Relevant bibliographies by topics / Discretization

Academic literature on the topic 'Discretization'

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Published: 4 June 2021
Last updated: 8 June 2024

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Journal articles on the topic "Discretization"

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STRUCKMEIER, JENS, and KONRAD STEINER. "SECOND-ORDER SCHEME FOR THE SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITH MAXWELLIAN MOLECULES." Mathematical Models and Methods in Applied Sciences 06, no. 01 (February 1996): 137–47. http://dx.doi.org/10.1142/s0218202596000080.

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In the standard approach particle methods for the Boltzmann equation are obtained using an explicit time discretization of the spatially homogeneous Boltzmann equation. This kind of discretization leads to a restriction on the discretization parameter as well as on the differential cross-section in the case of the general Boltzmann equation. Recently, construction of an implicit particle scheme for the Boltzmann equation with Maxwellian molecules was shown. This paper combines both approaches using a linear combination of explicit and implicit discretizations. It is shown that the new method leads to a second-order particle method when using an equiweighting of explicit and implicit discretization.
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GUIHÉNEUF, PIERRE-ANTOINE. "Dynamical properties of spatial discretizations of a generic homeomorphism." Ergodic Theory and Dynamical Systems 35, no. 5 (April 23, 2014): 1474–523. http://dx.doi.org/10.1017/etds.2013.108.

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This paper concerns the link between the dynamical behaviour of a dynamical system and the dynamical behaviour of its numerical simulations. Here, we model numerical truncation as a spatial discretization of the system. Some previous works on well-chosen examples (such as Gambaudo and Tresser [Some difficulties generated by small sinks in the numerical study of dynamical systems: two examples. Phys. Lett. A 94(9) (1983), 412–414]) show that the dynamical behaviours of dynamical systems and of their discretizations can be quite different. We are interested in generic homeomorphisms of compact manifolds. So our aim is to tackle the following question: can the dynamical properties of a generic homeomorphism be detected on the spatial discretizations of this homeomorphism? We will prove that the dynamics of a single discretization of a generic conservative homeomorphism does not depend on the homeomorphism itself, but rather on the grid used for the discretization. Therefore, dynamical properties of a given generic conservative homeomorphism cannot be detected using a single discretization. Nevertheless, we will also prove that some dynamical features of a generic conservative homeomorphism (such as the set of the periods of all periodic points) can be read on a sequence of finer and finer discretizations.
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Mollet, Christian. "Stability of Petrov–Galerkin Discretizations: Application to the Space-Time Weak Formulation for Parabolic Evolution Problems." Computational Methods in Applied Mathematics 14, no. 2 (April 1, 2014): 231–55. http://dx.doi.org/10.1515/cmam-2014-0001.

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Abstract. This paper is concerned with the stability of Petrov–Galerkin discretizations with application to parabolic evolution problems in space-time weak form. We will prove that the discrete inf-sup condition for an a priori fixed Petrov–Galerkin discretization is satisfied uniformly under standard approximation and smoothness conditions without any further coupling between the discrete trial and test spaces for sufficiently regular operators. It turns out that one needs to choose different discretization levels for the trial and test spaces in order to obtain a positive lower bound for the discrete inf-sup condition which is independent of the discretization levels. In particular, we state the required number of extra layers in order to guarantee uniform boundedness of the discrete inf-sup constants explicitly. This general result will be applied to the space-time weak formulation of parabolic evolution problems as an important model example. In this regard, we consider suitable hierarchical families of discrete spaces. The results apply, e.g., for finite element discretizations as well as for wavelet discretizations. Due to the Riesz basis property, wavelet discretizations allow for optimal preconditioning independently of the grid spacing. Moreover, our predictions on the stability, especially in view of the dependence on the refinement levels w.r.t. the test and trial spaces, are underlined by numerical results. Furthermore, it can be observed that choosing the same discretization levels would, indeed, lead to stability problems.
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Fischer, Jens V., and Rudolf L. Stens. "On the Reversibility of Discretization." Mathematics 8, no. 4 (April 17, 2020): 619. http://dx.doi.org/10.3390/math8040619.

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“Discretization” usually denotes the operation of mapping continuous functions to infinite or finite sequences of discrete values. It may also mean to map the operation itself from one that operates on functions to one that operates on infinite or finite sequences. Advantageously, these two meanings coincide within the theory of generalized functions. Discretization moreover reduces to a simple multiplication. It is known, however, that multiplications may fail. In our previous studies, we determined conditions such that multiplications hold in the tempered distributions sense and, hence, corresponding discretizations exist. In this study, we determine, vice versa, conditions such that discretizations can be reversed, i.e., functions can be fully restored from their samples. The classical Whittaker-Kotel’nikov-Shannon (WKS) sampling theorem is just one particular case in one of four interwoven symbolic calculation rules deduced below.
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Bassi, Francesco, Lorenzo Botti, and Alessandro Colombo. "Agglomeration-based physical frame dG discretizations: An attempt to be mesh free." Mathematical Models and Methods in Applied Sciences 24, no. 08 (May 4, 2014): 1495–539. http://dx.doi.org/10.1142/s0218202514400028.

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In this work we consider agglomeration-based physical frame discontinuous Galerkin (dG) discretization as an effective way to increase the flexibility of high-order finite element methods. The mesh free concept is pursued in the following (broad) sense: the computational domain is still discretized using a mesh but the computational grid should not be a constraint for the finite element discretization. In particular the discrete space choice, its convergence properties, and even the complexity of solving the global system of equations resulting from the dG discretization should not be influenced by the grid choice. Physical frame dG discretization allows to obtain mesh-independent h-convergence rates. Thanks to mesh agglomeration, high-order accurate discretizations can be performed on arbitrarily coarse grids, without resorting to very high-order approximations of domain boundaries. Agglomeration-based h-multigrid techniques are the obvious choice to obtain fast and grid-independent solvers. These features (attractive for any mesh free discretization) are demonstrated in practice with numerical test cases.
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Beaude, L., R. Masson, S. Lopez, and P. Samier. "Combined face based and nodal based discretizations on hybrid meshes for non-isothermal two-phase Darcy flow problems." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 4 (July 2019): 1125–56. http://dx.doi.org/10.1051/m2an/2019014.

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In the last 20 years many discretization schemes have been developed to approximate the Darcy fluxes on polyhedral cells in heterogeneous anisotropic porous media. Among them, we can distinguished cell based approaches like the Two Point Flux Approximation (TPFA) or the Multi Point Flux Approximation (MPFA) schemes, face based approaches like the Hybrid Finite Volume (HFV) scheme belonging to the family of Hybrid Mimetic Mixed methods and nodal based discretizations like the Vertex Approximate Gradient (VAG) scheme. They all have their own drawbacks and advantages which typically depend on the type of cells and on the anisotropy of the medium. In this work, we propose a new methodology to combine the VAG and HFV discretizations on arbitrary subsets of cells or faces in order to choose the best suited scheme in different parts of the mesh. In our approach the TPFA discretization is considered as an HFV discretization for which the face unknowns can be eliminated. The coupling strategy is based on a node to face interpolation operator at the interfaces which must be chosen to ensure the consistency, the coercivity and the limit conformity properties of the combined discretization. The convergence analysis is performed in the gradient discretization framework and convergence is proved for arbitrary cell or face partitions of the mesh. For face partitions, an additional stabilisation local to the cell is required to ensure the coercivity while for cell partitions no additional stabilisation is needed. The framework preserves at the interface the discrete conservation properties of the VAG and HFV schemes with fluxes based on local to each cell transmissibility matrices. This discrete conservative form allows to naturally extend the VAG and HFV discretizations of two-phase Darcy flow models to the combined VAG–HFV schemes. The efficiency of our approach is tested for single phase and immiscible two-phase Darcy flows on 3D meshes using a combination of the HFV and VAG discretizations as well as for non-isothermal compositional liquid gas Darcy flows on a vertical 2D cross-section of the Bouillante geothermal reservoir (Guadeloupe) using a combination of the TPFA and VAG discretizations.
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Fang, Jian, Li Na Sui, and Hong Yi Jian. "Continuous Entropy Estimation with Different Unsupervised Discretization Methods." Applied Mechanics and Materials 380-384 (August 2013): 1617–20. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.1617.

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In this paper, we compare and analyze the performances of nine unsupervised discretization methods, i.e., equal width, equal frequency, k-means clustering discretization, ordinal, fixed frequency, non-disjoint, proportional, weight proportional, mean value and standard deviation discretizations in the framework of continues entropy estimation based on 15 probability density distributions, i.e., Beta, Cauchy, Central Chi-Squared, Exponential, F, Gamma, Laplace, Logistic, Lognormal, Normal, Rayleigh, Student's-t, Triangular, Uniform, and Weibull distributions.
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Voulis, Igor, and Arnold Reusken. "Discontinuous Galerkin time discretization methods for parabolic problems with linear constraints." Journal of Numerical Mathematics 27, no. 3 (September 25, 2019): 155–82. http://dx.doi.org/10.1515/jnma-2018-0013.

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Abstract We consider time discretization methods for abstract parabolic problems with inhomogeneous linear constraints. Prototype examples that fit into the general framework are the heat equation with inhomogeneous (time-dependent) Dirichlet boundary conditions and the time-dependent Stokes equation with an inhomogeneous divergence constraint. Two common ways of treating such linear constraints, namely explicit or implicit (via Lagrange multipliers) are studied. These different treatments lead to different variational formulations of the parabolic problem. For these formulations we introduce a modification of the standard discontinuous Galerkin (DG) time discretization method in which an appropriate projection is used in the discretization of the constraint. For these discretizations (optimal) error bounds, including superconvergence results, are derived. Discretization error bounds for the Lagrange multiplier are presented. Results of experiments confirm the theoretically predicted optimal convergence rates and show that without the modification the (standard) DG method has sub-optimal convergence behavior.
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Mönkölä, Sanna. "On the Accuracy and Efficiency of Transient Spectral Element Models for Seismic Wave Problems." Advances in Mathematical Physics 2016 (2016): 1–15. http://dx.doi.org/10.1155/2016/9431583.

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This study concentrates on transient multiphysical wave problems for simulating seismic waves. The presented models cover the coupling between elastic wave equations in solid structures and acoustic wave equations in fluids. We focus especially on the accuracy and efficiency of the numerical solution based on higher-order discretizations. The spatial discretization is performed by the spectral element method. For time discretization we compare three different schemes. The efficiency of the higher-order time discretization schemes depends on several factors which we discuss by presenting numerical experiments with the fourth-order Runge-Kutta and the fourth-order Adams-Bashforth time-stepping. We generate a synthetic seismogram and demonstrate its function by a numerical simulation.
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Oyono Ngou, Polynice, and Cody Hyndman. "A Fourier Interpolation Method for Numerical Solution of FBSDEs: Global Convergence, Stability, and Higher Order Discretizations." Journal of Risk and Financial Management 15, no. 9 (August 31, 2022): 388. http://dx.doi.org/10.3390/jrfm15090388.

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The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs) was originally formulated using Euler time discretizations and a uniform space grid. In this paper, we utilize a tree-like spatial discretization that approximates the BSDE on the tree, so that no spatial interpolation procedure is necessary. In addition to suppressing extrapolation error, leading to a globally convergent numerical solution for the FBSDE, we provide explicit convergence rates. On this alternative grid the conditional expectations involved in the time discretization of the BSDE are computed using Fourier analysis and the fast Fourier transform (FFT) algorithm. The method is then extended to higher-order time discretizations of FBSDEs. Numerical results demonstrating convergence are presented using a commodity price model, incorporating seasonality, and forward prices.
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Dissertations / Theses on the topic "Discretization"

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Yang, Ying. "Discretization for Naive-Bayes learning." Monash University, School of Computer Science and Software Engineering, 2003. http://arrow.monash.edu.au/hdl/1959.1/9393.

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Nucinkis, Daniel. "A discretization of quasiperiodic motion." Thesis, Queen Mary, University of London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265698.

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Böhm, Walter, and Sri Gopal Mohanty. "Discretization of Markovian Queueing Systems." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1990. http://epub.wu.ac.at/140/1/document.pdf.

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Recently it turned out, that discretizing the time in a markovian queueing model makes it possible to apply powerfull combinatorid methods which often yield surprisingly simple answeres to complicated questions. In this paper we show that the continuous time solution of a markovian queueing model may be obtain from the solution of its discrete time analogue by a simple limiting procedure. Under mild regularity conditions these limiting forms can be shown to be the unique solutions of Kolmogorov's backward differential equations. Furthermore some additional methodological results concerning taboo probabilities and first passage densities are obtained. In a final section some examples are given. (author's abstract)
Series: Forschungsberichte / Institut für Statistik
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Sugiyama, Mahito. "Studies on Computational Learning via Discretization." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157472.

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Bauer, David. "Towards Discretization by Piecewise Pseudoholomorphic Curves." Doctoral thesis, Universitätsbibliothek Leipzig, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-132065.

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This thesis comprises the study of two moduli spaces of piecewise J-holomorphic curves. The main scheme is to consider a subdivision of the 2-sphere into a collection of small domains and to study collections of J-holomorphic maps into a symplectic manifold. These maps are coupled by Lagrangian boundary conditions. The work can be seen as finding a 2-dimensional analogue of the finite-dimensional path space approximation by piecewise geodesics on a Riemannian manifold (Q,g). For a nice class of target manifolds we consider tangent bundles of Riemannian manifolds and symplectizations of unit tangent bundles. Via polarization they provide a rich set of Lagrangians which can be used to define appropriate boundary value problems for the J-holomorphic pieces. The work focuses on existence theory as a pre-stage to global questions such as combinatorial refinement and the quality of the approximation. The first moduli space of lifted type is defined on a triangulation of the 2-sphere and consists of disks in the tangent bundle whose boundary projects onto geodesic triangles. The second moduli space of punctured type is defined on a circle packing domain and consists of boundary punctured disks in the symplectization of the unit tangent bundle. Their boundary components map into single fibers and at punctures the disks converge to geodesics. The coupling boundary conditions are chosen such that the piecewise problem always is Fredholm of index zero and both moduli spaces only depend on discrete data. For both spaces existence results are established for the J-holomorphic pieces which hold true on a small scale. Each proof employs a version of the implicit function theorem in a different setting. Here the argument for the moduli space of punctured type is more subtle. It rests on a connection to tropical geometry discovered by T. Ekholm for 1-jet spaces. The boundary punctured disks are constructed in the vicinity of explicit Morse flow trees which correspond to the limiting objects under degeneration of the boundary condition.
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Pavlov, Dmitry Marsden Jerrold E. Marsden Jerrold E. Desbrun Mathieu. "Structure-preserving discretization of incompressible fluids /." Diss., Pasadena, Calif. : California Institute of Technology, 2009. http://resolver.caltech.edu/CaltechETD:etd-05222009-125630.

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Wang, Bin, and s3115026@student rmit edu au. "On Discretization of Sliding Mode Control Systems." RMIT University. Electrical and Computer Engineering, 2008. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080822.145013.

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Sliding mode control (SMC) has been successfully applied to many practical control problems due to its attractive features such as invariance to matched uncertainties. The characteristic feature of a continuous-time SMC system is that sliding mode occurs on a prescribed manifold, where switching control is employed to maintain the state on the surface. When a sliding mode is realized, the system exhibits some superior robustness properties with respect to external matched uncertainties. However, the realization of the ideal sliding mode requires switching with an infinite frequency. Control algorithms are now commonly implemented in digital electronics due to the increasingly affordable microprocessor hardware although the essential conceptual framework of the feedback design still remains to be in the continuous-time domain. Discrete sliding mode control has been extensively studied to address some basic questions associated with the sliding mode control of discrete-time systems with relatively low switching frequencies. However, the complex dynamical behaviours due to discretization in continuous-time SMC systems have not yet been fully explored. In this thesis, the discretization behaviours of SMC systems are investigated. In particular, one of the most frequently used discretization schemes for digital controller implementation, the zero-order-holder discretization, is studied. First, single-input SMC systems are discretized, stability and boundary conditions of the digitized SMC systems are derived. Furthermore, some inherent dynamical properties such as periodic phenomenon, of the discretized SMC systems are studied. We also explored the discretization behaviours of the disturbed SMC systems. Their steady-state behaviours are discussed using a symbolic dynamics approach under the constant and periodic matched uncertainties. Next, discretized high-order SMC systems and sliding mode based observers are explored using the same analysis method. At last, the thesis investigates discretization effects on the SMC systems with multiple inputs. Some conditions are first derived for ensuring the
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Chen, Heli. "The quadrature discretization method and its applications." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0002/NQ34540.pdf.

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Ho, Colin Kok Meng. "Discretization and defragmentation for decision tree learning." Thesis, University of Essex, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299072.

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ANDRADE, SELENE DIAS RICARDO DE. "A COMPARISON BETWEEN DISCRETIZATION METHODS FOR CONTROLLERS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1999. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=1017@1.

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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Esta dissertação apresenta uma comparação entre técnicas de discretização de controladores, considerando diferentes estruturas de controle. Os tipos de sistemas estudados neste trabalho de pesquisa serão sistemas lineares, invariantes no tempo, determinísticos, causais e monovariáveis. O desempenho das técnicas de discretização serão comparados via figuras de mérito tradicionais, considerando os métodos de discretização, as estruturas dos controladores e os tipos de planta habituais (incluindo problemas benchmarch), sob especificações dadas quanto aos regimes permanente e transiente.
This essay proposes a comparison between techniques of controllers´ discretization considering different controlling structures. The types of systems studied in this research will be linear systems, time-invariant, deterministic, casual and single-variable. The performance of discretization techniques will be compared through figures of traditional aptitude, considering the discretization methods, the controller structures and the kinds of plants (including - benchmarch - problems), under given specifications according to permanent and transitory systems.
Esta disertación presenta una comparación entre técnicas de discretización de controladores, considerando diferentes extructuras de control. Los tipos de sistemas estudiados en este trabajo de investigación son sistemas lineales, invariantes en el tiempo, determinísticos, causales y univariados. Se compara el desempeño de las técnicas de discretización utilizando figuras de mérito tradicionales, considerando los métodos de discretización, las extructuras de los controladores y los tipos de planta habituales (incluyendo problemas - benchmarch - ), bajo especificaciones dadasen relación a los régimenes permanente y transiente.
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Books on the topic "Discretization"

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Jacod, Jean, and Philip Protter. Discretization of Processes. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-24127-7.

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F, Miranda Guillermo, ed. Mimetic discretization methods. Boca Raton: CRC Press, 2013.

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E, Protter Philip, and SpringerLink (Online service), eds. Discretization of Processes. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2012.

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Ventura, Giulio, and Elena Benvenuti, eds. Advances in Discretization Methods. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-41246-7.

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IUTAM/IACM Symposium (1989 Vienna, Austria). Discretization methods in structural mechanics. Berlin: Springer-Verlag, 1990.

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Robert, Christian P., ed. Discretization and MCMC Convergence Assessment. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1716-9.

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Kuhn, Günther, and Herbert Mang, eds. Discretization Methods in Structural Mechanics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-49373-7.

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Luo, Albert C. J. Discretization and Implicit Mapping Dynamics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-47275-0.

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Baumeister, Kenneth J. Discretization formulas for unstructured grids. [Washington, DC]: National Aeronautics and Space Administration, 1988.

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1961-, Robert Christian P., ed. Discretization and MCMC convergence assessment. New York: Springer, 1998.

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Book chapters on the topic "Discretization"

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Rabbath, C. A., and N. Léchevin. "Discretization." In Discrete-Time Control System Design with Applications, 31–50. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9290-0_3.

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Schroeder, Dietmar. "Discretization." In Computational Microelectronics, 185–99. Vienna: Springer Vienna, 1994. http://dx.doi.org/10.1007/978-3-7091-6644-4_9.

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Ansorge, Cedrick. "Discretization." In Analyses of Turbulence in the Neutrally and Stably Stratified Planetary Boundary Layer, 29–48. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45044-5_3.

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García, Salvador, Julián Luengo, and Francisco Herrera. "Discretization." In Intelligent Systems Reference Library, 245–83. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10247-4_9.

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Webb, Geoffrey I., Johannes Fürnkranz, Johannes Fürnkranz, Johannes Fürnkranz, Geoffrey Hinton, Claude Sammut, Joerg Sander, et al. "Discretization." In Encyclopedia of Machine Learning, 287–88. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-0-387-30164-8_221.

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Sengupta, Nandita, and Jaya Sil. "Discretization." In Intrusion Detection, 27–46. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-2716-6_2.

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Chen, Tongwen, and Bruce Allen Francis. "Discretization." In Optimal Sampled-Data Control Systems, 33–64. London: Springer London, 1995. http://dx.doi.org/10.1007/978-1-4471-3037-6_3.

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Lohmann, Christoph. "Discretization." In Physics-Compatible Finite Element Methods for Scalar and Tensorial Advection Problems, 35–52. Wiesbaden: Springer Fachmedien Wiesbaden, 2019. http://dx.doi.org/10.1007/978-3-658-27737-6_3.

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Luo, Albert C. J., and Chuan Guo. "Discretization." In Nonlinear Vibration Reduction, 9–19. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-17499-5_3.

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Richter, Thomas. "Discretization." In Lecture Notes in Computational Science and Engineering, 117–99. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63970-3_4.

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Conference papers on the topic "Discretization"

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Mankame, Nilesh D., and Anupam Saxena. "Analysis of the Hex Cell Discretization for Topology Synthesis of Compliant Mechanisms." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35244.

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We use non-linear finite element simulations to study the convergence behavior of the honeycomb or hex cell design discretization for optimization-based synthesis of compliant mechanisms in this paper. Adjacent elements share exactly one common edge in the hex cell discretization, unlike the square cell discretization in which adjacent elements can be connected by a single node. As the single node connections in bilinear quadrilateral plane stress elements allow strain-free relative rotations, compliant mechanism designs obtained from square cell discretizations with these elements often contain elements with single node connections or point flexures. Point flexures are sites of lumped compliance, and as such, are undesirable as they lead to compliant mechanisms designs which deviate from the ideal of distributed compliance. The hex cell design discretization circumvents the problem of point flexures without any additional computational expense (e.g. filtering, extra constraints, etc.) by exploiting the geometry of the discretization. In this work we compare the elastic response of a group of four cells in which two adjacent cells have the least connectivity in both: the square and the hex discretizations. Simulations show that the hex cell discretization leads to a more accurate modeling of the displacement, stress and strain energy fields in the vicinity of the least connectivity regions than the square cell discretization. Therefore, the hex cell discretization does not suffer from stress singularities that plague the square cell discretization. These properties ensure that continuous optimization-based compliant mechanism synthesis procedures that use the hex cell discretization, exhibit a faster and more stable convergence to designs that can be readily manufactured than those that use the square cell discretization.
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Zhou, Hong, and Nitin M. Dhembare. "The Comparision of Hybrid and Quadrilateral Discretization Models for the Topology Optimization of Compliant Mechanisms." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62329.

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The design domain of a synthesized compliant mechanism is discretized into quadrilateral design cells in both hybrid and quadrilateral discretization models. However, quadrilateral discretization model allows for point connection between two diagonal design cells. Hybrid discretization model completely eliminates point connection by subdividing each quadrilateral design cell into triangular analysis cells and connecting any two contiguous quadrilateral design cells using four triangular analysis cells. When point connection is detected and suppressed in quadrilateral discretization, the local topology search space is dramatically reduced and slant structural members are serrated. In hybrid discretization, all potential local connection directions are utilized for topology optimization and any structural members can be smooth whether they are in the horizontal, vertical or diagonal direction. To compare the performance of hybrid and quadrilateral discretizations, the same design and analysis cells, genetic algorithm parameters, constraint violation penalties are employed for both discretization models. The advantages of hybrid discretization over quadrilateral discretization are obvious from the results of two classical synthesis examples of compliant mechanisms.
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Jin, Ruoming, Yuri Breitbart, and Chibuike Muoh. "Data Discretization Unification." In Seventh IEEE International Conference on Data Mining (ICDM 2007). IEEE, 2007. http://dx.doi.org/10.1109/icdm.2007.35.

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Pinto, Carlos, and Joao Gama. "Partition Incremental Discretization." In 2005 Purtuguese Conference on Artificial Intelligence. IEEE, 2005. http://dx.doi.org/10.1109/epia.2005.341288.

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Jha, Rajesh K., and Robert G. Parker. "Spatial Discretization of Axially Moving Media Vibration Problems." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-2008.

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Abstract Spatial discretization of axially moving media eigenvalue problems is examined from the perspectives of moving versus stationary system basis functions, configuration space versus state space form discretization, and subcritical versus supercritical speed convergence. The moving string eigenfunctions, which have previously been shown to give excellent discretization convergence under certain conditions, become linearly dependent and cause numerical problems as the number of terms increases. This problem does not occur in a discretization of the state space form of the eigenvalue problem, although convergence is slower, not monotonic, and not necessarily from above. Use of the moving string basis at supercritical speeds yields strikingly poor results with either the configuration or state space discretizations. The stationary system eigenfunctions provide reliable eigenvalue predictions across the range of problems examined. Because they have known, exact solutions, the moving string on elastic foundation and the traveling, tensioned beam are used as illustrative examples. Many of the findings, however, apply to more complex moving media problems, including non-trivial equilibria of nonlinear models.
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Gama, João, and Carlos Pinto. "Discretization from data streams." In the 2006 ACM symposium. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1141277.1141429.

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Shang, Lin, Shaoyue Yu, Xiuyi Jia, and Yangsheng Ji. "ROGAND: A Discretization Model." In Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007). IEEE, 2007. http://dx.doi.org/10.1109/fskd.2007.492.

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Hill, D. "Adjoint-based Discretization Schemes." In 41st Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2003. http://dx.doi.org/10.2514/6.2003-270.

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Lampton, Amanda, John Valasek, and Mrinal Kumar. "Multi-resolution state-space discretization for Q-Learning with pseudo-randomized discretization." In 2010 International Joint Conference on Neural Networks (IJCNN). IEEE, 2010. http://dx.doi.org/10.1109/ijcnn.2010.5596516.

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Jiang, Sheng-yi, Xia Li, Qi Zheng, and Lian-xi Wang. "Approximate Equal Frequency Discretization Method." In 2009 WRI Global Congress on Intelligent Systems. IEEE, 2009. http://dx.doi.org/10.1109/gcis.2009.131.

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Reports on the topic "Discretization"

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Соловйов, Володимир Миколайович, V. Saptsin, and D. Chabanenko. Markov chains applications to the financial-economic time series predictions. Transport and Telecommunication Institute, 2011. http://dx.doi.org/10.31812/0564/1189.

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In this research the technology of complex Markov chains is applied to predict financial time series. The main distinction of complex or high-order Markov Chains and simple first-order ones is the existing of after-effect or memory. The technology proposes prediction with the hierarchy of time discretization intervals and splicing procedure for the prediction results at the different frequency levels to the single prediction output time series. The hierarchy of time discretizations gives a possibility to use fractal properties of the given time series to make prediction on the different frequencies of the series. The prediction results for world’s stock market indices are presented.
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Restrepo, J. M., and G. K. Leaf. Wavelet=Galerkin discretization of hyperbolic equations. Office of Scientific and Technical Information (OSTI), December 1994. http://dx.doi.org/10.2172/432435.

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Haire, Sophia M. Quantifying Discretization Effects on Brain Trauma Simulations. Fort Belvoir, VA: Defense Technical Information Center, January 2016. http://dx.doi.org/10.21236/ad1001413.

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Zacks, S., and M. Yadin. Discretization of a Semi-Markov Shadowing Process. Fort Belvoir, VA: Defense Technical Information Center, October 1986. http://dx.doi.org/10.21236/ada175399.

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Roberts, R. M. Hexahedron, wedge, tetrahedron, and pyramid diffusion operator discretization. Office of Scientific and Technical Information (OSTI), August 1996. http://dx.doi.org/10.2172/442193.

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Vassilevski, P. Novel Two-Scale Discretization Schemes for Lagrangian Hydrodynamics. Office of Scientific and Technical Information (OSTI), May 2008. http://dx.doi.org/10.2172/945760.

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Till, Andrew. Discretization Writeup for Grey Flux-Limited Radiation Diffusion. Office of Scientific and Technical Information (OSTI), November 2020. http://dx.doi.org/10.2172/1716739.

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Hansen, Michael, and Travis Fisher. Entropy Stable Discretization of Compressible Flows in Thermochemical Nonequilibrium. Office of Scientific and Technical Information (OSTI), August 2019. http://dx.doi.org/10.2172/1763209.

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Trask, Nathaniel, Marta D'Elia, David Littlewood, Stewart Silling, Jeremy Trageser, and Michael Tupek. ASCEND: Asymptotically compatible strong form foundations for nonlocal discretization. Office of Scientific and Technical Information (OSTI), September 2021. http://dx.doi.org/10.2172/1820006.

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Schunert, Sebastian, Robert Carlsen, Nolan MacDonald, Joshua Hansel, and Alexander Lindsay. Finite Volume Discretization of the Euler Equations in Pronghorn. Office of Scientific and Technical Information (OSTI), June 2020. http://dx.doi.org/10.2172/1907648.

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