb.info/1236573048/34.

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Burri, Stefan. "Methodische Aspekte der Armutsforschung /." [S.l.] : [s.n.], 1998. http://www.ub.unibe.ch/content/bibliotheken_sammlungen/sondersammlungen/dissen_bestellformular/index_ger.html.

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Chauvin, Rémi. "Un modèle unifié pour les phénomènes de givrage en aéronautique et les systèmes de protection thermiques." Thesis, Toulouse, ISAE, 2015. http://www.theses.fr/2015ESAE0036/document.

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Le givrage a été identifié comme un danger important dès le début de l'aéronautique.L'accrétion de givre sur les ailes d'avion, due à la présence de gouttelettes surfonduesdans les nuages, cause parmi d'autres conséquences néfastes une dégradation des performancesaérodynamiques pouvant conduire au décrochage. C'est pourquoi les avionneursdéveloppent depuis longtemps des systèmes de protection. Comme les essais en vols ou ensoufflerie sont souvent complexes à mettre en oeuvre et onéreux, la simulation numériqueest devenue un outil efficace et complémentaire pour dimensionner ces systèmes.Cette

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Schwartz, Uwe [Verfasser], and Gernot [Akademischer Betreuer] Längst. "Functional Chromatin Extraction: A method to study DNA accessibility in higher-order structures of chromatin / Uwe Schwartz ; Betreuer: Gernot Längst." Regensburg : Universitätsbibliothek Regensburg, 2021. http://d-nb.info/1238897096/34.

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Buckow, Benjamin [Verfasser], Harald [Gutachter] Schwarz, and Przemyslaw [Gutachter] Janik. "Entwicklung von Modellen und Methoden zur Qualifizierung für die Netzbetriebsführung unter Einbeziehung eines neuartigen dynamischen Netzsimulators / Benjamin Buckow ; Gutachter: Harald Schwarz, Przemyslaw Janik." Cottbus : BTU Cottbus - Senftenberg, 2020. http://d-nb.info/1216506647/34.

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Linares, Juan Carlos. "Methoden, Instrumente und Strategien des Währungsrisiko-Managements in international tätigen Unternehmen /." [S.l.] : [s.n.], 1999. http://aleph.unisg.ch/hsgscan/hm00002126.pdf.

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Rais, Rania. "Couplage entre éléments finis et représentation intégrale pour les problèmes de diffraction acoustique et électromagnétique : analyse de convergence des méthodes de Krylov et méthodes multipôles rapides." Thesis, Rennes 1, 2014. http://www.theses.fr/2014REN1S013/document.

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Le travail effectué dans cette thèse a consisté à analyser différents aspects mathématiques et numériques d'une stratégie de résolution des problèmes de propagation d'onde acoustique et électromagnétique en domaine extérieur. Nous nous intéressons plus particulièrement à la méthode de couplage entre éléments finis et représentation intégrale (CEFRI) où nous analysons un algorithme de résolution itérative par analogie avec une méthode de décomposition de domaine ainsi que l'utilisation de la méthode multipôles rapide (FMM). Le système à résoudre fait intervenir des opérateurs intégraux ce qui r

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Dixon, Glen W. "Modelling the statistical behaviour of temperature using a modified Brennan and Schwarts (1982) interest rate model /." [St. Lucia, Qld], 2004. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe18235.pdf.

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Eibner, Tino. "A fast and efficient algorithm to compute BPX- and overlapping preconditioner for adaptive 3D-FEM." Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200801271.

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Abstract:

In this paper we consider the well-known BPX-preconditioner in conjunction with adaptive FEM. We present an algorithm which enables us to compute the preconditioner with optimal complexity by a total of only O(DoF) additional memory. Furthermore, we show how to combine the BPX-preconditioner with an overlapping Additive-Schwarz-preconditioner to obtain a preconditioner for finite element spaces with arbitrary polynomial degree distributions. Numerical examples illustrate the efficiency of the algorithms.

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