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Articoli di riviste sul tema "Optimized domain decomposition method":

1

Ouyang, Chun-Juan, Chang-Xin Liu, Ming Leng e Huan Liu. "An OMP Steganographic Algorithm Optimized by SFLA". International Journal of Pattern Recognition and Artificial Intelligence 31, n. 01 (gennaio 2017): 1754001. http://dx.doi.org/10.1142/s0218001417540015.

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In this paper, we propose a novel steganographic method, which utilizes the sparsity and integrity of the image compressed sensing to reduce the risk of being detected by steganalysis. In the proposed algorithm, the message hiding process is integrated into the image sparse decomposition process without affecting the image perceptibility. First, the cover image is decomposed by the orthogonal matching pursuit algorithm of image sparse decomposition, and the shuffled frog leaping algorithm (SFLA) is used to select the optimal atom in each decomposition iteration. Then, different quantization bits are adopted to quantify the sparse decomposition coefficients. Finally, via LSB[Formula: see text] steganographic strategy, the secret message is embedded in the least significant bits of the quantized coefficients. Experimental results show that the embedded data are invisible perceptually. Simultaneously, experiments show that the new steganography has good expandability in embedding capacity, owing to less sensitivity to the embedding bits. The security of the proposed method is also evaluated comparatively, by using four steganalyzers with rich feature, which indicates superior performance of the proposed method comparing with other steganographies conducted in sparse decomposition domain and the LSB[Formula: see text] methods used in spatial domain and DCT domain.
2

Chen, Jia-Fen, Xian-Ming Gu, Liang Li e Ping Zhou. "An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method". Entropy 25, n. 4 (19 aprile 2023): 693. http://dx.doi.org/10.3390/e25040693.

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An optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based on a triangular mesh of the computational domain. The discretized linear system of the HDG method on each subdomain is solved by a sparse direct solver. The solution of the interface linear system in the domain decomposition framework is accelerated by a Krylov subspace method. We study the spectral radius of the iteration matrix of the Schwarz method for the LORM problems, and thus propose an optimized parameter for the transmission condition, which is different from that for the classical electromagnetic problems. The numerical results show that the proposed method is effective.
3

GOTOH, Hitoshi, Abbas KHAYYER, Hiroyuki IKARI e Chiemi HORI. "Development of 3D Parallelized CMPS Method with Optimized Domain Decomposition". Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering) 65, n. 1 (2009): 41–45. http://dx.doi.org/10.2208/kaigan.65.41.

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4

Li, Hui, Bangji Fan, Rong Jia, Fang Zhai, Liang Bai e Xingqi Luo. "Research on Multi-Domain Fault Diagnosis of Gearbox of Wind Turbine Based on Adaptive Variational Mode Decomposition and Extreme Learning Machine Algorithms". Energies 13, n. 6 (16 marzo 2020): 1375. http://dx.doi.org/10.3390/en13061375.

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Since variational mode decomposition (VMD) was proposed, it has been widely used in condition monitoring and fault diagnosis of mechanical equipment. However, the parameters K and α in the VMD algorithm need to be set before decomposition, which causes VMD to be unable to decompose adaptively and obtain the best result for signal decomposition. Therefore, this paper optimizes the VMD algorithm. On this basis, this paper also proposes a method of multi-domain feature extraction of signals and combines an extreme learning machine (ELM) to realize comprehensive and accurate fault diagnosis. First, VMD is optimized according to the improved grey wolf optimizer; second, the feature vectors of the time, frequency, and time-frequency domains are calculated, which are synthesized after dimensionality reduction; ultimately, the synthesized vectors are input into the ELM for training and classification. The experimental results show that the proposed method can decompose the signal adaptively, which produces the best decomposition parameters and results. Moreover, this method can extract the fault features of the signal more completely to realize accurate fault identification.
5

Amattouch, M. R., N. Nagid e H. Belhadj. "Optimized Domain Decomposition Method for Non Linear Reaction Advection Diffusion Equation". European Scientific Journal, ESJ 12, n. 27 (30 settembre 2016): 63. http://dx.doi.org/10.19044/esj.2016.v12n27p63.

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This work is devoted to an optimized domain decomposition method applied to a non linear reaction advection diffusion equation. The proposed method is based on the idea of the optimized of two order (OO2) method developed this last two decades. We first treat a modified fixed point technique to linearize the problem and then we generalize the OO2 method and modify it to obtain a new more optimized rate of convergence of the Schwarz algorithm. To compute the new rate of convergence we have used Fourier analysis. For the numerical computation we minimize this rate of convergence using a global optimization algorithm. Several test-cases of analytical problems illustrate this approach and show the efficiency of the proposed new method.
6

Loisel, S., J. Côté, M. J. Gander, L. Laayouni e A. Qaddouri. "Optimized Domain Decomposition Methods for the Spherical Laplacian". SIAM Journal on Numerical Analysis 48, n. 2 (gennaio 2010): 524–51. http://dx.doi.org/10.1137/080727014.

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Gander, Martin J., e Yingxiang Xu. "Optimized Schwarz methods with nonoverlapping circular domain decomposition". Mathematics of Computation 86, n. 304 (17 maggio 2016): 637–60. http://dx.doi.org/10.1090/mcom/3127.

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8

Ali Hassan, Sarah, Caroline Japhet, Michel Kern e Martin Vohralík. "A Posteriori Stopping Criteria for Optimized Schwarz Domain Decomposition Algorithms in Mixed Formulations". Computational Methods in Applied Mathematics 18, n. 3 (1 luglio 2018): 495–519. http://dx.doi.org/10.1515/cmam-2018-0010.

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AbstractThis paper develops a posteriori estimates for domain decomposition methods with optimized Robin transmission conditions on the interface between subdomains. We choose to demonstrate the methodology for mixed formulations, with a lowest-order Raviart–Thomas–Nédélec discretization, often used for heterogeneous and anisotropic porous media diffusion problems. Our estimators allow to distinguish the spatial discretization and the domain decomposition error components. We propose an adaptive domain decomposition algorithm wherein the iterations are stopped when the domain decomposition error does not affect significantly the overall error. Two main goals are thus achieved. First, a guaranteed bound on the overall error is obtained at each step of the domain decomposition algorithm. Second, important savings in terms of the number of domain decomposition iterations can be realized. Numerical experiments illustrate the efficiency of our estimates and the performance of the adaptive stopping criteria.
9

Dolean, Victorita, St�phane Lanteri e Fr�d�ric Nataf. "Optimized interface conditions for domain decomposition methods in fluid dynamics". International Journal for Numerical Methods in Fluids 40, n. 12 (2002): 1539–50. http://dx.doi.org/10.1002/fld.410.

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10

Gander, Martin J., e Hui Zhang. "Schwarz methods by domain truncation". Acta Numerica 31 (maggio 2022): 1–134. http://dx.doi.org/10.1017/s0962492922000034.

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Abstract (sommario):
Schwarz methods use a decomposition of the computational domain into subdomains and need to impose boundary conditions on the subdomain boundaries. In domain truncation one restricts the unbounded domain to a bounded computational domain and must also put boundary conditions on the computational domain boundaries. In both fields there are vast bodies of literature and research is very active and ongoing. It turns out to be fruitful to think of the domain decomposition in Schwarz methods as a truncation of the domain onto subdomains. Seminal precursors of this fundamental idea are papers by Hagstrom, Tewarson and Jazcilevich (1988), Després (1990) and Lions (1990). The first truly optimal Schwarz method that converges in a finite number of steps was proposed by Nataf (1993), and used precisely transparent boundary conditions as transmission conditions between subdomains. Approximating these transparent boundary conditions for fast convergence of Schwarz methods led to the development of optimized Schwarz methods – a name that has become common for Schwarz methods based on domain truncation. Compared to classical Schwarz methods, which use simple Dirichlet transmission conditions and have been successfully used in a wide range of applications, optimized Schwarz methods are much less well understood, mainly due to their more sophisticated transmission conditions.A key application of Schwarz methods with such sophisticated transmission conditions turned out to be time-harmonic wave propagation problems, because classical Schwarz methods simply do not work in this case. The past decade has given us many new Schwarz methods based on domain truncation. One review from an algorithmic perspective (Gander and Zhang 2019) showed the equivalence of many of these new methods to optimized Schwarz methods. The analysis of optimized Schwarz methods, however, is lagging behind their algorithmic development. The general abstract Schwarz framework cannot be used for the analysis of these methods, and thus there are many open theoretical questions about their convergence. Just as for practical multigrid methods, Fourier analysis has been instrumental for understanding the convergence of optimized Schwarz methods and for tuning their transmission conditions. Similar to local Fourier mode analysis in multigrid, the unbounded two-subdomain case is used as a model for Fourier analysis of optimized Schwarz methods due to its simplicity. Many aspects of the actual situation, e.g. boundary conditions of the original problem and the number of subdomains, were thus neglected in the unbounded two-subdomain analysis. While this gave important insight, new phenomena beyond the unbounded two-subdomain models were discovered.This present situation is the motivation for our survey: to give a comprehensive review and precise exploration of convergence behaviours of optimized Schwarz methods based on Fourier analysis, taking into account the original boundary conditions, many-subdomain decompositions and layered media. We consider as our model problem the operator $-\Delta + \eta $ in the diffusive case $\eta>0$ (screened Laplace equation) or the oscillatory case $\eta <0$ (Helmholtz equation), in order to show the fundamental difference in behaviour of Schwarz solvers for these problems. The transmission conditions we study include the lowest-order absorbing conditions (Robin), and also more advanced perfectly matched layers (PMLs), both developed first for domain truncation. Our intensive work over the last two years on this review has led to several new results presented here for the first time: in the bounded two-subdomain analysis for the Helmholtz equation, we see strong influence of the original boundary conditions imposed on the global problem on the convergence factor of the Schwarz methods, and the asymptotic convergence factors with small overlap can differ from the unbounded two-subdomain analysis. In the many-subdomain analysis, we find the scaling with the number of subdomains, e.g. when the subdomain size is fixed, robust convergence of the double-sweep Schwarz method for the free-space wave problem, either with fixed overlap and zeroth-order Taylor conditions or with a logarithmically growing PML, and we find that Schwarz methods with PMLs work like smoothers that converge faster for higher Fourier frequencies; in particular, for the free-space wave problem, plane waves (in the error) passing through interfaces at a right angle converge more slowly. In addition to our main focus on analysis in Sections 2 and 3, we start in Section 1 with an expository historical introduction to Schwarz methods, and in Section 4 we give a brief interpretation of the recently proposed optimal Schwarz methods for decompositions with cross-points from the viewpoint of transmission conditions. We conclude in Section 5 with a summary of open research problems. In Appendix A we provide a Matlab program for a block LU form of an optimal Schwarz method with cross-points, and in Appendix B we give the Maple program for the two-subdomain Fourier analysis.

Tesi sul tema "Optimized domain decomposition method":

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.

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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.

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Mathematics
Ph.D.
Asynchronous iterative algorithms are parallel iterative algorithms in which communications and iterations are not synchronized among processors. Thus, as soon as a processing unit finishes its own calculations, it starts the next cycle with the latest data received during a previous cycle, without waiting for any other processing unit to complete its own calculation. These algorithms increase the number of updates in some processors (as compared to the synchronous case) but suppress most idle times. This usually results in a reduction of the (execution) time to achieve convergence. Optimized Schwarz methods (OSM) are domain decomposition methods in which the transmission conditions between subdomains contain operators of the form \linebreak $\partial/\partial \nu +\Lambda$, where $\partial/\partial \nu$ is the outward normal derivative and $\Lambda$ is an optimized local approximation of the global Steklov-Poincar\'e operator. There is more than one family of transmission conditions that can be used for a given partial differential equation (e.g., the $OO0$ and $OO2$ families), each of these families containing a particular approximation of the Steklov-Poincar\'e operator. These transmission conditions have some parameters that are tuned to obtain a fast convergence rate. Optimized Schwarz methods are fast in terms of iteration count and can be implemented asynchronously. In this thesis we analyze the convergence behavior of the synchronous and asynchronous implementation of OSM applied to solve partial differential equations with a shifted Laplacian operator in bounded rectangular domains. We analyze two cases. In the first case we have a shift that can be either positive, negative or zero, a one-way domain decomposition and transmission conditions of the $OO2$ family. In the second case we have Poisson's equation, a domain decomposition with cross-points and $OO0$ transmission conditions. In both cases we reformulate the equations defining the problem into a fixed point iteration that is suitable for our analysis, then derive convergence proofs and analyze how the convergence rate varies with the number of subdomains, the amount of overlap, and the values of the parameters introduced in the transmission conditions. Additionally, we find the optimal values of the parameters and present some numerical experiments for the second case illustrating our theoretical results. To our knowledge this is the first time that a convergence analysis of optimized Schwarz is presented for bounded subdomains with multiple subdomains and arbitrary overlap. The analysis presented in this thesis also applies to problems with more general domains which can be decomposed as a union of rectangles.
Temple University--Theses
3

Riaz, Samia. "Domain decomposition method for variational inequalities". Thesis, University of Birmingham, 2014. http://etheses.bham.ac.uk//id/eprint/4815/.

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

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L'objectif de cette thèse est la conception, l'analyse et l'implémentation d'une méthode de décomposition de domaine efficiente pour des problèmes de la mécanique des solides et des fluides. Pour cela les méthodes de Schwarz optimisée (OSM) sont considérées et révisées. Les méthodes de décomposition de domaine de Schwarz optimisées ont été introduites par P.L. Lions, elles apportent une amélioration aux méthodes de Schwarz classiques en substituant les conditions d'interface de Dirichlet par des conditions de type Robin et cela pour les méthodes avec ou sans recouvrement. Les conditions de Robin offrent un très bon levier qui nous permet d'aller vers l'optimalité des méthodes de Schwarz ainsi que la conception d'une méthode de décomposition de domaine robuste pour des problèmes de mécanique complexes comportant une nature presque incompressible. Dans cette thèse un nouveau cadre mathématique est introduit qui consiste à munir les méthodes de Schwarz optimisées (e.g. L'algorithme de Lions ) d'une théorie semblable à celle déjà existante pour des méthodes de Schwarz additives, on définit un espace grossier pour lequel le taux de convergence de la méthode à deux niveaux peut être prescrit, indépendamment des éventuelles hétérogénéités du problème traité. Une formulation sous forme de preconditioneur de la méthode à deux niveaux est proposée qui permettra la simulation parallèle d'un large spectre de problèmes mécanique, tel que le problème d'élasticité presque incompressible, le problème de Stokes incompressible ainsi que le problème instationnaire de Navier-Stokes. Des résultats numériques issues de simulations parallèles à grande échelle sur plusieurs milliers de processeurs sont présentés afin de montrer la robustesse de l'approche proposée
The objective of this thesis is to design an efficient domain decomposition method to solve solid and fluid mechanical problems, for this, Optimized Schwarz methods (OSM) are considered and revisited. The optimized Schwarz methods were introduced by P.L. Lions. They consist in improving the classical Schwarz method by replacing the Dirichlet interface conditions by a Robin interface conditions and can be applied to both overlapping and non overlapping subdomains. Robin conditions provide us an another way to optimize these methods for better convergence and more robustness when dealing with mechanical problem with almost incompressibility nature. In this thesis, a new theoretical framework is introduced which consists in providing an Additive Schwarz method type theory for optimized Schwarz methods, e.g. Lions' algorithm. We define an adaptive coarse space for which the convergence rate is guaranteed regardless of the regularity of the coefficients of the problem. Then we give a formulation of a two-level preconditioner for the proposed method. A broad spectrum of applications will be covered, such as incompressible linear elasticity, incompressible Stokes problems and unstationary Navier-Stokes problem. Numerical results on a large-scale parallel experiments with thousands of processes are provided. They clearly show the effectiveness and the robustness of the proposed approach
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.

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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 maillage
In 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.

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

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In this thesis, we study problems with heterogeneities using the zeroth order optimized Schwarz preconditioning. There are three main parts in this thesis. In the first part, we propose an Optimized Restricted Additive Schwarz Preconditioned Exact Newton approach (ORASPEN) for nonlinear diffusion problems, where Robin transmission conditions are used to communicate subdomain errors. We find out that for the problems with large heterogeneities, the Robin parameter has a significant impact to the convergence behavior when subdomain boundaries cut through the discontinuities. Therefore, we perform an algebraic analysis for a linear diffusion model problem with piecewise constant diffusion coefficients in the second main part. We carefully discuss two possible choices of Robin parameters on the artificial interfaces and derive asymptotic expressions of both the optimal Robin parameter and the convergence rate for each choice at the discrete level. Finally, in the third main part, we study the time-dependent nonequilibrium Richards equation, which can be used to model preferential flow in physics. We semi-discretize the problem in time, and then apply ORASPEN for the resulting elliptic problems with the Robin parameter studied in the second part.
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.

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Pieskä, J. (Jali). "Domain decomposition methods for continuous casting problem". Doctoral thesis, University of Oulu, 2004. http://urn.fi/urn:isbn:9514274679.

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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.

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Libri sul tema "Optimized domain decomposition method":

1

International Symposium on Domain Decomposition Methods for Partial Differential Equations (2nd 1988 Los Angeles, Calif.). Domain decomposition methods. Philadelphia: SIAM, 1989.

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M, Jameson Leland, e Langley Research Center, a cura di. A waverlet optimized adaptive multi-domain method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1997.

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3

Hesthaven, J. S. A wavelet optimized adaptive multi-domain method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1997.

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M, Jameson Leland, e Langley Research Center, a cura di. A waverlet optimized adaptive multi-domain method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1997.

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Hesthaven, Jan S. A waverlet optimized adaptive multi-domain method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1997.

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F, Magoulès, a cura di. Mesh partitioning techniques and domain decomposition methods. Kippen, Stirlingshire, Scotland: Saxe-Coburg Publications, 2007.

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F, Magoulès, a cura di. Mesh partitioning techniques and domain decomposition methods. Kippen, Stirlingshire, Scotland: Saxe-Coburg Publications, 2007.

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Quarteroni, Alfio. Domain decomposition preconditioners for the spectral collocation method. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, Institute for Computer Applications in Science and Engineering, 1988.

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Quarteroni, Alfio. Domain decomposition preconditioners for the spectral collection method. Hampton, Va: ICASE, 1988.

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International Conference on Domain Decomposition (15th 2003 Berlin, Germany). Domain decomposition methods in science and engineering. A cura di Kornhuber Ralf 1955-. Berlin: Springer, 2005.

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Capitoli di libri sul tema "Optimized domain decomposition method":

1

Gander, Martin J., e Michal Outrata. "Optimized Schwarz Methods With Data-Sparse Transmission Conditions". In Domain Decomposition Methods in Science and Engineering XXVI, 471–78. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95025-5_50.

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Gander, Martin J., Julian Hennicker e Roland Masson. "Optimized Coupling Conditions for Discrete Fracture Matrix Models". In Domain Decomposition Methods in Science and Engineering XXVI, 317–25. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95025-5_33.

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Ciaramella, Gabriele, Felix Kwok e Georg Müller. "A Nonlinear Optimized Schwarz Preconditioner for Elliptic Optimal Control Problems". In Domain Decomposition Methods in Science and Engineering XXVI, 391–98. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95025-5_41.

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Gander, Martin J., Roland Masson e Tommaso Vanzan. "A Numerical Algorithm Based on Probing to Find Optimized Transmission Conditions". In Domain Decomposition Methods in Science and Engineering XXVI, 597–605. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95025-5_65.

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Ciaramella, Gabriele, Martin J. Gander e Parisa Mamooler. "The Domain Decomposition Method of Bank and Jimack as an Optimized Schwarz Method". In Lecture Notes in Computational Science and Engineering, 285–93. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56750-7_32.

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Gander, Martin J., Lahcen Laayouni e Daniel B. Szyld. "SParse Approximate Inverse (SPAI) Based Transmission Conditions for Optimized Algebraic Schwarz Methods". In Domain Decomposition Methods in Science and Engineering XXVI, 399–406. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95025-5_42.

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Laayouni, Lahcen. "Optimized Domain Decomposition Methods for Three-dimensional Partial Differential Equations". In Lecture Notes in Computational Science and Engineering, 339–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75199-1_41.

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Lee, Chang-Ock, e Eun-Hee Park. "A Domain Decomposition Method Based on Augmented Lagrangian with an Optimized Penalty Parameter". In Lecture Notes in Computational Science and Engineering, 567–75. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-18827-0_58.

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Gander, Martin J., e Yingxiang Xu. "Optimized Schwarz Method with Two-Sided Transmission Conditions in an Unsymmetric Domain Decomposition". In Lecture Notes in Computational Science and Engineering, 631–39. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-18827-0_65.

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Antoine, X., e C. Geuzaine. "Optimized Schwarz Domain Decomposition Methods for Scalar and Vector Helmholtz Equations". In Modern Solvers for Helmholtz Problems, 189–213. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-28832-1_8.

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Atti di convegni sul tema "Optimized domain decomposition method":

1

Peng, Zhen. "Optimized integral equation domain decomposition methods for scattering by large and deep cavities". In 2014 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2014. http://dx.doi.org/10.1109/iceaa.2014.6903862.

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Barka, Andre, e Francois-Xavier Roux. "Parallel FETI-EM Domain Decomposition Methods optimized for antenna arrays and metamaterials periodic structures". In 2010 IEEE International Symposium Antennas and Propagation and CNC-USNC/URSI Radio Science Meeting. IEEE, 2010. http://dx.doi.org/10.1109/aps.2010.5561925.

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Puente, R., G. Paniagua e T. Verstraete. "Aerodynamic Characterization of Transonic Turbine Vanes Optimized to Attenuate Rotor Forcing". In ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/gt2011-46553.

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Abstract (sommario):
A multi-objective optimization procedure is applied to the 3D design of a transonic turbine vane row, considering efficiency and stator outlet pressure distortion, which is directly related to induced rotor forcing. The characteristic features that define different individuals along the Pareto Front are described, analyzing the differences between high efficiency airfoils and low interaction. Pressure distortion is assessed by means of a model that requires only of the computation the steady flow field in the domain of the stator. The reduction of aerodynamic rotor forcing is checked via unsteady multistage aerodynamic computations. A well known loss prediction method is used to drive the efficiency of one optimization run, while CFD analysis is used for another, in order to assess the reliability of both methods. In both cases, the decomposition of total losses is performed to quantify the influence on efficiency of reducing rotor forcing. Results show that when striving for efficiency, the rotor is affected by few, but intense shocks. On the other hand, when the objective is the minimization of distortion, multiple shocks will appear.
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Yıldız, Ali R., e Kazuhiro Saitou. "Topology Synthesis of Multi-Component Structural Assemblies in Continuum Domains". In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-50037.

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Abstract (sommario):
Most structural products have complex geometry to meet customer’s demand of high functionality. Since manufacturing those products in one piece is either impossible or uneconomical, most structural products are assemblies of components with simpler geometries. The conventional way to design structural assemblies is to design overall geometry first, and then decompose the geometry to determine the part boundary and joint locations. This two-step process, however, can lead to sub-optimal designs since the product geometry, even if optimized as one piece, would not be optimal after decomposition. This paper presents a method for synthesizing structural assemblies directly from the design specifications, without going through the two-step process. Given an extended design domain with boundary and loading conditions, the method simultaneously optimizes the topology and geometry of an entire structure and the location and configuration of joints, considering structural performance, manufacturability, and assembleability. As a relaxation of our previous work utilizing a beam-based ground structure [1], this paper presents a new formulation in a continuum design domain, which greatly enhances the ability to represent complex structural geometry observed in real-world products. A multi-objective genetic algorithm is used to obtain Pareto optimal solutions that exhibits trade-offs among stiffness, weight, manufacturability, and assembleability.
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HAIJIANG, LI, LI RUBIN, AO QIUHUA, WANG WEICHENG, WANG XIUFENG, DU LEILEI, WEN JUN e ZHU LILI. "AN INTELLIGENT METHOD FOR BEARING FAULT DIAGNOSIS BASED ON IMPROVED VMD AND GSM-SVM". In 3rd International Workshop on Structural Health Monitoring for Railway System (IWSHM-RS 2021). Destech Publications, Inc., 2021. http://dx.doi.org/10.12783/iwshm-rs2021/36024.

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In industrial sites, the running state of rolling bearings is often judged by hearing the sound with human ears. This method relies on long-term accumulation of human experience and is prone to cause occupational noise hazards. To solve this problem, this paper proposed an intelligent diagnosis method for the running state of bearings based on machine hearing. Firstly, bearing vibration signal was decomposed using an improved Variational Mode Decomposition (VMD) algorithm, by which the best mode component containing the fault characteristic was determined according to a time-frequency weighted kurtosis maximization criterion. Then, the time-domain feature indexes and psychoacoustic indexes of the best mode component were calculated to define a feature vector. Finally, the feature vectors were input into a fault classification model based on Support Vector Machine optimized by Grid Search Method (GSM-SVM) for training. The trained model was used to diagnose unknown faults of bearings. The proposed method was applied to the traction motors of EMU train for automatic bearing fault diagnose. Field test in the manufacturing factory showed that it could quickly diagnose bearing faults with a high accuracy rate.
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Lie, K. A., O. Møyner e Ø. A. Klemetsdal. "An Adaptive Newton–ASPEN Solver for Complex Reservoir Models". In SPE Reservoir Simulation Conference. SPE, 2023. http://dx.doi.org/10.2118/212199-ms.

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Abstract Standard Newton methods that are used to advance fully implicit or adaptive implicit schemes in time often suffer from slow or stagnant convergence when natural initial guesses are too far from the solution or the discrete flow equations contain nonlinearities that are unbalanced in time and space. Nonlinear solvers based on local-global, domain-decomposition strategies have proved to be significantly more robust than regular Newton but come at a higher computational cost per iteration. The chief example of one such strategy is additive Schwarz preconditioned exact Newton (ASPEN) that rigorously couples local solves, which in sum have little cost compared with a Newton update, with a global update that has a cost comparable to a regular Newton solve. We present strategies for combining Newton and ASPEN to accelerate the nonlinear solution process. The main feature is a set of novel monitoring strategies and systematic switching criteria that prevent oversolving and enable us to optimize the choice of solution strategy. At the start of each nonlinear iteration, convergence monitors are computed and can be used to choose the type of nonlinear iteration to perform as well as methods, tolerances, and other parameters used for the optional local domain solves. The convergence monitors and switching criteria are inexpensive to compute. We observe the advantages and disadvantages of local-global domain decomposition for practical models of interest for oil recovery and CO2 storage and demonstrate how the computational runtime can be (significantly) reduced by adaptively switching to regular Newton's method when nonlinearities are balanced throughout the physical domain and the local solves provide little benefit relative to their computational cost.
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Tao, Shaozhe, Yifan Sun e Daniel Boley. "Inverse Covariance Estimation with Structured Groups". In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/395.

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Estimating the inverse covariance matrix of p variables from n observations is challenging when n is much less than p, since the sample covariance matrix is singular and cannot be inverted. A popular solution is to optimize for the L1 penalized estimator; however, this does not incorporate structure domain knowledge and can be expensive to optimize. We consider finding inverse covariance matrices with group structure, defined as potentially overlapping principal submatrices, determined from domain knowledge (e.g. categories or graph cliques). We propose a new estimator for this problem setting that can be derived efficiently via the conditional gradient method, leveraging chordal decomposition theory for scalability. Simulation results show significant improvement in sample complexity when the correct group structure is known. We also apply these estimators to 14,910 stock closing prices, with noticeable improvement when group sparsity is exploited.
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McNeill, S. I., e P. Agarwal. "Efficient Modal Decomposition and Reconstruction of Riser Response due to VIV". In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-49469.

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Vortex-Induced-Vibrations (VIV) due to ocean currents can consume a sizable portion of the allotted fatigue life of marine risers. Vibration monitoring and concurrent estimation of fatigue damage due to VIV can significantly enhance the safe and reliable operation of risers. To this end, riser response can be characterized by using sensors (e.g. accelerometers and/or angular rate sensors) to measure the motion of the riser at a few locations. Fatigue damage can be predicted along the entire length of riser from measured data using the method of modal decomposition and reconstruction. In this method the structural response of interest, such as stress and fatigue damage, is expressed by modal superposition, where the modal weights are estimated using measured data and analytical modeshapes. However the accuracy of this method declines as the sensor density (number of sensors per unit riser length) decreases, especially when the riser vibrates in high-order modes and exhibits traveling wave behavior. In this paper, an efficient frequency-domain methodology allowing for accurate reconstruction of the riser response along the entire riser using a limited number of sensors is proposed. We first identify the excited VIV modes (natural frequency and modeshape) using principal vectors of the cross spectral density. Modal decomposition and reconstruction is performed separately for each VIV band surrounding each excited mode. This allows us to use several (as many as the number of sensors) participating modes in each band, and thus improve the accuracy. Since the stress distribution is sensitive to the chosen set of participating modes, we optimize over several candidate sets, selecting the set of modes that result in the lowest prediction error. In order to improve the reconstruction of complex modes, particularly traveling waves, the modeshapes can be augmented with additional basis vectors. The additional basis vectors are obtained by shifting the phase of the normal modes by 90 degrees at every wave number using the Hilbert transform. Though developed in the context of VIV, the method can be used to estimate fatigue damage due to vibrations regardless of the excitation mechanism. The methodology is demonstrated using the NDP (Norwegian Deepwater Program) test data on a 38 meter long slender riser, using data from eight accelerometers. Results show that the proposed algorithm can reconstruct stresses and fatigue damage accurately along the length of the riser in the presence of traveling wave behavior using relatively few sensors.
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Praharaj, S., e Shapour Azarm. "Two-Level Nonlinear Mixed Discrete-Continuous Optimization-Based Design: An Application to Printed Circuit Board Assemblies". In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0135.

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Abstract In this paper, a new approach for optimization-based design of non-linearly mixed discrete-continuous problems has been developed. The approach is based on a two-level decomposition strategy in which the entire domain of variables is partitioned into two levels, one involving the continuous variables and the other involving the discrete variables. Variables in one level are optimized for fixed values of the variable from the other level. A modified penalty function is formed, based on monotonicity analysis, to solve for the discrete variables, and a conventional optimization method was used to solve for the continuous variables. To improve the computational effectiveness of the approach, a constrained derivative relationship was also adopted. The performance of the entire algorithm is then demonstrated through an example involving printed circuit board assemblies. The objective in the example is to maximize assembly reliability by: (1) adding redundant components to the boards and (2) optimally distributing allocated mass flow to the individual channels of the circuit boards. Number of variables in the example is then varied to investigate the effectiveness and potential of the approach for large-scale problems.
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Fang, Baoyan, Shuangliang Tian e Zhigang Wang. "Domain decomposition method with wavelet collocation". In 3rd International Congress on Image and Signal Processing (CISP 2010). IEEE, 2010. http://dx.doi.org/10.1109/cisp.2010.5647545.

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Rapporti di organizzazioni sul tema "Optimized domain decomposition method":

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Em Karniadakis, George. An Adaptive Random Domain Decomposition Method for Stochastic CFD and MHD Problems. Fort Belvoir, VA: Defense Technical Information Center, febbraio 2009. http://dx.doi.org/10.21236/ada586697.

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Tan, Peng, e Nicholas Sitar. Parallel Level-Set DEM (LS-DEM) Development and Application to the Study of Deformation and Flow of Granular Media. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, marzo 2023. http://dx.doi.org/10.55461/kmiz5819.

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We present a systematic investigation of computational approaches to the modeling of granular materials. Granular materials are ubiquitous in everyday life and in a variety of engineering and industrial applications. Despite the apparent simplicity of the laws governing particle-scale interactions, predicting the continuum mechanical response of granular materials still poses extraordinary challenges. This is largely due to the complex history dependence resulting from continuous rearrangement of the microstructure of granular material, as well as the mechanical interlocking due to grain morphology and surface roughness. X-Ray Computed Tomography (XRCT) is used to characterize the grain morphology and the fabric of the granular media, naturally deposited sand in this study. The Level-Set based Discrete Element Method (LS-DEM) is then used to bridge the granular behavior gap between the micro and macro scale. The LS-DEM establishes a one-to-one correspondence between granular objects and numerical avatars and captures the details of grain morphology and surface roughness. However, the high-fidelity representation significantly increases the demands on computational resources. To this end a parallel version of LS-DEM is introduced to significantly decrease the computational demands. The code employs a binning algorithm, which reduces the search complexity of contact detection from O(n2) to O(n), and a domain decomposition strategy is used to elicit parallel computing in a memory- and communication-efficient manner. The parallel implementation shows good scalability and efficiency. High fidelity LS avatars obtained from XRCT images of naturally deposited sand are then used to replicate the results of triaxial tests using the new, parallel LS-DEM code. The result show that both micro- and macro-mechanical behavior of natural material is well captured and is consistent with experimental data, confirming experimental observation that the primary source of peak strength of sand is the mechanical interlocking between irregularly shaped grains. Specifically, triaxial test simulations with a flexible membrane produce a very good match to experimentally observed relationships between deviatoric stress and mobilized friction angle for naturally deposited sand. We then explore the viability of modeling dynamic problems with a new formulation of an impulse based LS-DEM. The new formulation is stable, fast, and energy conservative. However, it can be numerically stiff when the assembly has substantial mass differences between particles. We also demonstrate the feasibility of modeling deformable structures in the rigid body framework and propose several enhancements to improve the convergence of collision resolution, including a hybrid time integration scheme to separately handle at rest contacts and dynamic collisions. Finally, we extend the impulse-based LS-DEM to include arbitrarily shaped topographic surfaces and exploit its algorithmic advantages to demonstrate the feasibility of modeling realistic behavior of granular flows. The novel formulation significantly improves performance of dynamic simulations by allowing larger time steps, which is advantageous for observing the full development of physical phenomena such as rock avalanches, which we present as an illustrative example.
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Multiple Engine Faults Detection Using Variational Mode Decomposition and GA-K-means. SAE International, marzo 2022. http://dx.doi.org/10.4271/2022-01-0616.

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As a critical power source, the diesel engine is widely used in various situations. Diesel engine failure may lead to serious property losses and even accidents. Fault detection can improve the safety of diesel engines and reduce economic loss. Surface vibration signal is often used in non-disassembly fault diagnosis because of its convenient measurement and stability. This paper proposed a novel method for engine fault detection based on vibration signals using variational mode decomposition (VMD), K-means, and genetic algorithm. The mode number of VMD dramatically affects the accuracy of extracting signal components. Therefore, a method based on spectral energy distribution is proposed to determine the parameter, and the quadratic penalty term is optimized according to SNR. The results show that the optimized VMD can adaptively extract the vibration signal components of the diesel engine. In the actual fault diagnosis case, it is difficult to obtain the data with labels. The clustering algorithm can complete the classification without labeled data, but it is limited by the low accuracy. In this paper, the optimized VMD is used to decompose and standardize the vibration signal. Then the correlation-based feature selection method is implemented to obtain the feature results after dimensionality reduction. Finally, the results are input into the classifier combined by K-means and genetic algorithm (GA). By introducing and optimizing the genetic algorithm, the number of classes can be selected automatically, and the accuracy is significantly improved. This method can carry out adaptive multiple fault detection of a diesel engine without labeled data. Compared with many supervised learning algorithms, the proposed method also has high accuracy.

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