Tesi sul tema "Optimized domain decomposition method"
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1
Loisel, Sébastien. "Optimal and optimized domain decomposition methods on the sphere". Thesis, McGill University, 2005. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=85572.
Abstract (sommario):
The numerical solution of partial differential equations and boundary value problems is one of the most important tools of modern science. For various reasons (parellelizing, improving condition numbers, finding good preconditioners, etc...) it is desirable to turn a boundary value problem over a large domain O into a set of boundary value problems over domains O1,...,O n such that ∪kO k; this is the domain decomposition method. The solutions u1,...,un of the local problems rarely glue together into a solution u of the global problem, hence we must use an iteration whereby we repeatedly solve the local problems. Between each iteration, some information is exchanged between the subdomains, so that the local solutions at the next iteration better approximate the global solution. The method of Schwarz exchanges Dirichlet data along subdomain boundaries, but other methods exist. We recall a construction of nonlocal operators that lead to iterations that converge in 2d + 1 steps, where d is the diameter of the connectivity graph of the domain decomposition, if this graph is a tree. We discuss a graph algorithm linked to these operators in the general case. For the Laplacian on the sphere, we also give local approximations to these optimal nonlocal operators. We also discuss its application for solving the shallow water equations on the sphere as a model for numerical weather prediction.
2
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.
Abstract (sommario):
MathematicsPh.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
3
Riaz, Samia. "Domain decomposition method for variational inequalities". Thesis, University of Birmingham, 2014. http://etheses.bham.ac.uk//id/eprint/4815/.
Abstract (sommario):
Variational inequalities have found many applications in applied science. A partial list includes obstacles problems, fluid flow in porous media, management science, traffic network, and financial equilibrium problems. However, solving variational inequalities remain a challenging task as they are often subject to some set of complex constraints, for example the obstacle problem. Domain decomposition methods provide great flexibility to handle these types of problems. In our thesis we consider a general variational inequality, its finite element formulation and its equivalence with linear and quadratic programming. We will then present a non-overlapping domain decomposition formulation for variational inequalities. In our formulation, the original problem is reformulated into two subproblems such that the first problem is a variational inequality in subdomain Ω\(^i\) and the other is a variational equality in the complementary subdomain Ω\(^e\). This new formulation will reduce the computational cost as the variational inequality is solved on a smaller region. However one of the main challenges here is to obtain the global solution of the problem, which is to be coupled through an interface problem. Finally, we validate our method on a two dimensional obstacle problem using quadratic programming.
4
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.
Abstract (sommario):
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 proposéeThe 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
5
Badia, Ismaïl. "Couplage par décomposition de domaine optimisée de formulations intégrales et éléments finis d’ordre élevé pour l’électromagnétisme". Electronic Thesis or Diss., Université de Lorraine, 2022. http://www.theses.fr/2022LORR0058.
Abstract (sommario):
La résolution numérique d’un problème de diffraction électromagnétique tridimensionnel en régime harmonique est connue pour être difficile, notamment en haute fréquence et pour des objets diffractants diélectriques et inhomogènes. En effet, elle nécessite de discrétiser un système d’équations aux dérivées partielles posé sur un domaine infini. De plus, le fait de considérer une petite longueur d’onde λ dans ce cas, nécessite naturellement un maillage très fin, ce qui conduit par conséquent à un très grand nombre de degrés de liberté. Une approche standard consiste à combiner une méthode d’équations intégrales pour le domaine extérieur et une formulation variationnelle volumique pour le domaine intérieur (objet diffractant), conduisant à une formulation couplant la méthode des éléments de frontière (BEM) et la méthode des éléments finis (FEM). Bien que naturelle, cette approche présente quelques inconvénients majeurs. Tout d’abord, cette méthode de couplage mène à un système linéaire de très grande taille caractérisé par une matrice composée à la fois de parties creuses et denses. Un tel système est généralement difficile à résoudre et n’est pas directement adapté aux méthodes de compression. Ajouté à cela, il n’est pas possible de combiner facilement deux solveurs pré-existants, à savoir un solveur FEM pour le domaine intérieur et un solveur BEM pour le domaine extérieur, afin de construire un solveur global du problème original. Dans cette thèse, nous présentons un couplage faible bien conditionné entre la méthode des éléments de frontière et celle des éléments finis d’ordre élevé, permettant une simple construction d’un tel solveur. L’approche est basée sur l’utilisation d’une méthode de décomposition de domaine sans recouvrement impliquant des opérateurs de transmission optimaux. Ces derniers sont construits par le biais d’un processus de localisation basé sur des approximations rationnelles complexes de Padé des opérateurs Magnetic-to-Electric non locaux. Le nombre d’itérations nécessaires à la résolution du couplage faible ne dépend que faiblement de la configuration géométrique, de la fréquence, du contraste entre les sous-domaines et du raffinement de maillageIn terms of computational methods, solving three-dimensional time-harmonic electromagnetic scattering problems is known to be a challenging task, most particularly in the high frequency regime and for dielectric and inhomogeneous scatterers. Indeed, it requires to discretize a system of partial differential equations set in an unbounded domain. In addition, considering a small wavelength λ in this case, naturally requires very fine meshes, and therefore leads to very large number of degrees of freedom. A standard approach consists in combining integral equations for the exterior domain and a weak formulation for the interior domain (the scatterer) resulting in a formulation coupling the Boundary Element Method (BEM) and the Finite Element Method (FEM). Although natural, this approach has some major drawbacks. First, this standard coupling method yields a very large system having a matrix with sparse and dense blocks, which is therefore generally hard to solve and not directly adapted to compression methods. Moreover, it is not possible to easily combine two pre-existing solvers, one FEM solver for the interior domain and one BEM solver for the exterior domain, to construct a global solver for the original problem. In this thesis, we present a well-conditioned weak coupling formulation between the boundary element method and the high-order finite element method, allowing the construction of such a solver. The approach is based on the use of a non-overlapping domain decomposition method involving optimal transmission operators. The associated transmission conditions are constructed through a localization process based on complex rational Padé approximants of the nonlocal Magnetic-to-Electric operators. The number of iterations required to solve this weak coupling is only slightly dependent on the geometry configuration, the frequency, the contrast between the subdomains and the mesh refinement
6
Lee, Wee Siang. "Exterior domain decomposition method for fluid-structure interaction problems". Thesis, Imperial College London, 1999. http://hdl.handle.net/10044/1/8533.
7
Gu, Yaguang. "Nonlinear optimized Schwarz preconditioning for heterogeneous elliptic problems". HKBU Institutional Repository, 2019. https://repository.hkbu.edu.hk/etd_oa/637.
Abstract (sommario):
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.
8
Zhao, Kezhong. "A domain decomposition method for solving electrically large electromagnetic problems". Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1189694496.
9
Pieskä, J. (Jali). "Domain decomposition methods for continuous casting problem". Doctoral thesis, University of Oulu, 2004. http://urn.fi/urn:isbn:9514274679.
Abstract (sommario):
Abstract
Several numerical methods and algorithms, for solving the mathematical model of a continuous casting process, are presented, and theoretically studied, in this work. The numerical algorithms can be divided in to three different groups: the Schwarz type overlapping methods, the nonoverlapping Splitting iterative methods, and the Predictor-Corrector type nonoverlapping methods. These algorithms are all so-called parallel algorithms i.e., they are highly suitable for parallel computers.
Multiplicative, additive Schwarz alternating method and two asynchronous domain decomposition methods, which appear to be a two-stage Schwarz alternating algorithms, are theoretically and numerically studied. Unique solvability of the fully implicit and semi-implicit finite difference schemes as well as monotone dependence of the solution on the right-hand side are proved. Geometric rate of convergence for the iterative methods is investigated.
Splitting iterative methods for the sum of maximal monotone and single-valued monotone operators in a finite-dimensional space are studied. Convergence, rate of convergence and optimal iterative parameters are derived. A two-stage iterative method with inner iterations is analyzed in the case when both operators are linear, self-adjoint and positive definite.
Several new finite-difference schemes for a nonlinear convection-diffusion problem are constructed and numerically studied. These schemes are constructed on the basis of non-overlapping domain decomposition and predictor-corrector approach. Different non-overlapping decompositions of a domain, with cross-points and angles, schemes with grid refinement in time in some subdomains, are used. All proposed algorithms are extensively numerically tested and are founded stable and accurate under natural assumptions for time and space grid steps.
The advantages and disadvantages of the numerical methods are clearly seen in the numerical examples. All of the algorithms presented are quite easy and straight forward, from an implementation point of view. The speedups show that splitting iterative method can be parallelized better than multiplicative or additive Schwarz alternating method.
The numerical examples show that the multidecomposition method is a very effective numerical method for solving the continuous casting problem. The idea of dividing the subdomains to smaller subdomains seems to be very beneficial and profitable. The advantages of multidecomposition methods over other methods is obvious. Multidecomposition methods are extremely quick, while being just as accurate as other methods. The numerical results for one processor seem to be very promising.
10
Synn, Sang-Youp. "Practical domain decomposition approaches for parallel finite element analysis". Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/17032.
11
Nassor, Alice. "Domain decomposition method for acoustic-elastic coupled problems in time-domain. Application to underwater explosions". Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAE015.
Abstract (sommario):
Ce travail étudie les approches globales en temps de décomposition de domaine pour résoudre des problèmes transitoires d'interaction fluide-structure. Afin de déterminer un algorithme optimal, nous étudions dans un premier temps la solvabilité des problèmes élastodynamiques et acoustiques transitoires avec des conditions aux frontières de type Robin et de Neumann. Nous énonçons des résultats de solvabilité, en soulignant les différentes régularités espace-temps des solutions. Nous étudions également la solvabilité du problème couplé élastodynamique-acoustique transitoire. Puis en nous basant sur ces résultats mathématiques, nous proposons ensuite un algorithme itératif global en temps basé sur les conditions aux limites de type Robin pour le problème couplé et prouvons sa convergence.Ces résultats sont ensuite mis en oeuvre pour coupler deux méthodes numériques efficaces. La réponse du fluide en temps discret est obtenue à l'aide d'une approche Z-BEM qui combine (i) une méthode d'éléments de frontière (BEM) accélérée par la méthode des matrices hiérarchiques dans le domaine de Laplace et (ii) une quadrature de convolution. La réponse de la structure est modélisée à l'aide de la méthode des éléments finis. Nous développons de cette manière une méthode numérique de couplage itérative globale en temps à convergence garantie, permettant en outre d'utiliser deux méthodes numériques distinctes de manière non intrusive.Plusieurs améliorations sont ensuite proposées: une méthode d'accélération de convergence est mise en œuvre et une approximation à haute fréquence est proposée pour améliorer l'efficacité de la Z-BEM. On propose ensuite un deuxième couplage itératif global-en-temps basé sur une interface acoustique-acoustique, dont la convergence est également démontrée. Ce couplage permet ensuite d'introduire des effets non linéaires dus au phénomène de cavitation pour préciser le modèle fluide. La Z-BEM est enfin adaptée en utilisant la méthode des images pour permettre la prise en compte d'une surface libre.Cette méthode est appliquées à des problèmes à dynamique rapide de dispersion d'ondes de choc acoustiques par des structures élastiques immergées et permet de simuler des configurations réalistes rencontrées dans l'industrie navaleThis work addresses global-in-time domain decomposition approaches for the numerical solution of transient fluid-structure interaction problems. To determine an optimal algorithm, we first study the solvability for the transient acoustic and elastodynamic problems with Robin and Neumann boundary conditions. We state solvability results along with the different space-time regularities of the solutions. We also study the solvability for the transient coupled elastodynamic-acoustic problem. Using on these mathematical results we then propose a global-in-time iterative algorithm based on Robin boundary conditions for the coupled elastodynamicacoustic problem and we prove its convergence.These results are leveraged to design a computational methodology by coupling two efficient numerical methods. The fluid response is formulated in the discrete-time domain, using a Z-BEM approach that combines (i) a boundary element method (BEM) accelerated with hierarchical matrix implemented in the Laplace domain and (ii) a convolution quadrature method. The structure response is modelled using the finite elements method. We thus propose a global-in-time iterative coupling with guaranteed convergence, which enables the use of two distinct numerical methods in a non-intrusive manner.Several improvements are then explored: an acceleration method is implemented and a high-frequency approximation is proposed to improved the Z-BEM efficiency. A second iterative global-in-time coupling based on an acoustic-acoustic interface is then proposed and its convergence is also proved. This coupling enables the addition of non linear effects due to the cavitation phenomenon to derive a more realistic fluid model. The Z-BEM is lastly adapted using the method of images to take a free surface into account.This method is applied on fast-time problems of acoustic shock wave scattering by submerged elastic structures and enables to simulate realistic configurations from naval industry
12
Ludick, Daniel Jacobus. "Efficient numerical analysis of finite antenna arrays using domain decomposition methods". Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/96124.
Abstract (sommario):
Thesis (PhD) -- Stellenbosch University, 2014.ENGLISH ABSTRACT: This work considers the efficient numerical analysis of large, aperiodic finite antenna arrays. A Method of Moments (MoM) based domain decomposition technique called the Domain Green's Function Method (DGFM) is formulated to address a wide range of array problems in a memory and runtime efficient manner. The DGFM is a perturbation approach that builds on work initially conducted by Skrivervik and Mosig for disjoint arrays on multi-layered substrates, a detailed review of which will be provided in this thesis. Novel extensions considered for the DGFM are as follows: a formulation on a higher block matrix factorisation level that allows for the treatment of a wider range of applications, and is essentially independent of the elemental basis functions used for the MoM matrix formulation of the problem. As an example of this, both conventional Rao-Wilton-Glisson elements and also hierarchical higher order basis functions were used to model large array structures. Acceleration techniques have been developed for calculating the impedance matrix for large arrays including one based on using the Adaptive Cross Approximation (ACA) algorithm. Accuracy improvements that extend the initial perturbation assumption on which the method is based have also been formulated. Finally, the DGFM is applied to array geometries in complex environments, such as that in the presence of finite ground planes, by using the Numerical Green's Function (NGF) method in the hybrid NGF-DGFM formulation. In addition to the above, the DGFM is combined with the existing domain decomposition method, viz., the Characteristic Basis Function Method (CBFM), to be used for the analysis of very large arrays consisting of sub-array tiles, such as the Low-Frequency Array (LOFAR) for radio astronomy. Finally, interesting numerical applications for the DGFM are presented, in particular their usefulness for the electromagnetic analysis of large, aperiodic sparse arrays. For this part, the accuracy improvements of the DGFM are used to calculate quantities such as embedded element patterns, which is a major extension from its original formulation. The DGFM has been integrated as part of an efficient array analysis tool in the commercial computational electromagnetics software package, FEKO.
AFRIKAANSE OPSOMMING: In hierdie werkstuk word die doeltre ende analise van eindige, aperiodiese antenna samestellings behandel. Eindige gebied benaderings wat op die Moment Metode (MoM) berus, word as vetrekpunt gebruik. `n Tegniek genaamd die Gebied Green's Funksie Metode (GGFM) word voorgestel en is geskik vir die analise van `n verskeidenheid van ontkoppelde samestellings. Die e ektiewe gebruik van rekenaargeheue en looptyd is onderliggend in die implementasie daarvan. Die GGFM is 'n perturbasie metode wat op die oorspronklike werk van Skrivervik en Mosig berus. Laasgenoemde is hoofsaaklik ontwikkel vir die analise van ontkoppelde antenna samestellings op multilaag di elektrikums. `n Deeglike oorsig van voorafgaande word in die tesis verskaf. In hierdie tesis is die bogenoemde werk op `n unieke wyse uitgebrei: `n ho er blok matriks vlak formulering is ontwikkel wat dit moontlik maak vir die analise van `n verskeidenheid strukture en wat onafhanklik is van die onderliggende basis funksies. Beide lae-vlak Rao-Wilton-Glisson (RWG) basis funksies, asook ho er orde hierargiese basis funksies word gebruik vir die modellering van groot antenna samestellings. Die oorspronklike perturbasie aanname is uitgebrei deur akkuraatheidsverbeteringe vir die tegniek voor te stel. Die Aanpasbare Kruis Benaderings (AKB) tegniek is onder andere gebruik om spoed verbeteringe vir die GGFM te bewerkstellig. Die GGFM is verder uitgebrei vir die analise van antenna samestellings in `n komplekse omgewing, bv. `n antenna samestelling bo `n eindige grondplaat. Die Numeriese Green's Funksie (NGF) metode is hiervoor ingespan en die hibriede NGF-GGFM is ontwikkel. Die GGFM is verder met die Karakteristieke Basis Funksie Metode (KBFM) gekombineer. Die analise van groot skikkings wat bestaan uit sub-skikkings, soos die wat tans by die \Low- Frequency Array (LOFAR) " vir radio astronomie in Nederland gebruik word, kan hiermee gedoen word. In die werkstuk word die GGFM ook toegepas op `n reeks interessante numeriese voorbeelde, veral die toepaslike EM analise van groot aperiodiese samestellings. Die akkuraatheidsverbeteringe vir die GGFM maak die berekening van elementpatrone vir skikkings moontlik. Die GGFM is by the sagteware pakket FEKO geintegreer.
13
Stylianopoulos, Nikalaos Stavros. "A domain decomposition method for numerical conformal mapping onto a rectangle". Thesis, Brunel University, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.257545.
14
Cheung, Charissa Chui-yee. "A domain decomposition method for some partial differential equations with singularities". HKBU Institutional Repository, 1997. http://repository.hkbu.edu.hk/etd_ra/160.
15
Jones, Adam. "Development of a near-wall domain decomposition method for turbulent flows". Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/development-of-a-nearwall-domain-decomposition-method-for-turbulent-flows(bf7149b7-c26a-4924-9886-42a92cce4f51).html.
Abstract (sommario):
In computational fluid dynamics (CFD), there are two widely-used methods for computing the near-wall regions of turbulent flows: high Reynolds number (HRN) models and low Reynolds number (LRN) models. HRN models do not resolve the near-wall region, but instead use wall functions to compute the required parameters over the near-wall region. In contrast, LRN models resolve the flow right down to the wall. Simulations with HRN models can take an order of magnitude less time than with LRN models, however the accuracy of the solution is reduced and certain requirements on the mesh must be met if the wall function is to be valid. It is often difficult or impossible to satisfy these requirements in industrial computations. In this thesis the near-wall domain decomposition (NDD) method of Utyuzhnikov (2006) is developed and implemented into the industrial code, Code_Saturne, for the first time. With the NDD approach, the near-wall regions of a fluid flow are removed from the main computational mesh. Instead, the mesh extends down to an interface boundary, which is located a short distance from the wall, denoted y*. A simplified boundary layer equation is used to calculate boundary conditions at the interface. When implemented with a turbulence model which can resolve down to the wall, there is no lower limit on the value of y*. There is a Reynolds number-dependent upper limit on y*, as there is with HRN models. Thus for large y*, the model functions as a HRN model and as y*→ 0 the LRN solution is recovered. NDD is implemented for the k−ε and Spalart-Allmaras turbulence models and is tested on five test cases: a channel flow at two different Reynolds numbers, an annular flow, an impinging jet flow and the flow in an asymmetric diffuser. The method is tested as a HRN and LRN model and it is found that the method behaves competitively with the scalable wall function (SWF) on simpler flows, and performs better on the asymmetric diffuser flow, where the NDD solution correctly captures the recirculation region whereas the SWF does not. The method is then tested on a ribbed channel flow. Particular focus is given to investigating how much of the rib can be excluded from the main computational mesh. It is found that it is possible to remove 90% of the rib from the mesh with less than 2% error in the friction factor compared to the LRN solution. The thesis then focuses on the industrial case of the flow in an annulus where the inner wall, referred to as the pin, has a rib on its surface that protrudes into the annulus. Comparison is made between CFD calculations, experimental data and empirical correlations. It is found that the experimental friction factors are significantly larger than those found with CFD, and that the trend in the friction factor with Reynolds number found in the experiments is different. Simulations are performed to quantify the effect that a non-smooth surface finish on the pin and rib surface has on the flow. This models the situation that occurs in an advanced gas-cooled nuclear reactor, when a carbon deposit forms on the fuel pins. The relationship between the friction factor and surface finish is plotted. It is demonstrated that surface roughness left over by the manufacturing process in the experiments is not the source of the discrepancy between the experimental and CFD results.
16
Malhotra, Laura (Laura A. ). "Finite element method with hierarchical domain decomposition : enabling experimentally relevant mesoscale models". Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/112558.
Abstract (sommario):
Thesis: S.B., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2017.Cataloged from PDF version of thesis.
Includes bibliographical references (page 23).
Mesoscale materials such as metallic glass present a difficult modeling challenge because their time and length scales place them in a gap where neither continuum mechanics nor quantum mechanics-based models are computationally tractable. The STZ dynamics model is a mesoscale approach to modeling this class of materials. However, modeling the response of such amorphous metals to deformation is still very computationally expensive. As meshes get larger, the runtimes of the mesoscale models get much longer, particularly in three dimensions; in fact, the computation is currently not efficient enough to run on experimentally relevant length scales. This thesis focuses on a hierarchical domain decomposition method that will be combined with other strategies to speed up the current models. A hierarchical mesh was generated, and then used to make the finite-element portion more efficient. The runtime and error of this accelerated model were then studied in order to assess the usefulness of the technique. The results show a mediocre runtime speedup that could become more impressive after optimization. More importantly, error drops off superlinearly with distance from the strained element, so accuracy is not sacrificed when using the accelerated method. Therefore, hierarchical domain decomposition can be used with the other speedup strategies to enable larger mesoscale simulations.
by Laura Malhotra.
S.B.
17
Vouvakis, Marinos N. "A Non-Conformal Domain Decomposition Method for Solving Large Electromagnetic Wave Problems". The Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=osu1125498071.
18
Dinevik, Vilhelm. "Comparative Analysis of Adaptive Domain Decomposition Algorithms for a Time-Spectral Method". Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-289366.
Abstract (sommario):
Time-spectral solvers for partial differential equations (PDE) have been explored in various forms during the last few decades. The generalized weighted residual method (GWRM) is one such method with a high accuracy and efficiency. The GWRM has so far been implemented almost exclusively with a uniform grid of subdomains in the spatial domain. Recent research has indicated that an adaptive grid can yield a significant improvement in accuracy and efficiency of the GWRM. In this thesis a comparison is performed between a uniform grid and three different adaptive grid decomposition methods. Three initial- value PDEs are used to benchmark these methods; the one-dimensional Burger’s equation, the 4th order Fisher-Kolmogorov equation and the non-linear Schrödinger equation. It was found that the average adaptive algorithm is the most efficient out of the algorithms evaluated in this thesis. The average adaptive algorithms solution time was up to 1.6 times faster than the uniform algorithm when solving the Fisher-Kolmogorov equation and with an error up to a factor of 22.5 smaller than the uniform algorithm when solving the one- dimensional Burger’s equation. The uniform algorithm needed 25 spatial subdomains to get errors of the same order of magnitude as the average adaptive algorithm got using only 12 spatial subdomains. The average subdomain decomposition algorithm is a fast, robust and efficient method, which can be applied to a variety of different problems to further increase the efficiency of the GWRM.Tidsspektrala lösningar av partiella differential ekvationer (PDE) har utforskats på många olika sätt under de senaste årtiondena. Den generaliserade viktade residual metoden (GWRM) är en sådan metod som har uppnått hög noggrannhet och effektivitet. Metoden har hittills, nästan enbart, implementerats med en likformig subdomänsuppdelning i rumsdomänen. Nyligen utförd forskning indikerar att GWRM kan ge signifikant förbättrad precision och effektivitet om man implementerar adaptiva rums- och tidsdomäner. I detta examensarbete utförs en jämförelse mellan en likformig subdomänsuppdelning i rummet och tre olika adaptiva algoritmer för subdomänsuppdelning. Dessa algoritmer testas på tre olika PDE, endimensionella Burgers ekvation, fjärde ordningens Fisher-Kolmogorovs ekvation och den icke-linjära Schrödingerekvationen. Slutsatsen var att den medelvärdesbildande adaptiva algoritmen var den mest effektiva metoden. Den löste ekvationerna upp till 2.7 gånger snabbare än den likformiga algoritmen, med ett fel som var upp till 22.5 gånger mindre än den likformiga metodens fel. Den likformiga metoden behövde 25 rumsdomäner för att få en precision av samma potens som de adaptiva algoritmerna åstadkom med enbart 12 rumsdomäner. Den medelvärdesbildande algoritmens subdomänsuppdelning är snabb, robust och effektiv. Den kan appliceras på en mängd olika problem för att öka effektiviteten av GWRM.
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Utzmann, Jens. "A domain decomposition method for the efficient direct simulation of aeroacoustic problems". [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-38383.
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Ozgun, Ozlem. "Finite Element Modeling Of Electromagnetic Radiation/scattering Problems By Domain Decomposition". Phd thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/3/12608290/index.pdf.
Abstract (sommario):
The Finite Element Method (FEM) is a powerful numerical method to solve wave propagation problems for open-region electromagnetic radiation/scattering problems involving objects with arbitrary geometry and constitutive parameters. In high-frequency applications, the FEM requires an electrically large computational domain, implying a large number of unknowns, such that the numerical solution of the problem is not feasible even on state-of-the-art computers. An appealing way to solve a large FEM problem is to employ a Domain Decomposition Method (DDM) that allows the decomposition of a large problem into several coupled subproblems which can be solved independently, thus reducing considerably the memory storage requirements. In this thesis, two new domain decomposition algorithms (FB-DDM and ILF-DDM) are implemented for the finite element solution of electromagnetic radiation/scattering problems. For this purpose, a nodal FEM code (FEMS2D) employing triangular elements and a vector FEM code (FEMS3D) employing
tetrahedral edge elements have been developed for 2D and 3D problems, respectively. The unbounded domain of the radiation/scattering problem, as well as the boundaries of the subdomains in the DDMs, are truncated by the Perfectly Matched Layer (PML) absorber. The PML is implemented using two new approaches: Locally-conformal PML and Multi-center PML. These approaches are based on a locally-defined complex coordinate transformation which makes possible to handle challenging PML geometries, especially with curvature discontinuities. In order to implement these PML methods, we also introduce the concept of complex space FEM using elements with complex nodal coordinates. The performances of the DDMs and the PML methods are investigated numerically in several applications.
21
Wang, Xiaochuan. "A Domain Decomposition Method for Analysis of Three-Dimensional Large-Scale Electromagnetic Compatibility Problems". The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1338376950.
22
Wang, Mianzhi. "Numerical Analysis of Transient Teflon Ablation with a Domain Decomposition Finite Volume Implicit Method on Unstructured Grids". Digital WPI, 2012. https://digitalcommons.wpi.edu/etd-theses/284.
Abstract (sommario):
This work investigates numerically the process of Teflon ablation using a finite-volume discretization, implicit time integration and a domain decomposition method in three-dimensions. The interest in Teflon stems from its use in Pulsed Plasma Thrusters and in thermal protection systems for reentry vehicles. The ablation of Teflon is a complex process that involves phase transition, a receding external boundary where the heat flux is applied, an interface between a crystalline and amorphous (gel) phase and a depolymerization reaction which happens on and beneath the ablating surface. The mathematical model used in this work is based on a two-phase model that accounts for the amorphous and crystalline phases as well as the depolymerization of Teflon in the form of an Arrhenius reaction equation. The model accounts also for temperature-dependent material properties, for unsteady heat inputs and boundary conditions in 3D. The model is implemented in 3D domains of arbitrary geometry with a finite volume discretization on unstructured grids. The numerical solution of the transient reaction-diffusion equation coupled with the Arrhenius-based ablation model advances in time using implicit Crank-Nicolson scheme. For each time step the implicit time advancing is decomposed into multiple sub-problems by a domain decomposition method. Each of the sub-problems is solved in parallel by Newton-Krylov non-linear solver. After each implicit time-advancing step, the rate of ablation and the fraction of depolymerized material are updated explicitly with the Arrhenius-based ablation model. After the computation, the surface of ablation front and the melting surface are recovered from the scalar field of fraction of depolymerized material and the fraction of melted material by post-processing. The code is verified against analytical solutions for the heat diffusion problem and the Stefan problem. The code is validated against experimental data of Teflon ablation. The verification and validation demonstrates the ability of the numerical method in simulating three dimensional ablation of Teflon.
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Chen, Jixin. "Some Domain Decomposition and Convex Optimization Algorithms with Applications to Inverse Problems". Doctoral thesis, Universite Libre de Bruxelles, 2018. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/271782.
Abstract (sommario):
Domain decomposition and convex optimization play fundamental roles in current computation and analysis in many areas of science and engineering. These methods have been well developed and studied in the past thirty years, but they still require further study and improving not only in mathematics but in actual engineering computation with exponential increase of computational complexity and scale. The main goal of this thesis is to develop some efficient and powerful algorithms based on domain decomposition method and convex optimization. The topicsstudied in this thesis mainly include two classes of convex optimization problems: optimal control problems governed by time-dependent partial differential equations and general structured convex optimization problems. These problems have acquired a wide range of applications in engineering and also demand a very high computational complexity. The main contributions are as follows: In Chapter 2, the relevance of an adequate inner loop starting point (as opposed to a sufficient inner loop stopping rule) is discussed in the context of a numerical optimization algorithm consisting of nested primal-dual proximal-gradient iterations. To study the optimal control problem, we obtain second order domain decomposition methods by combining Crank-Nicolson scheme with implicit Galerkin method in the sub-domains and explicit flux approximation along inner boundaries in Chapter 3. Parallelism can be easily achieved for these explicit/implicit methods. Time step constraints are proved to be less severe than that of fully explicit Galerkin finite element method. Based on the domain decomposition method in Chapter 3, we propose an iterative algorithm to solve an optimal control problem associated with the corresponding partial differential equation with pointwise constraint for the control variable in Chapter 4. In Chapter 5, overlapping domain decomposition methods are designed for the wave equation on account of prediction-correction" strategy. A family of unit decomposition functions allow reasonable residual distribution or corrections. No iteration is needed in each time step. This dissertation also covers convergence analysis from the point of view of mathematics for each algorithm we present. The main discretization strategy we adopt is finite element method. Moreover, numerical results are provided respectivelyto verify the theory in each chapter.Doctorat en Sciences
info:eu-repo/semantics/nonPublished
24
Ivanov, S. A., e V. G. Korneev. "On the preconditioning in the domain decomposition technique for the p-version finite element method. Part I". Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800856.
Abstract (sommario):
Abstract P-version finite element method for the second order elliptic equation in an arbitrary sufficiently smooth domain is studied in the frame of DD method. Two types square reference elements are used with the products of the integrated Legendre's polynomials for the coordinate functions. There are considered the estimates for the condition numbers, preconditioning of the problems arising on subdomains and the Schur complement, the derivation of the DD preconditioner. For the result we obtain the DD preconditioner to which corresponds the generalized condition number of order (logp )2 . The paper consists of two parts. In part I there are given some preliminary re- sults for 1D case, condition number estimates and some inequalities for 2D reference element.
25
Ivanov, S. A., e V. G. Korneev. "On the preconditioning in the domain decomposition technique for the p-version finite element method. Part II". Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800862.
Abstract (sommario):
P-version finite element method for the second order elliptic equation in an arbitrary sufficiently smooth domain is studied in the frame of DD method. Two types square reference elements are used with the products of the integrated Legendre's polynomials for the coordinate functions. There are considered the estimates for the condition numbers, preconditioning of the problems arising on subdomains and the Schur complement, the derivation of the DD preconditioner. For the result we obtain the DD preconditioner to which corresponds the generalized condition number of order (logp )2 . The paper consists of two parts. In part I there are given some preliminary results for 1D case, condition number estimates and some inequalities for 2D reference element. Part II is devoted to the derivation of the Schur complement preconditioner and conditionality number estimates for the p-version finite element matrixes. Also DD preconditioning is considered.
26
Ott, Julian [Verfasser], e A. [Akademischer Betreuer] Kirsch. "Halfspace Matching: a Domain Decomposition Method for Scattering by 2D Open Waveguides / Julian Ott ; Betreuer: A. Kirsch". Karlsruhe : KIT-Bibliothek, 2017. http://d-nb.info/113602171X/34.
27
Su, G. H., of Western Sydney Nepean University e School of Civic Engineering and Environment. "A new development in domain decomposition techniques for analysis of plates with mixed edge supports". THESIS_XXX_CEE_Su_G.xml, 2000. http://handle.uws.edu.au:8081/1959.7/277.
Abstract (sommario):
The importance of plates, with discontinuities in boundary supports in aeronautical and marine structures, have led to various techniques to solve plate problems with mixed edge support conditions. The domain decomposition method is one of the most effective of these techniques, providing accurate numerical solutions. This method is used to investigate the vibration and buckling of flat, isotropic, thin and elastic plates with mixed edge support conditions. Two practical approaches have been developed as an extension of the domain decomposition method, namely, the primary-secondary domain (PSD) approach and the line-domains (LD) approach. The PSD approach decomposes a plate into one primary domain and one/two secondary domain(s). The LD approach considers interconnecting boundaries as dominant domains whose basic functions take a higher edge restraint from the neighbouring edges. Convergence and comparison studies are carried out on a number of selected rectangular plate cases. Extensive practical plate problems with various shapes, combinations of mixed boundary conditions and different inplane loading conditions have been solved by the PSD and LD approaches.Master of Engineering (Hons)
28
Killian, Tyler Norton Rao S. M. "Fast solution of large-body problems using domain decomposition and null-field generation in the method of moments". Auburn, Ala, 2009. http://hdl.handle.net/10415/1881.
29
Rawat, Vineet. "Finite Element Domain Decomposition with Second Order Transmission Conditions for Time-Harmonic Electromagnetic Problems". The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1243360543.
30
Galia, Antonio. "A Dynamic Homogenization Method for Nuclear Reactor Core Calculations". Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASP042.
Abstract (sommario):
Dans les calculs de réacteurs à trois dimensions, nombreuses techniques d'homogénéisation ont été développées pour l'utilisation du schéma de calcul classique à deux étapes, basé sur les sections efficaces homogénéisées au préalable et utilisées ensuite par interpolation pour un état physique donné.D'autre part, les schémas de calcul basées principalement sur les méthodes des caractéristiques, qui visent le calcul direct du réacteur sans homogénéisation, ont des performances encore limitées en raison des capacités des machines et font alors le recours à des solutions de transport simplifiées. Ce travail a pour objectif d'étudier une nouvelle approche dans laquelle l'homogénéisation dynamique est utilisée pourproduire le flux neutronique de pondération sur les modèles d'assemblage tridimensionnels. L'application de la méthode pour un calcul d'un REP en 3D est comparée aux résultats issus d'un calcul de référence numérique en transport 3D et d'un calcul classique à deux-étapes. La réalisation repose sur le calcul de haute performance et avec un haut niveau de parallélismeThree-dimensional deterministic core calculations are typically based on the classical two-step approach, where the homogenized cross sections of an assembly type are pre-calculated and then interpolated to the actual state in the reactor. The weighting flux used for cross-section homogenization is determined assuming the fundamental mode condition and using a critical-leakage modelthat does not account for the actual environment of an assembly. On the other hand, 3D direct transport calculations and the 2D/1D Fusion method, mostly based on the method of characteristics, have recently been applied showing excellent agreement with reference Monte-Carlo code, but still remaining computationally expensive for multiphysics applications and core depletioncalculations.In the present work, we propose a method of Dynamic Homogenization as an alternative technique for 3D core calculations, in the framework of domain decomposition method that can be massively parallelized. It consists of an iterative process between core and assembly calculationsthat preserves assembly exchanges. The main features of this approach are:i) cross-sections homogenization takes into account the environment of each assembly in the core;ii) the reflector can be homogenized with its realistic 2D geometry and its environment;iii) the method avoids expensive 3D transport calculations;iv) no “off-line” calculation and therefore v) no cross-section interpolation is required.The verification tests on 2D and 3D full core problems are presented applying several homogenization and equivalence techniques, comparing against direct 3D transport calculation. For this analysis, we solved the NEA “PWR MOX/UO2 Core Benchmark” problem, which is characterized by strong radial heterogeneities due to the presence of different types of UOx and MOx assemblies at different burnups. The obtained results show the advantages of the proposed method in terms of precision with respect to two-step and performances with respect to the direct approach
31
Eliasson, Bengt. "Numerical Vlasov–Maxwell Modelling of Space Plasma". Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-2929.
Abstract (sommario):
The Vlasov equation describes the evolution of the distribution function of particles in phase space (x,v), where the particles interact with long-range forces, but where shortrange "collisional" forces are neglected. A space plasma consists of low-mass electrically charged particles, and therefore the most important long-range forces acting in the plasma are the Lorentz forces created by electromagnetic fields. What makes the numerical solution of the Vlasov equation a challenging task is that the fully three-dimensional problem leads to a partial differential equation in the six-dimensional phase space, plus time, making it hard even to store a discretised solution in a computer’s memory. Solutions to the Vlasov equation have also a tendency of becoming oscillatory in velocity space, due to free streaming terms (ballistic particles), in which steep gradients are created and problems of calculating the v (velocity) derivative of the function accurately increase with time. In the present thesis, the numerical treatment is limited to one- and two-dimensional systems, leading to solutions in two- and four-dimensional phase space, respectively, plus time. The numerical method developed is based on the technique of Fourier transforming the Vlasov equation in velocity space and then solving the resulting equation, in which the small-scale information in velocity space is removed through outgoing wave boundary conditions in the Fourier transformed velocity space. The Maxwell equations are rewritten in a form which conserves the divergences of the electric and magnetic fields, by means of the Lorentz potentials. The resulting equations are solved numerically by high order methods, reducing the need for numerical over-sampling of the problem. The algorithm has been implemented in Fortran 90, and the code for solving the one-dimensional Vlasov equation has been parallelised by the method of domain decomposition, and has been implemented using the Message Passing Interface (MPI) method. The code has been used to investigate linear and non-linear interaction between electromagnetic fields, plasma waves, and particles.
32
Edme, Pascal. "Can we apply the receiver function method to OBC data?" Paris, Institut de physique du globe, 2007. http://www.theses.fr/2007GLOB0018.
Abstract (sommario):
In this thesis, we review the Receiver Function (RF) method, conceived many years ago in earthquake seismology, to see whether it can also be used in reflection seismology, and more specifically to see whether it can be applied to ocean-bottom-cable (OBC) data. The conventional RF method is used to determine the local PS wave response of a target zone below a multi-component 3C receiver and has been originally designed to process individual earthquake data of constant ray parameter p, acquired at the free surface. The target is illuminated from below. The converted PS wavefield generated at the receiver side is isolated from the global earth response by deconvolving the horizontal Ux component with the vertical Uz component, where Uz is assumed to contain only the impinging P waves (i. E. The unpredictable effective source function). Simultaneously to the source signature removal, the effect of the deconvolution can be subdivided into two steps: (1) P-PS wave separation and (2) multiples removal. The keyword is combination between components (by adaptive subtraction) or equivalently ratio between components. Our motivation is to reproduce these two steps with OBC data, in order to determine the (separated) primary PP and PS responses generated in the sub-seafloor area. However, there are several issues that require special attention when we implement the RF technique to OBC acquisition geometry. Firstly, the target (i. E. The sub-seafloor) is illuminated from above. Therefore there exist three types of incident waves at the receiver level: the upgoing P and PS wavefields (Pup and Sup as for land data) but also the additional downgoing P wavefield (Pdown). Secondly these wavefields are mixed between the components with time varying ray parameters, which precludes the possibility of applying the RF approach in the conventional time-offset domain. These problems can be addressed by taking into account the additional measurement of the pressure wavefield by the hydrophone Uh and by transforming the data in the ¿ -p domain (requiring fine receiver spacing usually afforded by OBCs). This transformation reorders the data by incidence angle at the receiver level, such that the pure upgoing PP and PS wavefields can be separated, based on polarization angle discrimination. This first step partially addresses the problem of multiples in the data by removing the downgoing (receiver side) water multiples, but it requires the knowledge of the seafloor properties as inputs. The other advantage of the ¿ ¡ p domain is that the water multiple reverberation becomes periodic. Remaining pure upgoing (source-side) water multiples are fully predictable (in contrast to overlapping source-side and receiver-side multiples) and can therefore be removed using predictive deconvolution (this is the required second step). Our adapted version of the RF technique uses the various ratios between components to estimate the elastic properties at the seafloor, as well as calibration operators, required for the decomposition. Our data-driven method can be automatically applied with a minimum of user-defined inputs, by taking advantages of the coherency between adjacent p traces and the redundancy of informations within the multiples. The strategy has been successfully applied to field data. Our results suggest several avenues for further processing
33
Touzeau, Josselyn. "Approches numérique multi-échelle/multi-modèle de la dégradation des matériaux composites". Phd thesis, Ecole Centrale Paris, 2012. http://tel.archives-ouvertes.fr/tel-00837874.
Abstract (sommario):
Nos travaux concernent la mise en oeuvre d'une méthode multiéchelle pour faciliter la simulation numérique de structures complexes, appliquée à la modélisation de composants aéronautiques (notamment pour les pièces tournantes de turboréacteur et des structures composites stratifiées). Ces développements sont basés autour de la méthode Arlequin qui permet d'enrichir des modélisations numériques, à l'aide de patchs, autour de zones d'intérêt où des phénomènes complexes se produisent. Cette méthode est mise en oeuvre dans un cadre général permettant la superposition de maillages incompatibles au sein du code de calcul Z-set{Zébulon, en utilisant une formulation optimale des opérateurs de couplage. La précision et la robustesse de cette approche ont été évaluées sur différents problèmes numériques. Afin d'accroître les performances de la méthode Arlequin, un solveur spécifique basé sur les techniques de décomposition de domaine a été développé pour bénéficier des capacités de calcul offertes par les machines à architectures parallèles. Ces performances ont été évaluées sur différents cas tests académiques et quasi-industriels. Enfin, ces développements ont été appliqué à la simulation de problèmes de structures composites stratifiées.
34
Venet, Cédric. "Méthodes numériques pour la simulation de problèmes acoustiques de grandes tailles". Thesis, Châtenay-Malabry, Ecole centrale de Paris, 2011. http://www.theses.fr/2011ECAP0019.
Abstract (sommario):
Cette thèse s’intéresse à la simulation acoustique de problèmes de grandes tailles. La parallélisation des méthodes numériques d’acoustique est le sujet principal de cette étude. Le manuscrit est composé de trois parties : lancé de rayon, méthodes de décomposition de domaines et algorithmes asynchronesThis thesis studies numerical methods for large-scale acoustic problems. The parallelization of the numerical acoustic methods is the main focus. The manuscript is composed of three parts: ray-tracing, optimized interface conditions for domain decomposition methods and asynchronous iterative algorithms
35
Badillo, Almaraz Hiram. "Numerical modelling based on the multiscale homogenization theory. Application in composite materials and structures". Doctoral thesis, Universitat Politècnica de Catalunya, 2012. http://hdl.handle.net/10803/83924.
Abstract (sommario):
A multi-domain homogenization method is proposed and developed in this thesis based on a two-scale technique. The method is capable of analyzing composite structures with several periodic distributions by partitioning the entire domain of the composite into substructures making use of the classical homogenization theory following a first-order standard continuum mechanics formulation. The need to develop the multi-domain homogenization method arose because current homogenization methods are based on the assumption that the entire domain of the composite is represented by one periodic or quasi-periodic distribution. However, in some cases the structure or composite may be formed by more than one type of periodic domain distribution, making the existing homogenization techniques not suitable to analyze this type of cases in which more than one recurrent configuration appears. The theoretical principles used in the multi-domain homogenization method were applied to assemble a computational tool based on two nested boundary value problems represented by a finite element code in two scales: a) one global scale, which treats the composite as an homogeneous material and deals with the boundary conditions, the loads applied and the different periodic (or quasi-periodic) subdomains that may exist in the composite; and b) one local scale, which obtains the homogenized response of the representative volume element or unit cell, that deals with the geometry distribution and with the material properties of the constituents.
The method is based on the local periodicity hypothesis arising from the periodicity of the internal structure of the composite. The numerical implementation of the restrictions on the displacements and forces corresponding to the degrees of freedom of the domain's boundary derived from the periodicity was performed by means of the Lagrange multipliers method. The formulation included a method to compute the homogenized non-linear tangent constitutive tensor once the threshold of nonlinearity of any of the unit cells has been surpassed. The procedure is based in performing a numerical derivation applying a perturbation technique. The tangent constitutive tensor is computed for each load increment and for each iteration of the analysis once the structure has entered in the non-linear range. The perturbation method was applied at the global and local scales in order to analyze the performance of the method at both scales. A simple average method of the constitutive tensors of the elements of the cell was also explored for comparison purposes. A parallelization process was implemented on the multi-domain homogenization method in order to speed-up the computational process due to the huge computational cost that the nested incremental-iterative solution embraces. The effect of softening in two-scale homogenization was investigated following a smeared cracked approach. Mesh objectivity was discussed first within the classical one-scale FE formulation and then the concepts exposed were extrapolated into the two-scale homogenization framework. The importance of the element characteristic length in a multi-scale analysis was highlighted in the computation of the specific dissipated energy when strain-softening occurs.
Various examples were presented to evaluate and explore the capabilities of the computational approach developed in this research. Several aspects were studied, such as analyzing different composite arrangements that include different types of materials, composites that present softening after the yield point is reached (e.g. damage and plasticity) and composites with zones that present high strain gradients. The examples were carried out in composites with one and with several periodic domains using different unit cell configurations. The examples are compared to benchmark solutions obtained with the classical one-scale FE method.En esta tesis se propone y desarrolla un método de homogeneización multi-dominio basado en una técnica en dos escalas. El método es capaz de analizar estructuras de materiales compuestos con varias distribuciones periódicas dentro de un mismo continuo mediante la partición de todo el dominio del material compuesto en subestructuras utilizando la teoría clásica de homogeneización a través de una formulación estándar de mecánica de medios continuos de primer orden. La necesidad de desarrollar este método multi-dominio surgió porque los métodos actuales de homogeneización se basan en el supuesto de que todo el dominio del material está representado por solo una distribución periódica o cuasi-periódica. Sin embargo, en algunos casos, la estructura puede estar formada por más de un tipo de distribución de dominio periódico. Los principios teóricos desarrollados en el método de homogeneización multi-dominio se aplicaron para ensamblar una herramienta computacional basada en dos problemas de valores de contorno anidados, los cuales son representados por un código de elementos finitos (FE) en dos escalas: a) una escala global, que trata el material compuesto como un material homogéneo. Esta escala se ocupa de las condiciones de contorno, las cargas aplicadas y los diferentes subdominios periódicos (o cuasi-periódicos) que puedan existir en el material compuesto; y b) una escala local, que obtiene la respuesta homogenizada de un volumen representativo o celda unitaria. Esta escala se ocupa de la geometría, y de la distribución espacial de los constituyentes del compuesto así como de sus propiedades constitutivas. El método se basa en la hipótesis de periodicidad local derivada de la periodicidad de la estructura interna del material. La implementación numérica de las restricciones de los desplazamientos y las fuerzas derivadas de la periodicidad se realizaron por medio del método de multiplicadores de Lagrange. La formulación incluye un método para calcular el tensor constitutivo tangente no-lineal homogeneizado una vez que el umbral de la no-linealidad de cualquiera de las celdas unitarias ha sido superado. El procedimiento se basa en llevar a cabo una derivación numérica aplicando una técnica de perturbación. El tensor constitutivo tangente se calcula para cada incremento de carga y para cada iteración del análisis una vez que la estructura ha entrado en el rango no-lineal. El método de perturbación se aplicó tanto en la escala global como en la local con el fin de analizar la efectividad del método en ambas escalas. Se lleva a cabo un proceso de paralelización en el método con el fin de acelerar el proceso de cómputo debido al enorme coste computacional que requiere la solución iterativa incremental anidada. Se investiga el efecto de ablandamiento por deformación en el material usando el método de homogeneización en dos escalas a través de un enfoque de fractura discreta. Se estudió la objetividad en el mallado dentro de la formulación clásica de FE en una escala y luego los conceptos expuestos se extrapolaron en el marco de la homogeneización de dos escalas. Se enfatiza la importancia de la longitud característica del elemento en un análisis multi-escala en el cálculo de la energía específica disipada cuando se produce el efecto de ablandamiento. Se presentan varios ejemplos para evaluar la propuesta computacional desarrollada en esta investigación. Se estudiaron diferentes configuraciones de compuestos que incluyen diferentes tipos de materiales, así como compuestos que presentan ablandamiento después de que el punto de fluencia del material se alcanza (usando daño y plasticidad) y compuestos con zonas que presentan altos gradientes de deformación. Los ejemplos se llevaron a cabo en materiales compuestos con uno y con varios dominios periódicos utilizando diferentes configuraciones de células unitarias. Los ejemplos se comparan con soluciones de referencia obtenidas con el método clásico de elementos finitos en una escala.
36
Badillo, Almaraz Hiram. "Numerial modelling based on the multiscale homogenization theory. Application in composite materials and structures". Doctoral thesis, Universitat Politècnica de Catalunya, 2012. http://hdl.handle.net/10803/83924.
Abstract (sommario):
A multi-domain homogenization method is proposed and developed in this thesis based on a two-scale technique. The method is capable of analyzing composite structures with several periodic distributions by partitioning the entire domain of the composite into substructures making use of the classical homogenization theory following a first-order standard continuum mechanics formulation. The need to develop the multi-domain homogenization method arose because current homogenization methods are based on the assumption that the entire domain of the composite is represented by one periodic or quasi-periodic distribution. However, in some cases the structure or composite may be formed by more than one type of periodic domain distribution, making the existing homogenization techniques not suitable to analyze this type of cases in which more than one recurrent configuration appears. The theoretical principles used in the multi-domain homogenization method were applied to assemble a computational tool based on two nested boundary value problems represented by a finite element code in two scales: a) one global scale, which treats the composite as an homogeneous material and deals with the boundary conditions, the loads applied and the different periodic (or quasi-periodic) subdomains that may exist in the composite; and b) one local scale, which obtains the homogenized response of the representative volume element or unit cell, that deals with the geometry distribution and with the material properties of the constituents.
The method is based on the local periodicity hypothesis arising from the periodicity of the internal structure of the composite. The numerical implementation of the restrictions on the displacements and forces corresponding to the degrees of freedom of the domain's boundary derived from the periodicity was performed by means of the Lagrange multipliers method. The formulation included a method to compute the homogenized non-linear tangent constitutive tensor once the threshold of nonlinearity of any of the unit cells has been surpassed. The procedure is based in performing a numerical derivation applying a perturbation technique. The tangent constitutive tensor is computed for each load increment and for each iteration of the analysis once the structure has entered in the non-linear range. The perturbation method was applied at the global and local scales in order to analyze the performance of the method at both scales. A simple average method of the constitutive tensors of the elements of the cell was also explored for comparison purposes. A parallelization process was implemented on the multi-domain homogenization method in order to speed-up the computational process due to the huge computational cost that the nested incremental-iterative solution embraces. The effect of softening in two-scale homogenization was investigated following a smeared cracked approach. Mesh objectivity was discussed first within the classical one-scale FE formulation and then the concepts exposed were extrapolated into the two-scale homogenization framework. The importance of the element characteristic length in a multi-scale analysis was highlighted in the computation of the specific dissipated energy when strain-softening occurs.
Various examples were presented to evaluate and explore the capabilities of the computational approach developed in this research. Several aspects were studied, such as analyzing different composite arrangements that include different types of materials, composites that present softening after the yield point is reached (e.g. damage and plasticity) and composites with zones that present high strain gradients. The examples were carried out in composites with one and with several periodic domains using different unit cell configurations. The examples are compared to benchmark solutions obtained with the classical one-scale FE method.En esta tesis se propone y desarrolla un método de homogeneización multi-dominio basado en una técnica en dos escalas. El método es capaz de analizar estructuras de materiales compuestos con varias distribuciones periódicas dentro de un mismo continuo mediante la partición de todo el dominio del material compuesto en subestructuras utilizando la teoría clásica de homogeneización a través de una formulación estándar de mecánica de medios continuos de primer orden. La necesidad de desarrollar este método multi-dominio surgió porque los métodos actuales de homogeneización se basan en el supuesto de que todo el dominio del material está representado por solo una distribución periódica o cuasi-periódica. Sin embargo, en algunos casos, la estructura puede estar formada por más de un tipo de distribución de dominio periódico. Los principios teóricos desarrollados en el método de homogeneización multi-dominio se aplicaron para ensamblar una herramienta computacional basada en dos problemas de valores de contorno anidados, los cuales son representados por un código de elementos finitos (FE) en dos escalas: a) una escala global, que trata el material compuesto como un material homogéneo. Esta escala se ocupa de las condiciones de contorno, las cargas aplicadas y los diferentes subdominios periódicos (o cuasi-periódicos) que puedan existir en el material compuesto; y b) una escala local, que obtiene la respuesta homogenizada de un volumen representativo o celda unitaria. Esta escala se ocupa de la geometría, y de la distribución espacial de los constituyentes del compuesto así como de sus propiedades constitutivas. El método se basa en la hipótesis de periodicidad local derivada de la periodicidad de la estructura interna del material. La implementación numérica de las restricciones de los desplazamientos y las fuerzas derivadas de la periodicidad se realizaron por medio del método de multiplicadores de Lagrange. La formulación incluye un método para calcular el tensor constitutivo tangente no-lineal homogeneizado una vez que el umbral de la no-linealidad de cualquiera de las celdas unitarias ha sido superado. El procedimiento se basa en llevar a cabo una derivación numérica aplicando una técnica de perturbación. El tensor constitutivo tangente se calcula para cada incremento de carga y para cada iteración del análisis una vez que la estructura ha entrado en el rango no-lineal. El método de perturbación se aplicó tanto en la escala global como en la local con el fin de analizar la efectividad del método en ambas escalas. Se lleva a cabo un proceso de paralelización en el método con el fin de acelerar el proceso de cómputo debido al enorme coste computacional que requiere la solución iterativa incremental anidada. Se investiga el efecto de ablandamiento por deformación en el material usando el método de homogeneización en dos escalas a través de un enfoque de fractura discreta. Se estudió la objetividad en el mallado dentro de la formulación clásica de FE en una escala y luego los conceptos expuestos se extrapolaron en el marco de la homogeneización de dos escalas. Se enfatiza la importancia de la longitud característica del elemento en un análisis multi-escala en el cálculo de la energía específica disipada cuando se produce el efecto de ablandamiento. Se presentan varios ejemplos para evaluar la propuesta computacional desarrollada en esta investigación. Se estudiaron diferentes configuraciones de compuestos que incluyen diferentes tipos de materiales, así como compuestos que presentan ablandamiento después de que el punto de fluencia del material se alcanza (usando daño y plasticidad) y compuestos con zonas que presentan altos gradientes de deformación. Los ejemplos se llevaron a cabo en materiales compuestos con uno y con varios dominios periódicos utilizando diferentes configuraciones de células unitarias. Los ejemplos se comparan con soluciones de referencia obtenidas con el método clásico de elementos finitos en una escala.
37
Lu, Jiaqing. "Numerical Modeling and Computation of Radio Frequency Devices". The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1543457620064355.
38
ECHEVERRI, BAUTISTA MARIO ALBERTO. "Fast solvers for integral equations in electromagnetics". Doctoral thesis, Politecnico di Torino, 2016. http://hdl.handle.net/11583/2643088.
Abstract (sommario):
The purpose of this thesis is the advancement of numerical techniques in computational
electromagnetics (CEM), specifically in the area of integral equation formulations in the
frequency domain. The research has been focused on the solution of multi-scale, realistic,
3D surface problems using the Method of Moments (MoM). Several state of the art (e.g.
with computational costs lower than N2, with N the number of unknowns in the problem)
solutions to well-known issues are proposed.
The research addresses two important branches in CEM: compression techniques and
convergence improvement for iterative solutions. In the compression techniques area, the
objective were the so called kernel independent schemes, which work directly on matrix
entries (e.g. MoM matrix elements) rather than modifying the computation of these;
this kind of schemes is applicable to a broad span of problems (with different kernels)
without substantial modifications. The convergence acceleration of iterative solutions
was tackled from the low frequency stabilization of kernel independent solvers to a new
Domain Decomposition scheme for intermediate and high frequencies.
39
Hamadi, Riad. "Méthodes de décompositions de domaines pour la résolution des CSP : application au système OSIRIS". Université Joseph Fourier (Grenoble ; 1971-2015), 1997. http://www.theses.fr/1997GRE10203.
Abstract (sommario):
La premiere partie de ce travail presente une approche de decomposition de domaines pour resoudre les problemes de satisfaction de contraintes (csp) discrets et continus lineaires. L'approche repose sur : 1 - la representation d'un csp par un graphe appele la micro-structure du csp. 2- la decomposition du csp en sous-csp definis a partir de cliques maximales de la micro-structure. Dans la premiere partie, on presente la methode de decomposition de domaine developpee par jegou en 1993 pour resoudre les csp binaires discrets. Puis on propose une extension de cette methode pour resoudre les csp discrets n-aires et les csp continus lineaires. La seconde partie de ce travail presente l'utilisation de la methode de decomposition de domaine pour definir et resoudre les csp discrets et continus lineaires dans un systeme de representation de connaissances, osiris, ainsi que l'utilisation de micro-structures pour le classement d'objets.
40
Sombra, Tiago GuimarÃes. "An adaptive parametric surface mesh generation parallel method guided by curvatures". Universidade Federal do CearÃ, 2016. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=16628.
Abstract (sommario):
CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel SuperiorThis work describes a technique for generating parametric surfaces meshes using parallel computing, with distributed memory processors. The input for the algorithm is a set of parametric patches that model the surface of a given object. A structure for spatial partitioning is proposed to decompose the domain in as many subdomains as processes in the parallel system. Each subdomain consists of a set of patches and the division of its load is guided following an estimate. This decomposition attempts to balance the amount of work in all the subdomains. The amount of work, known as load, of any mesh generator is usually given as a function of its output size, i.e., the size of the generated mesh. Therefore, a technique to estimate the size of this mesh, the total load of the domain, is needed beforehand. This work makes use of an analytical average curvature calculated for each patch, which in turn is input data to estimate this load and the decomposition is made from this analytical mean curvature. Once the domain is decomposed, each process generates the mesh on that subdomain or set of patches by a quad tree technique for inner regions, advancing front technique for border regions and is finally applied an improvement to mesh generated. This technique presented good speed-up results, keeping the quality of the mesh comparable to the quality of the serially generated mesh.
Este trabalho descreve uma tÃcnica para gerar malhas de superfÃcies paramÃtricas utilizando computaÃÃo paralela, com processadores de memÃria compartilhada. A entrada para o algoritmo à um conjunto de patches paramÃtricos que modela a superfÃcie de um determinado objeto. Uma estrutura de partiÃÃo espacial à proposta para decompor o domÃnio em tantos subdomÃnios quantos forem os processos no sistema paralelo. Cada subdomÃnio à formado por um conjunto de patches e a divisÃo de sua carga à guiada seguindo uma estimativa de carga. Esta decomposiÃÃo tenta equilibrar a quantidade de trabalho em todos os subdomÃnios. A quantidade de trabalho, conhecida como carga, de qualquer gerador de malha à geralmente dada em funÃÃo do tamanho da saÃda do algoritmo, ou seja, do tamanho da malha gerada. Assim, faz-se necessÃria uma tÃcnica para estimar previamente o tamanho dessa malha, que à a carga total do domÃnio. Este trabalho utiliza-se de um cÃlculo de curvatura analÃtica mÃdia para cada patch, que por sua vez, à dado de entrada para estimar esta carga e a decomposiÃÃo à feita a partir dessa curvatura analÃtica mÃdia. Uma vez decomposto o domÃnio, cada processo gera a malha em seu subdomÃnio ou conjunto de patches pela tÃcnica de quadtree para regiÃes internas, avanÃo de fronteira para regiÃes de fronteira e por fim à aplicado um melhoramento na malha gerada. Esta tÃcnica apresentou bons resultados de speed-up, mantendo a qualidade da malha comparÃvel à qualidade da malha gerada de forma sequencial.
41
Fu, Lin [Verfasser], Xiangyu [Akademischer Betreuer] [Gutachter] Hu, Takayuki [Gutachter] Aoki e Nikolaus A. [Gutachter] Adams. "Numerical methods for computational fluid dynamics - a new ENO paradigm and a new domain decomposition method / Lin Fu ; Gutachter: Takayuki Aoki, Nikolaus A. Adams, Xiangyu Hu ; Betreuer: Xiangyu Hu". München : Universitätsbibliothek der TU München, 2017. http://d-nb.info/1141904691/34.
42
PIOLDI, Fabio. "Time and Frequency Domain output-only system identification from earthquake-induced structural response signals". Doctoral thesis, Università degli studi di Bergamo, 2017. http://hdl.handle.net/10446/77137.
Abstract (sommario):
Output-only Time and Frequency Domain system identification techniques are developed in this doctoral dissertation towards the challenging assessment of current structural dynamic properties of buildings from earthquake-induced structural response signals, at simultaneous heavy damping. Three different Operational Modal Analysis (OMA) techniques, namely a refined Frequency Domain Decomposition (rFDD) algorithm, an improved Data-Driven Stochastic Subspace Identification (SSI-DATA) procedure and a novel Full Dynamic Compound Inverse Method (FDCIM) are formulated and implemented within MATLAB, and exploited for the strong ground motion modal dynamic identification of selected buildings.
First, the three OMA methods are validated by the adoption of synthetic earthquake-induced structural response signals, generated from numerical integration on benchmark linear shear-type frames. Then, real seismic response signals are effectively processed, by getting even closer to real Earthquake Engineering identification scenarios. In the end, the three OMA methods are systematically applied and compared.
The present thesis demonstrates the reliability and effectiveness of such advanced OMA methods, as convenient output-only modal identification tools for Earthquake Engineering and Structural Health Monitoring purposes.
43
Cetin, Halil Ibrahim. "Mathematical Modeling Of Supercritical Fluid Extraction Of Biomaterials". Phd thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/2/12608657/index.pdf.
Abstract (sommario):
Supercritical fluid extraction has been used to recover biomaterials from natural matrices. Mathematical modeling of the extraction is required for process design and scale up. Existing models in literature are correlative and dependent upon the experimental data. Construction of predictive models giving reliable results in the lack of experimental data is precious. The long term objective of this study was to construct a predictive mass transfer model, representing supercritical fluid extraction of biomaterials in packed beds by the method of volume averaging. In order to develop mass transfer equations in terms of volume averaged variables, velocity and velocity deviation fields, closure variables were solved for a specific case and the coefficients of
volume averaged mass transfer equation for the specific case were computed using one and two-dimensional geometries via analytical and numerical solutions, respectively. Spectral Element method with Domain Decomposition technique, Preconditioned Conjugate Gradient algorithm and Uzawa method were used for
the numerical solution. The coefficients of convective term with additional terms of volume averaged mass transfer equation were similar to superficial velocity. The coefficients of dispersion term were close to diffusivity of oil in supercritical carbon dioxide. The
coefficients of interphase mass transfer term were overestimated in both geometries. Modifications in boundary conditions, change in geometry of particles and use of three-dimensional computations would improve the value of the coefficient of interphase mass transfer term.
44
Oumaziz, Paul. "Une méthode de décomposition de domaine mixte non-intrusive pour le calcul parallèle d’assemblages". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLN030/document.
Abstract (sommario):
Les assemblages sont des éléments critiques pour les structures industrielles. De fortes non-linéarités de type contact frottant, ainsi que des précharges mal maîtrisées rendent complexe tout dimensionnement précis. Présents en très grand nombre sur les structures industrielles (quelques millions pour un A380), cela implique de rafiner les modèles localement et donc de gérer des problèmes numé-riques de très grandes tailles. Les nombreuses interfaces de contact frottant sont des sources de difficultés de convergence pour les simulations numériques. Il est donc nécessaire de faire appel à des méthodes robustes. Il s’agit d’utiliser des méthodes itératives de décomposition de domaine, permettant de gérer des modèles numériques extrêmement grands, couplées à des techniques adaptées afin de prendre en compte les non-linéarités de contact aux interfaces entre sous-domaines. Ces méthodes de décomposition de domaine restent encore très peu utilisées dans un cadre industriel. Des développements internes aux codes éléments finis sont souvent nécessaires et freinent ce transfert du monde académique au monde industriel.Nous proposons, dans ces travaux de thèse, une mise-en-oeuvre non intrusive de ces méthodes de décomposition de domaine : c’est-à-dire sans développement au sein du code source. En particulier, nous nous intéressons à la méthode Latin dont la philosophie est particulièrement adaptée aux problèmes non linéaires. La structure est décomposée en sous-domaines reliés entre eux au travers d’interfaces. Avec la méthode Latin, les non-linéarités sont résolues séparément des aspects linéaires. La résolution est basée sur un schéma itératif à deux directions de recherche qui font dialoguer les problèmes linéaires globaux etles problèmes locaux non linéaires.Au cours de ces années de thèse, nous avons développé un outil totalement non intrusif sous Code_Aster permettant de résoudre par une technique de décomposition de domaine mixte des problèmes d’assemblage. Les difficultés posées par le caractère mixte de la méthode Latin sont résolues par l’introduction d’une direction de recherche non locale. Des conditions de Robin sur les interfaces des sous-domaines sont alors prises en compte simplement sans modifier les sources de Code_Aster. Nous avons proposé une réécriture algébrique de l’approche multi-échelle assurant l’extensibilité de la méthode. Nous nous sommes aussi intéressés à coupler la méthode Latin en décomposition de domaine à un algorithme de Krylov. Appliqué uniquement à un problème sous-structuré avec interfaces parfaites, ce couplage permet d’accélérer la convergence. Des structures préchargées avec de nombreuses interfaces de contact frottant ont été traitées. Des simulations qui n’auraient pu être menées par un calcul direct sous Code_Aster ont été réalisées via cette stratégie de décomposition de domaine non intrusiveAbstract : Assemblies are critical elements for industrial structures. Strong non-linearities such as frictional contact, as well as poorly controlled preloads make complex all accurate sizing. Present in large numbers on industrial structures (a few million for an A380), this involves managing numerical problems of very large size. The numerous interfaces of frictional contact are sources of difficulties of convergence for the numerical simulations. It is therefore necessary to use robust but also reliable methods. The use of iterative methods based on domain decomposition allows to manage extremely large numerical models. This needs to be coupled with adaptedtechniques in order to take into account the nonlinearities of contact at the interfaces between subdomains. These methods of domain decomposition are still scarcely used in industries. Internal developments in finite element codes are often necessary, and thus restrain this transfer from the academic world to the industrial world.In this thesis, we propose a non-intrusive implementation of these methods of domain decomposition : that is, without development within the source code. In particular, we are interested in the Latin method whose philosophy is particularly adapted to nonlinear problems. It consists in decomposing the structure into sub-domains that are connected through interfaces. With the Latin method the non-linearities are solved separately from the linear differential aspects. Then the resolution is based on an iterative scheme with two search directions that make the global linear problems and the nonlinear local problems dialogue.During this thesis, a totally non-intrusive tool was developed in Code_Aster to solve assembly problems by a mixed domain decomposition technique. The difficulties posed by the mixed aspect of the Latin method are solved by the introduction of a non-local search direction. Robin conditions on the subdomain interfaces are taken into account simply without modifying the sources of Code_Aster. We proposed an algebraic rewriting of the multi-scale approach ensuring the extensibility of the method. We were also interested in coupling the Latin method in domain decomposition to a Krylov algorithm. Applied only to a substructured problem with perfect interfaces, this coupling accelerates the convergence. Preloaded structures with numerous contact interfaces have been processed. Simulations that could not be carried out by a direct computationwith Code_Aster were performed via this non-intrusive domain decomposition strategy
45
Rizzi, Rogerio Luis. "Modelo computacional paralelo para a hidrodinâmica e para o transporte de substâncias bidimensional e tridimensional". reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2002. http://hdl.handle.net/10183/10416.
Abstract (sommario):
Neste trabalho desenvolveu-se e implementou-se um modelo computacional paralelo multifísica para a simulação do transporte de substâncias e do escoamento hidrodinâmico, bidimensional (2D) e tridimensional (3D), em corpos de água. Sua motivação está centrada no fato de que as margens e zonas costeiras de rios, lagos, estuários, mares e oceanos são locais de aglomerações de seres humanos, dada a sua importância para as atividades econômica, de transporte e de lazer, causando desequilíbrios a esses ecossistemas. Esse fato impulsiona o desenvolvimento de pesquisas relativas a esta temática. Portanto, o objetivo deste trabalho é o de construir um modelo computacional com alta qualidade numérica, que possibilite simular os comportamentos da hidrodinâmica e do transporte escalar de substâncias em corpos de água com complexa configuração geométrica, visando a contribuir para seu manejo racional. Visto que a ênfase nessa tese são os aspectos numéricos e computacionais dos algoritmos, analisaram-se as características e propriedades numérico-computacionais que as soluções devem contemplar, tais como a estabilidade, a monotonicidade, a positividade e a conservação da massa. As estratégias de soluções enfocam os termos advectivos e difusivos, horizontais e verticais, da equação do transporte. Desse modo, a advecção horizontal é resolvida empregando o método da limitação dos fluxos de Sweby, e o transporte vertical (advecção e difusão) é resolvido com os métodos beta de Gross e de Crank-Nicolson. São empregadas malhas com distintas resoluções para a solução do problema multifísica. O esquema numérico resultante é semi-implícito, computacionalmente eficiente, estável e fornece acurácia espacial e temporal de segunda ordem. Os sistemas de equações resultantes da discretização, em diferenças finitas, das equações do escoamento e do transporte 3D, são de grande porte, lineares, esparsos e simétricos definidos-positivos (SDP). No caso 2D os sistemas são lineares, mas os sistemas de equações para a equação do transporte não são simétricos. Assim, para a solução de sistemas de equações SDP e dos sistemas não simétricos empregam-se, respectivamente, os métodos do subespaço de Krylov do gradiente conjugado e do resíduo mínimo generalizado. No caso da solução dos sistemas 3-diagonal, utiliza-se o algoritmo de Thomas e o algoritmo de Cholesky. A solução paralela foi obtida sob duas abordagens. A decomposição ou particionamento de dados, onde as operações e os dados são distribuídos entre os processos disponíveis e são resolvidos em paralelo. E, a decomposição de domínio, onde obtém-se a solução do problema global combinando as soluções de subproblemas locais. Em particular, emprega-se neste trabalho, o método de decomposição de domínio aditivo de Schwarz, como método de solução, e como pré-condicionador. Para maximizar a relação computação/comunicação, visto que a eficiência computacional da solução paralela depende diretamente do balanceamento de carga e da minimização da comunicação entre os processos, empregou-se algoritmos de particionamento de grafos para obter localmente os subproblemas, ou as partes dos dados. O modelo computacional paralelo resultante mostrou-se computacionalmente eficiente e com alta qualidade numérica.A multi-physics parallel computational model was developed and implemented for the simulation of substance transport and for the two-dimensional (2D) and threedimensional (3D) hydrodynamic flow in water bodies. The motivation for this work is focused in the fact that the margins and coastal zones of rivers, lakes, estuaries, seas and oceans are places of human agglomeration, because of their importance for economic, transport, and leisure activities causing ecosystem disequilibrium. This fact stimulates the researches related to this topic. Therefore, the goal of this work is to build a computational model of high numerical quality, that allows the simulation of hydrodynamics and of scalar transport of substances behavior in water bodies of complex configuration, aiming at their rational management. Since the focuses of this thesis are the numerical and computational aspects of the algorithms, the main numerical-computational characteristics and properties that the solutions need to fulfill were analyzed. That is: stability, monotonicity, positivity and mass conservation. Solution strategies focus on advective and diffusive terms, horizontal and vertical terms of the transport equation. In this way, horizontal advection is solved using Sweby’s flow limiting method; and the vertical transport (advection and diffusion) is solved with Gross and Crank-Nicolson’s beta methods. Meshes of different resolutions are employed in the solution of the multi-physics problem. The resulting numerical scheme is semi-implicit, computationally efficient, stable and provides second order accuracy in space and in time. The equation systems resulting of the discretization, in finite differences, of the flow and 3D transport are of large scale, linear, sparse and symmetric positive definite (SPD). In the 2D case, the systems are linear, but the equation systems for the transport equation are not symmetric. Therefore, for the solution of SPD equation systems and of the non-symmetric systems we employ, respectively, the methods of Krylov’s sub-space of the conjugate gradient and of the generalized minimum residue. In the case of the solution of 3-diagonal systems, Thomas algorithm and Cholesky algorithm are used. The parallel solution was obtained through two approaches. In data decomposition or partitioning, operation and data are distributed among the processes available and are solved in parallel. In domain decomposition the solution of the global problem is obtained combining the solutions of the local sub-problems. In particular, in this work, Schwarz additive domain decomposition method is used as solution method and as preconditioner. In order to maximize the computation/communication relation, since the computational efficiency of the parallel solution depends directly of the load balancing and of the minimization of the communication between processes, graph-partitioning algorithms were used to obtain the sub-problems or part of the data locally. The resulting parallel computational model is computationally efficient and of high numerical quality.
46
Hendili, Sofiane. "Structures élastiques comportant une fine couche hétérogénéités : étude asymptotique et numérique". Thesis, Montpellier 2, 2012. http://www.theses.fr/2012MON20051/document.
Abstract (sommario):
Cette thèse est consacrée à l'étude de l'influence d'une fine couche hétérogène sur le comportement élastique linéaire d'une structure tridimensionnelle.Deux types d'hétérogénéités sont pris en compte : des cavités et des inclusions élastiques. Une étude complémentaire, dans le cas d'inclusions de grande rigidité, a été réalisée en considérant un problème de conduction thermique.Une analyse formelle par la méthode des développements asymptotiques raccordés conduit à un problème d'interface qui caractérise le comportement macroscopique de la structure. Le comportement microscopique de la couche est lui déterminé sur une cellule de base. Le modèle asymptotique obtenu est ensuite implémenté dans un code éléments finis. Une étude numérique permet de valider les résultats de l'analyse asymptotiqueThis thesis is devoted to the study of the influence of a thin heterogeneous layeron the linear elastic behavior of a three-dimensional structure. Two types of heterogeneties are considered : cavities and elastic inclusions. For inclusions of high rigidty a further study was performed in the case of a heat conduction problem.A formal analysis using the matched asymptotic expansions method leads to an interface problem which characterizes the macroscopic behavior of the structure. The microscopic behavior of the layer is determined in a basic cell.The asymptotic model obtained is then implemented in a finite element software.A numerical study is used to validate the results of the asymptotic analysis
47
Parolin, Émile. "Méthodes de décomposition de domaine sans recouvrement avec opérateurs de transmission non-locaux pour des problèmes de propagation d'ondes harmoniques". Thesis, Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAE011.
Abstract (sommario):
Les premiers travaux de B. Després, puis M. Gander, F. Magoulès et F. Nataf ont montré qu'il est nécessaire, du moins dans le contexte des équations d'ondes, d'utiliser des conditions de transmission de type impédante pour le couplage des sous-domaines afin d'obtenir la convergence des méthodes de décomposition de domaine sans-recouvrement. L'approche standard considérée dans la littérature utilise un opérateur d'impédance local permettant une convergence algébrique dans les meilleurs cas. Des travaux ultérieurs dus à F. Collino, S. Ghanemi et P. Joly puis F. Collino, P. Joly et M. Lecouvez ont permis de montrer que l'utilisation d'opérateurs d'impédance non-locaux, comme par exemple des opérateurs intégraux avec des noyaux singuliers adaptés, peut permettre une convergence géométrique des méthodes de décomposition de domaine.Cette thèse prolonge ces travaux (qui ont principalement concerné l'équation de Helmholtz scalaire) pour dans un premier temps étendre l'analyse au cas de la propagation d'ondes électromagnétiques. De plus, l'analyse numérique de la méthode est pour la première fois effectuée, démontrant la stabilité du taux de convergence par rapport au paramètre de discrétisation, et ainsi la robustesse de l'approche. Plusieurs opérateurs intégraux sont ensuite proposés comme opérateurs de transmission pour les équations de Maxwell dans le même esprit que ceux construits pour le cas de l'acoustique. Une alternative aux opérateurs intégraux, fondée sur la résolution de problèmes auxiliaires elliptiques, est par ailleurs proposée et étudiée. De nombreuses expériences numériques ont été menées, illustrant le haut potentiel de cette nouvelle approche. A partir de récents travaux de X. Claeys, la dernière partie de ce travail consiste à exploiter le formalisme multi-trace afin d'étendre l'analyse au cas des partitions comportant des points de jonction, problème ayant attiré beaucoup d'attention récemment. Cette nouvelle approche met en jeu un nouvel opérateur permettant la communication d'informations entre sous-domaines, qui a vocation à remplacer l'opérateur point-à-point classique. Une preuve de convergence géométrique de l'algorithme itératif associé, également uniforme par rapport au paramètre de discrétisation, est disponible et l'on montre que l'on retrouve l'algorithme classique en l'absence de point de jonctionThe pioneering work of B. Després then M. Gander, F. Magoulès and F. Nataf have shown that it is mandatory, at least in the context of wave equations, to use impedance type transmission conditions in the coupling of subdomains in order to obtain convergence of non-overlapping domain decomposition methods (DDM). In the standard approach considered in the literature, the impedance operator involved in the transmission conditions is local and leads to algebraic convergence of the DDM in the best cases. In later works, F. Collino, S. Ghanemi and P. Joly then F. Collino, P. Joly and M. Lecouvez have observed that using non local impedance operators such as integral operators with suitable singular kernels could lead to a geometric convergence of the DDM.This thesis extends these works (that mainly concerned the scalar Helmholtz equation) with the extension of the analysis to electromagnetic wave propagation. Besides, the numerical analysis of the method is performed for the first time, proving the stability of the convergence rate with respect to the discretization parameter, hence the robustness of the approach. Several integral operators are then proposed as transmission operators for Maxwell equations in the spirit of those constructed for the acoustic setting. An alternative to integral operators, based on the resolution of elliptic auxiliary problems, is also advocated and analyzed. Extensive numerical results are conducted, illustrating the high potential of the new approach. Based on a recent work by X. Claeys, the last part of this work consists in exploiting the multi-trace formalism to extend the convergence analysis to the case of partitions with junction points, which is a difficult problem that attracted a lot of attention recently. The new approach relies on a new operator that communicates information between sub-domains, which replaces the classical point-to-point exchange operator. A proof of geometrical convergence of the associated iterative algorithm, again uniform with respect to the discretization parameter, is available and we show that one recovers the standard algorithm in the absence of junction points
48
Kosior, Francis. "Méthode de décomposition par sous-domaines et intégrales de frontières application à l'étude du contact entre deux solides déformables". Vandoeuvre-les-Nancy, INPL, 1997. http://docnum.univ-lorraine.fr/public/INPL_T_1997_KOSIOR_F.pdf.
Abstract (sommario):
Ce mémoire a pour objectif la modélisation du problème de contact avec frottement par une technique de décomposition couplée aux éléments frontières. La méthode de décomposition offre l'avantage de traiter le problème sur chaque solide séparément, ce qui diminue sensiblement la taille des systèmes à résoudre. Le contact étant régi par des conditions portant uniquement sur l'interface, la méthode du complément de Schur, technique de décomposition sans recouvrement, est particulièrement bien adaptée. Dans ce cas, seules les informations à l'interface sont transmises d'un sous-domaine à l'autre. Ceci nous conduit naturellement à l'associer à la méthode des éléments frontières. En effet, celle-ci nécessite simplement la discrétisation des frontières des solides. De plus, les déplacements et les contraintes à la frontière sont calculés directement et de façon plus précise qu'avec les éléments finis. Ce travail s'est concrétisé par la mise au point de trois codes de calculs sur micro-ordinateur : _ un code d'éléments frontières. Il se compose d'un mailleur et d'un solveur, traitant des structures planes en élasticité classique. Nous le testons avec succès par la résolution de problèmes de référence. Nous comparons ses performances à celles d'autres logiciels d'éléments finis et d'éléments frontières, _ un code de décomposition. Il met en œuvre une variante de la méthode d'Hennizel. Il se compose d'un solveur, traitant des structures planes constituées de plusieurs matériaux en élasticité classique, _ un code de résolution du contact. Il résout le problème du contact bilatéral ou unilatéral avec frottement de Coulomb entre deux solides déformables. Nous appliquons ce logiciel à l'étude de l'indentation d'un support par un poinçon plat et une bille. Dans ce dernier cas, nos résultats sont conformes à la théorie d’Hertz et en accord avec la solution analytique de Spence.
49
Cagniart, Nicolas. "Quelques approches non linéaires en réduction de complexité". Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS194/document.
Abstract (sommario):
Les méthodes de réduction de modèles offrent un cadre général permettant une réduction de coûts de calculs substantielle pour les simulations numériques. Dans cette thèse, nous proposons d’étendre le domaine d’application de ces méthodes. Le point commun des sujets discutés est la tentative de dépasser le cadre standard «bases réduites» linéaires, qui ne traite que les cas où les variétés solutions ont une petite épaisseur de Kolmogorov. Nous verrons comment tronquer, translater, tourner, étirer, comprimer etc. puis recombiner les solutions, peut parfois permettre de contourner le problème qui se pose lorsque cette épaisseur de Kolmogorov n’est pas petite. Nous évoquerons aussi le besoin de méthodes de stabilisation sur-mesure pour le cadre réduitModel reduction methods provide a general framework for substantially reducing computational costs of numerical simulations. In this thesis, we propose to extend the scope of these methods. The common point of the topics discussed here is the attempt to go beyond the standard linear "reduced basis" framework, which only deals with cases where the solution manifold have a small Kolmogorov width. We shall see how truncate, translate, rotate, stretch, compress etc. and then recombine the solutions, can sometimes help to overcome the problem when this Kolmogorov width is not small. We will also discuss the need for tailor-made stabilisation methods for the reduced frame
50
Palin, Marcelo Facio. "Técnicas de decomposição de domínio em computação paralela para simulação de campos eletromagnéticos pelo método dos elementos finitos". Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/3/3143/tde-08012008-122101/.
Abstract (sommario):
Este trabalho apresenta a aplicação de técnicas de Decomposição de Domínio e Processamento Paralelo na solução de grandes sistemas de equações algébricas lineares provenientes da modelagem de fenômenos eletromagnéticos pelo Método de Elementos Finitos. Foram implementadas as técnicas dos tipos Complemento de Schur e o Método Aditivo de Schwarz, adaptadas para a resolução desses sistemas em cluster de computadores do tipo Beowulf e com troca de mensagens através da Biblioteca MPI. A divisão e balanceamento de carga entre os processadores são feitos pelo pacote METIS. Essa metodologia foi testada acoplada a métodos, seja iterativo (ICCG), seja direto (LU) na etapa de resolução dos sistemas referentes aos nós internos de cada partição. Para a resolução do sistema envolvendo os nós de fronteira, no caso do Complemento de Schur, utilizou-se uma implementação paralisada do Método de Gradientes Conjugados (PCG). S~ao discutidos aspectos relacionados ao desempenho dessas técnicas quando aplicadas em sistemas de grande porte. As técnicas foram testadas na solução de problemas de aplicação do Método de Elementos Finitos na Engenharia Elétrica (Magnetostática, Eletrocinética e Magnetodinâmica), sejam eles de natureza bidimensional com malhas não estruturadas, seja tridimensional, com malhas estruturadas.This work presents the study of Domain Decomposition and Parallel Processing Techniques applied to the solution of systems of algebraic equations issued from the Finite Element Analysis of Electromagnetic Phenomena. Both Schur Complement and Schwarz Additive techniques were implemented. They were adapted to solve the linear systems in Beowulf clusters with the use of MPI library for message exchange. The load balance among processors is made with the aid of METIS package. The methodology was tested in association to either iterative (ICCG) or direct (LU) methods in order to solve the system related to the inner nodes of each partition. In the case of Schur Complement, the solution of the system related to the boundary nodes was performed with a parallelized Conjugated Gradient Method (PCG). Some aspects of the peformance of these techniques when applied to large scale problems have also been discussed. The techniques has been tested in the simulation of a collection of problems of Electrical Engineering, modelled by the Finite Element Method, both in two dimensions with unstructured meshes (Magnetostatics) and three dimensions with structured meshes (Electrokinetics).