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Dissertations / Theses on the topic 'Schwarz methods'

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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 size h, of the resulting convergence rate is found: it shows a weak dependence on h, if the overlap is 0(h) or no overlap is used. Numerical experiments illustrate the improved convergence of these optimized methods compared to other Schwarz methods, and also justify the continuous Fourier analysis performed on a simple model problem only. The theoretical asymptotic performance is also verified numerically.
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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.
"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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3

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
Ph.D.
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 convergence. Optimized Schwarz methods (OSM) are domain decomposition methods in which the transmission conditions between subdomains contain operators of the form \linebreak $\partial/\partial \nu +\Lambda$, where $\partial/\partial \nu$ is the outward normal derivative and $\Lambda$ is an optimized local approximation of the global Steklov-Poincar\'e operator. There is more than one family of transmission conditions that can be used for a given partial differential equation (e.g., the $OO0$ and $OO2$ families), each of these families containing a particular approximation of the Steklov-Poincar\'e operator. These transmission conditions have some parameters that are tuned to obtain a fast convergence rate. Optimized Schwarz methods are fast in terms of iteration count and can be implemented asynchronously. In this thesis we analyze the convergence behavior of the synchronous and asynchronous implementation of OSM applied to solve partial differential equations with a shifted Laplacian operator in bounded rectangular domains. We analyze two cases. In the first case we have a shift that can be either positive, negative or zero, a one-way domain decomposition and transmission conditions of the $OO2$ family. In the second case we have Poisson's equation, a domain decomposition with cross-points and $OO0$ transmission conditions. In both cases we reformulate the equations defining the problem into a fixed point iteration that is suitable for our analysis, then derive convergence proofs and analyze how the convergence rate varies with the number of subdomains, the amount of overlap, and the values of the parameters introduced in the transmission conditions. Additionally, we find the optimal values of the parameters and present some numerical experiments for the second case illustrating our theoretical results. To our knowledge this is the first time that a convergence analysis of optimized Schwarz is presented for bounded subdomains with multiple subdomains and arbitrary overlap. The analysis presented in this thesis also applies to problems with more general domains which can be decomposed as a union of rectangles.
Temple University--Theses
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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
Ph.D.
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 subdomain. These are called local problems. Second, if a coarse problem is introduced, they are optimal in the sense that bounds on the convergence rate of the preconditioned iterative method are independent (or slowly dependent) on the finite element mesh size and the number of subproblems. We study certain cases where the same optimality can be obtained without a coarse grid correction. In another part of this thesis we consider inexact GMRES when applied to singular (or nearly singular) linear systems. This applies when instead of matrix-vector products with A, one uses A = A+E for some error matrix E which usually changes from one iteration to the next. Following a similar study by Simoncini and Szyld (2003) for nonsingular systems, we prescribe how to relax the exactness of the matrixvector product and still achieve the desired convergence. In addition, similar criteria is given to guarantee that the computed residual with the inexact method is close to the true residual. Furthermore, we give a new computable criteria to determine the inexactness of matrix-vector product using in inexact CG, and applied it onto control problems governed by parabolic partial differential equations.
Temple University--Theses
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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 permits the analysis of the asymptotic behavior of the convergence.
In the first part of this work, we continue the study of optimized transmission conditions for advection-diffusion problems with smooth coefficients. We derive asymptotic formulas for the optimized parameters for small mesh sizes, in the overlapping and non-overlapping cases, and show that these formulas are accurate when the component of the advection tangential to the interface is not too large.
In a second part, we consider a diffusion problem with a discontinuous coefficient and non-overlapping domain decompositions. We derive several choices of optimized transmission conditions by thoroughly solving the associated min-max problems. We show in particular that the convergence of optimized Schwarz methods improves as the jump in the coefficient increases, if an appropriate scaling of the transmission conditions is used. Moreover, we prove that optimized two-sided Robin conditions lead to mesh-independent convergence. Numerical experiments with two subdomains are presented to verify the analysis. We also report the results of experiments using the decomposition of a rectangle into many vertical strips; some additional analysis is carried out to improve the optimized transmission conditions in that case.
On a third topic, we experiment with different coarse space corrections for the Schwarz method in a simple one-dimensional setting, for both overlapping and non-overlapping subdomains. The goal is to obtain a convergence that does not deteriorate as we increase the number of subdomains. We design a coarse space correction for the Schwarz method with Robin transmission conditions by considering an augmented linear system, which avoids merging the local approximations in overlapping regions. With numerical experiments, we demonstrate that the best Robin conditions are very different for the Schwarz iteration with, and without coarse correction.
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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 in terms of convergence rate, compared with the low order h-version with smaller element sizes and bigger mesh. However, the condition number of the Galerkin system grows subsequently. This causes surge in the amount of required storage, computational complexity and in the time required for computation. We use the following three approaches to keep the advantages and eliminate the disadvantages. The first approach will be a specific choice of basis functions which we call C1 polynomials. These ensure that the majority of integrals over the edge of the mesh elements disappears. This reduces the total number of non-zero elements in the resulting system. This decreases the computational complexity without loss in precision. This approach does not affect the number of iterations required by chosen Conjugate Gradients method when compared to the other choice of basis functions. It actually decreases the total number of algebraic operations performed. The second approach is the introduction of suitable preconditioners. In our case, the Additive two-layer Schwarz method, developed in [4], for the iterative Conjugate Gradients method is considered. This directly affects the spectral condition number of the system matrix and decreases the number of iterations required for the computation. This approach, however, increases the total number of algebraic operations and might require more operational time. To tackle the rise in the number of algebraic operations, we introduced a modified Additive two-layer non-overlapping Schwarz method with a Multigrid process. This using a fixed low-order approximation polynomial degree on a coarse grid. We show that this approach is spectrally equivalent to the first preconditioner, and requires less time for computation. The third approach is a development of an efficient mathematical framework for distributed data structure. This allows a high performance, massively parallel, implementation of the discontinuous Galerkin method. We demonstrate that it is possible to exploit properties of the system matrix and C1 polynomials as basis functions to optimize the parallel structures. The previously mentioned parallel data structure allows us to parallelize at the same time both the matrix-vector multiplication routines for the Conjugate Gradients method, as well as the preconditioner routines on the solver level. This minimizes the transfer ratio amongst the distributed system. Finally, we combined all three approaches and created a framework, which allowed us to successfully implement all of the above.
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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 (sometimes in conjuction with time-discretization schemes in the case of time-domain problems). As an active member of NACHOS pro ject (besides my main afiliation as an assistant professor at University of Nice), I had the opportunity to develop certain directions in my research, by interacting with permanent et non-permanent members (Post-doctoral researchers) or participating to supervision of PhD Students. This is strongly refflected in a part of my scientific contributions so far. This memoir is composed of three parts: the first is about the application of Schwarz methods to fluid dynamics problems; the second about the high order methods for the Maxwell's equations and the last about the domain decomposition algorithms for wave propagation problems.
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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 hexahedron meshes are considered. The dependence of the constant $\gamma$ on the Poisson ratio is presented graphically.
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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 Robin offrent un très bon levier qui nous permet d'aller vers l'optimalité des méthodes de Schwarz ainsi que la conception d'une méthode de décomposition de domaine robuste pour des problèmes de mécanique complexes comportant une nature presque incompressible. Dans cette thèse un nouveau cadre mathématique est introduit qui consiste à munir les méthodes de Schwarz optimisées (e.g. L'algorithme de Lions ) d'une théorie semblable à celle déjà existante pour des méthodes de Schwarz additives, on définit un espace grossier pour lequel le taux de convergence de la méthode à deux niveaux peut être prescrit, indépendamment des éventuelles hétérogénéités du problème traité. Une formulation sous forme de preconditioneur de la méthode à deux niveaux est proposée qui permettra la simulation parallèle d'un large spectre de problèmes mécanique, tel que le problème d'élasticité presque incompressible, le problème de Stokes incompressible ainsi que le problème instationnaire de Navier-Stokes. Des résultats numériques issues de simulations parallèles à grande échelle sur plusieurs milliers de processeurs sont présentés afin de montrer la robustesse de l'approche proposée
The objective of this thesis is to design an efficient domain decomposition method to solve solid and fluid mechanical problems, for this, Optimized Schwarz methods (OSM) are considered and revisited. The optimized Schwarz methods were introduced by P.L. Lions. They consist in improving the classical Schwarz method by replacing the Dirichlet interface conditions by a Robin interface conditions and can be applied to both overlapping and non overlapping subdomains. Robin conditions provide us an another way to optimize these methods for better convergence and more robustness when dealing with mechanical problem with almost incompressibility nature. In this thesis, a new theoretical framework is introduced which consists in providing an Additive Schwarz method type theory for optimized Schwarz methods, e.g. Lions' algorithm. We define an adaptive coarse space for which the convergence rate is guaranteed regardless of the regularity of the coefficients of the problem. Then we give a formulation of a two-level preconditioner for the proposed method. A broad spectrum of applications will be covered, such as incompressible linear elasticity, incompressible Stokes problems and unstationary Navier-Stokes problem. Numerical results on a large-scale parallel experiments with thousands of processes are provided. They clearly show the effectiveness and the robustness of the proposed approach
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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 architectures parallèles. Elles sont par nature plus adaptées au calcul parallèle et sont plus robustes en particulier lorsque les sous domaines sont résolus par des méthodes directes. Elles permettent aussi de traiter dans un cadre unique les couplages de modèles comme les puits ou les failles conductrices et s'étendent au cas des systèmes couplés. Le travail de thèse traite plus particulièrement de méthodes définies au niveau algébrique. On ne suppose pas avoir une connaissance préalable du problème continu dont la matrice provient. On n'a pas non plus accés aux matrices avant assemblage. Ce manque d'informations a priori rend plus difficile la construction de méthodes efficaces. On propose deux nouvelles méthodes de construction de méthodes de décomposition de domaine au niveau algébrique: la construction de conditions d'interface optimisées et d'une grille grossière. Ce dernier point est particulièrement important pour avoir des méthodes robustes vis à vis du nombre des sous-domaines. Les méthodes sont adaptatives et basées sur l'analyse de l'espace de Krylov généré durant les premières itérations de la méthode de Schwarz classique. A partir des vecteurs de Ritz correspondant aux plus basses valeurs propres, on construit des conditions d'interface et des grilles grossières qui annihilent l'erreur sur ces composantes. Les méthodes ont été testées sur des calculateurs parallèles pour des matrices issues de la simulation de milieux poreux.
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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 perform an algebraic analysis for a linear diffusion model problem with piecewise constant diffusion coefficients in the second main part. We carefully discuss two possible choices of Robin parameters on the artificial interfaces and derive asymptotic expressions of both the optimal Robin parameter and the convergence rate for each choice at the discrete level. Finally, in the third main part, we study the time-dependent nonequilibrium Richards equation, which can be used to model preferential flow in physics. We semi-discretize the problem in time, and then apply ORASPEN for the resulting elliptic problems with the Robin parameter studied in the second part.
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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 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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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 correctement les cas proposés. Par ailleurs, la méconnaissance des paramètres d’entrée d'une simulation macroscopique tels que les propriétés de transport, introduit parfois une mauvaise représentation de l’ensemble des processus diffusifs. La simulation à l'échelle microscopique, en l'occurrence la dynamique moléculaire classique (DM), peut pallier certains problèmes rencontrés par les approches macroscopiques, en permettant de mieux appréhender les divers processus physiques, notamment aux interfaces. Elle permet également de suppléer l’expérimentation, en permettant de calculer pour un fluide modèle les propriétés physiques du mélange étudié. Ainsi, à partir des ces données générées, il est possible de construire des corrélations palliant aux différents manques. Néanmoins, de par son caractère microscopique, cette approche ne permet de simuler que des échelles sub-micrométriques qui sont bien éloignées de la taille indispensable à la plupart des cas réalistes, qu’ils soient académiques ou industriels. En couplant les deux démarches, macroscopique et microscopique, de manière directe ou indirecte, il est donc envisageable d’accéder à des informations que l’une ou l’autre des ces approches ne peut fournir seule
Hybrid atomistic-continuum methods allow the simulation of complex flows, depending on the intimate connection of many spatiotemporal scales : from the nanoscale to the microscale and beyond. By limiting the molecular description within a small localized region, for example near fluid/fluid or fluid/solid interfaces (breakdown of the continuum), these methods are useful to study large systems for reasonable times. Besides, there is a wide variety of applications for such hybrid methods, ranging from the micro- or nano-scale devices, and other industrial processes such as wetting, droplet formation, and biomolecules near interfaces. In this work, we present one scheme for coupling the Navier-Stokes set of equations with Molecular Dynamics. Among the existing alternatives to couple these two approaches, we have chosen to implement a domain decomposition algorithm based on the alternating Schwarz method. In this method, the flow domain is decomposed into two overlapping regions : an atomistic region described by molecular dynamics and a continuum region described by a finite volume discretization of the incompressible Navier-Stokes equations. The fundamental assumption is that the atomistic and the continuum descriptions match in the overlapping region, where the exchange of information is performed. The information exchange, requires the imposition of velocity from one sub-domain in the form of boundary conditions (Dirichlet)/constraints on the solver of the other subdomain and vice versa. The spatial coupling as well as the temporal coupling of the two approaches has been investigated in this work. To show the feasibility of such a coupling, we have applied the multiscale method to a classical fluid mechanics problems
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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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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 étudier la méthode des tranches en combinant l'utilisation d'un modèle RANS et d'un modèle FEM non linéaire. D'une part, l'étude de l'asynchronicité dans le domaine FSI a révélé différents aspect d'intérêt qui doivent être approfondis avant que l'approche puisse être utilisée industriellement. Cependant, un premier traitement des points mentionnés ci-dessus a montré des signe d'amélioration qui pourraient conduire à un algorithme prometteur, qui se situe naturellement entre l'algorithme explicite et l'algorithme implicite. D'autre part, il a été montré que la méthode des tranches développée dans ce travail conduit à une réduction significative du temps de calcul sans dégradation de la précision
FSI industrial applications are often described by complex geometries and materials. In order to accurately predict their behavior, high computational costs are associated, both in time and in computational resources. To improve the quality of the prediction without penalizing the computational time, and to reduce the computational time without impacting the accuracy that is available today, two main axes are explored in this work. The first one is the study of an asynchronous algorithm that could allow the use of complex structural models. The second axis consists of the study of the strip method while combining the use of a RANS model and a non-linear FEM model. On the one hand, the study of asynchronicity in the FSI domain revealed different aspects of interest that must be addressed before the approach can be used industrially. However, a first treatment of the limitations found showed signs of an improvement that could lead to a promising algorithm, one that naturally lies between the implicit external algorithm and the implicit internal algorithm. On the other hand, it was shown that the strip method developed in this work achieves a significant reduction in calculation time while maintaining excellent accuracy
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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 relaxation d’ondes optimisées (OSWR), ce qui permet de traiter des maillages espace-temps non conformes. La principale difficulté réside dans l’obtention d’une discrétisation amont du flux convectif qui reste locale à un sous-domaine et telle que le schéma monodomaine soit équivalent au schéma multidomaine. Ces difficultés sont appréhendées d’abord en une dimension d’espace où différentes discrétisations sont étudiées. Le schéma retenu introduit une inconnue hybride sur les interfaces entre cellules. L’idée du décentrage amont par rapport à cette inconnue hybride est reprise en dimension deux d’espace, et adaptée au schéma DDFV. Le caractère bien posé de ce schéma et d’un schéma multidomaine équivalent est montré. Ce dernier est résolu par un algorithme OSWR dont la convergence est prouvée. Les paramètres optimisés des conditions de Robin sont obtenus par l'étude du taux de convergence continu ou discret. Différents cas-tests, dont l’un est inspiré du stockage des déchets nucléaires, illustrent ces résultats
In the context of nuclear waste repositories, we consider the numerical discretization of the non stationary convection diffusion equation. Discontinuous physical parameters and heterogeneous space and time scales lead us to use different space and time discretizations in different parts of the domain. In this work, we choose the discrete duality finite volume (DDFV) scheme and the discontinuous Galerkin scheme in time, coupled by an optimized Scwharz waveform relaxation (OSWR) domain decomposition method, because this allows the use of non-conforming space-time meshes. The main difficulty lies in finding an upwind discretization of the convective flux which remains local to a sub-domain and such that the multidomain scheme is equivalent to the monodomain one. These difficulties are first dealt with in the one-dimensional context, where different discretizations are studied. The chosen scheme introduces a hybrid unknown on the cell interfaces. The idea of upwinding with respect to this hybrid unknown is extended to the DDFV scheme in the two-dimensional setting. The well-posedness of the scheme and of an equivalent multidomain scheme is shown. The latter is solved by an OSWR algorithm, the convergence of which is proved. The optimized parameters in the Robin transmission conditions are obtained by studying the continuous or discrete convergence rates. Several test-cases, one of which inspired by nuclear waste repositories, illustrate these results
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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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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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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 mixed formulation leads to a symmetric indefinite linear system. Next, we study efficient iterative solvers for the symmetric indefinite linear system which arises from the mixed finite element discretization of the linear plane elasticity problem. The preconditioned Minimum Residual Method is considered. It is shown that the problem of constructing a preconditioner for the indefinite linear system can be reduced to the problem of constructing a preconditioner for the H(div) problem in the Arnold-Winther finite element space. Our main work involves developing an overlapping Schwarz preconditioner and a multigrid preconditioner for the H(div) problem. We give condition number estimates for the preconditioned systems together with supporting numerical results.
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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://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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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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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 von Momenten und Kumulanten der betrachteten linearen Integralfunktionale schwach korrelierter Prozesse nach der Korrelationslänge des Prozesses hergeleitet und eine Vermutung über die exakte Darstellung der Kumulanten formuliert. Für Integralfunktionale von schwach korrelierten Simulationsprozessen, welche aus der Interpolation von Moving-Average-Prozessen entstehen, werden die definierten Charakteristiken hergeleitet. Außerdem steht die Approximation der unbekannten Dichtefunktion im Fokus der Arbeit. Es werden verschiedene Zugänge genutzt. Eine alternative Herleitung zur bereits in der Literatur untersuchten Gram-Charlier-Entwicklung wird in Form der Edgeworth-Entwicklung angegeben. Des Weiteren werden die Sattelpunkt-Approximation und die Maximum-Entropie-Methode untersucht und anhand von Simulationsergebnissen für Integralfunktionale von Simulationsprozessen miteinander verglichen
In engineering applications stochastic influences which are characterized by weak dependencies can be modelled, among others, by weakly correlated random functions. The solutions of such problems shape up as integral functionals of weakly correlated random functions which motivates more detailed investigations. In general the exact calculation of stochastic characteristics of such integral functionals is impossible so that we have to be content with approximation methods this thesis focuses on. At the beginning expansions of moments and cumulants of linear integral functionals of weakly correlated random processes with respect to the correlation length are considered and an explicit formula of cumulants is conjectured. For integral functionals of weakly correlated random simulation processes, defined as interpolations of moving average processes, the required expansion coefficients are derived. Furthermore the approximation of the unknown probability density is requested. In the thesis there are different approaches used. First we state an alternative way to achieve the already known Gram Charlier approximation by means of Edgeworth expansion. Then we study two further methods, namely the saddlepoint approximation and the maximum entropy method and compare them on the basis of simulation results for integral functionals of simulation processes
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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 thèse s'inscrit dans le contexte de la modélisation de l'accrétion de givre, duruissellement et des systèmes de protection thermique. Elle s'articule en sept chapitres.Après avoir présenté les enjeux et contexte, on introduit une approche tricouche permettantde modéliser l'accrétion de givre et le ruissellement de manière instationnaire. Les troischapitres suivants traitent des méthodes de discrétisation de ce modèle ainsi que de soncouplage avec un modèle du système de protection thermique. Les deux derniers sontconsacrés à la présentation des résultats de simulations numériques montrant l'intérêt del'approche développée et la faisabilité de simulations complètes de phénomènes d'accrétionde givre sur une paroi chauffée ou non
Icing has been identified as a serious issue since the start of aeronautics. Ice accretion onwings, due to supercooled droplets inside clouds, leads to severe degradation of aerodynamicperformances, among other undesirable effects. Therefore, aircraft manufacturers have sincea long time developed ice protection systems. As flight tests or wind tunnel experimentsare often complicated to implement and expensive, numerical modeling is an effective andcomplementary tool to design those systems. This thesis concerns the modeling of ice accretion, runback and thermal ice protectionsystems. It consists of seven chapters. The first one is dedicated to the presentation of theconcerns and the context. Then a three layer approach allowing to model in an unsteadyway ice accretion and runback is presented. Following three chapters deal with this modeldiscretization as well as a method to couple it with a thermal ice protection system model.Two last chapters are dedicated to numerical simulations showing the sake of the approachand the feasibility of a whole simulation of ice accretion on a heated or unheated surface
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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 rend crucial le recours à des méthodes rapides telles que la FMM. L'analogie avec une méthode de décomposition de domaine s'obtient par extension au problème de Maxwell des résultats établis par F. Ben Belgacem et al. pour le problème de Helmholtz posé en domaine non borné. Pour cela, nous avons montré le lien entre la méthode CEFRI et la méthode de Schwarz avec recouvrement total pour la résolution du problème de Maxwell en domaine non borné. Cette relecture de la méthode CEFRI offre également une technique de préconditionnement pour les solveurs de Krylov et nous a permis d'avoir une idée préliminaire sur la convergence de ces méthodes. Ainsi, nous nous intéressons plutôt à des méthodes itératives rapides. Pour cela, nous avons mené une analyse théorique afin de montrer la convergence superlinéaire du GMRES dans une configuration sphérique. La validation de ces aspects a été réalisée par l'enrichissement de nombreux intégrants de la librairie éléments finis Mélina++, en C++
We are concerned with the study of different aspects of a numerical strategy for the resolution of acoustic and electromagnetic scattering problems. We focus more particu- larly on a coupling of finite element and integral representation (CEFRI) : we study an iterative algorithm by analogy with a domain decomposition method, and consider the use of the Fast Multipole Method (FMM). The system to be solved involves integral operators which requires the use of fast methods such as the FMM. The correspondence with a domain decomposition method is obtained by extending to the exterior Maxwell problem the results derived by F. Ben Belgacem et al. for the Helmholtz problem posed in unbounded domain. To this aim, we show the analogy to the Schwarz method with total overlap. This interpretation of CEFRI suggests a preconditioner for Krylov solvers and enables us to have a preliminary idea of their convergence. We derive in this context an analytical proof of a superlinear convergence of GMRES in a spherical configuration. The validation of these aspects has been achieved by the enrichment of the finite element library Mélina++ in C++
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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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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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