Relevant bibliographies by topics / Polyhedral approximation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Polyhedral approximation'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 May 2024

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Journal articles on the topic "Polyhedral approximation"

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Mokhnacheva, A. A., K. V. Gerasimova, and D. N. Ibragimov. "Methods of Numerical Simulation of 0-Controllable Sets of a Linear Discrete Dynamical System with Limited Control Based on Polyhedral Approximation Algorithms." Моделирование и анализ данных 13, no. 4 (December 28, 2023): 84–110. http://dx.doi.org/10.17759/mda.2023130405.

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<p>The article deals with the problem of constructing a polyhedral approximation of the 0-controllable sets of a linear discrete-time system with linear control constraints. To carry out the approximation, it is proposed to use two heuristic algorithms aimed at reducing the number of vertices of an arbitrary polyhedron while maintaining the accuracy of the description in the sense of the Hausdorff distance. The reduction of the problem of calculating the distance between nested polyhedra to the problem of convex programming is demonstrated. The issues of optimality of obtained approximations are investigated. Examples are given.</p>
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Horst, R., Ng V. Thoai, and H. Tuy. "Outer approximation by polyhedral convex sets." OR Spektrum 9, no. 3 (September 1987): 153–59. http://dx.doi.org/10.1007/bf01721096.

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Fonf, Vladimir P., Joram Lindenstrauss, and Libor Veselý. "Best approximation in polyhedral Banach spaces." Journal of Approximation Theory 163, no. 11 (November 2011): 1748–71. http://dx.doi.org/10.1016/j.jat.2011.06.011.

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Mitchell, Joseph S. B., and Subhash Suri. "Separation and approximation of polyhedral objects." Computational Geometry 5, no. 2 (September 1995): 95–114. http://dx.doi.org/10.1016/0925-7721(95)00006-u.

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Pugach, P. A., and V. A. Shlyk. "Piecewise Linear Approximation and Polyhedral Surfaces." Journal of Mathematical Sciences 200, no. 5 (July 1, 2014): 617–23. http://dx.doi.org/10.1007/s10958-014-1951-7.

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Schneider, Rolf. "Polyhedral approximation of smooth convex bodies." Journal of Mathematical Analysis and Applications 128, no. 2 (December 1987): 470–74. http://dx.doi.org/10.1016/0022-247x(87)90197-1.

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O’Dell, Brian D., and Eduardo A. Misawa. "Semi-Ellipsoidal Controlled Invariant Sets for Constrained Linear Systems." Journal of Dynamic Systems, Measurement, and Control 124, no. 1 (April 17, 2000): 98–103. http://dx.doi.org/10.1115/1.1434269.

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This paper investigates an alternative approximation to the maximal viability set for linear systems with constrained states and input. Current ellipsoidal and polyhedral approximations are either too conservative or too complex for many applications. As the primary contribution, it is shown that the intersection of a controlled invariant ellipsoid and a set of state constraints (referred to as a semi-ellipsoidal set) is itself controlled invariant under certain conditions. The proposed semi-ellipsoidal approach is less conservative than the ellipsoidal method but simpler than the polyhedral method. Two examples serve as proof-of-concept of the approach.
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Neyrinck, Mark C. "An Origami Approximation to the Cosmic Web." Proceedings of the International Astronomical Union 11, S308 (June 2014): 97–102. http://dx.doi.org/10.1017/s1743921316009686.

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AbstractThe powerful Lagrangian view of structure formation was essentially introduced to cosmology by Zel'dovich. In the current cosmological paradigm, a dark-matter-sheet 3D manifold, inhabiting 6D position-velocity phase space, was flat (with vanishing velocity) at the big bang. Afterward, gravity stretched and bunched the sheet together in different places, forming a cosmic web when projected to the position coordinates.Here, I explain some properties of an origami approximation, in which the sheet does not stretch or contract (an assumption that is false in general), but is allowed to fold. Even without stretching, the sheet can form an idealized cosmic web, with convex polyhedral voids separated by straight walls and filaments, joined by convex polyhedral nodes. The nodes form in ‘polygonal’ or ‘polyhedral’ collapse, somewhat like spherical/ellipsoidal collapse, except incorporating simultaneous filament and wall formation. The origami approximation allows phase-space geometries of nodes, filaments, and walls to be more easily understood, and may aid in understanding spin correlations between nearby galaxies. This contribution explores kinematic origami-approximation models giving velocity fields for the first time.
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Di Pietro, Daniele A., Jérôme Droniou, and Francesca Rapetti. "Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra." Mathematical Models and Methods in Applied Sciences 30, no. 09 (August 2020): 1809–55. http://dx.doi.org/10.1142/s0218202520500372.

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In this work, merging ideas from compatible discretisations and polyhedral methods, we construct novel fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra. The spaces and operators that appear in these sequences are directly amenable to computer implementation. Besides proving the exactness, we show that the usual three-dimensional sequence of trimmed Finite Element (FE) spaces forms, through appropriate interpolation operators, a commutative diagram with our sequence, which ensures suitable approximation properties. A discussion on reconstructions of potentials and discrete [Formula: see text]-products completes the exposition.
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Deville, Robert, Vladimir Fonf, and Petr Hájek. "Analytic and polyhedral approximation of convex bodies in separable polyhedral Banach spaces." Israel Journal of Mathematics 105, no. 1 (December 1998): 139–54. http://dx.doi.org/10.1007/bf02780326.

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Dissertations / Theses on the topic "Polyhedral approximation"

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Upadrasta, Ramakrishna. "Sub-Polyhedral Compilation using (Unit-)Two-Variables-Per-Inequality Polyhedra." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00818764.

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The goal of this thesis is to design algorithms that run with better complexity when compiling or parallelizing loop programs. The framework within which our algorithms operate is the polyhedral model of compilation which has been successful in the design and implementation of complex loop nest optimizers and parallelizing compilers. The algorithmic complexity and scalability limitations of the above framework remain one important weakness. We address it by introducing sub-polyhedral compilation by using (Unit-)Two-Variable-Per-Inequality or (U)TVPI Polyhedra, namely polyhedrawith restricted constraints of the type ax_{i}+bx_{j}\le c (\pm x_{i}\pm x_{j}\le c). A major focus of our sub-polyhedral compilation is the introduction of sub-polyhedral scheduling, where we propose a technique for scheduling using (U)TVPI polyhedra. As part of this, we introduce algorithms that can be used to construct under-aproximations of the systems of constraints resulting from affine scheduling problems. This technique relies on simple polynomial time algorithms to under approximate a general polyhedron into (U)TVPI polyhedra. The above under-approximation algorithms are generic enough that they can be used for many kinds of loop parallelization scheduling problems, reducing each of their complexities to asymptotically polynomial time. We also introduce sub-polyhedral code-generation where we propose algorithms to use the improved complexities of (U)TVPI sub-polyhedra in polyhedral code generation. In this problem, we show that the exponentialities associated with the widely used polyhedral code generators could be reduced to polynomial time using the improved complexities of (U)TVPI sub-polyhedra. The above presented sub-polyhedral scheduling techniques are evaluated in an experimental framework. For this, we modify the state-of-the-art PLuTo compiler which can parallelize for multi-core architectures using permutation and tiling transformations. We show that using our scheduling technique, the above under-approximations yield polyhedra that are non-empty for 10 out of 16 benchmarks from the Polybench (2.0) kernels. Solving the under-approximated system leads to asymptotic gains in complexity, and shows practically significant improvements when compared to a traditional LP solver. We also verify that code generated by our sub-polyhedral parallelization prototype matches the performance of PLuTo-optimized code when the under-approximation preserves feasibility.
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Cantin, Pierre. "Approximation of scalar and vector transport problems on polyhedral meshes." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1028/document.

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Cette thèse étudie, au niveau continu et au niveau discret sur des maillages polyédriques, les équations de transport tridimensionnelles scalaire et vectorielle. Ces équations sont constituées d'un terme diffusif, d'un terme advectif et d'un terme réactif. Dans le cadre des systèmes de Friedrichs, l'analyse mathématique est effectuée dans les espaces du graphe associés aux espaces de Lebesgue. Les conditions de positivité usuelles sur le tenseur de Friedrichs sont étendues au niveau continu et au niveau discret afin de prendre en compte les cas d'intérêt pratique où ce tenseur prend des valeurs nulles ou raisonnablement négatives. Un nouveau schéma convergeant à l'ordre 3/2 est proposé pour le problème d'advection-réaction scalaire en considérant des degrés de liberté scalaires associés aux sommets du maillage. Deux nouveaux schémas considérant également des degrés de libertés aux sommets sont proposés pour le problème de transport scalaire en traitant de manière robuste les différents régimes dominants. Le premier schéma converge à l'ordre 1/2 si les effets advectifs sont dominants et à l'ordre 1 si les effets diffusifs sont dominants. Le second schéma améliore la précision de ce schéma en convergeant à l'ordre 3/2 lorsque les effets advectifs sont dominants. Enfin, un nouveau schéma convergeant à l'ordre 1/2 est obtenu pour le problème d'advection-réaction vectoriel en considérant un seul et unique degré de liberté scalaire sur chaque arête du maillage. La précision et les performances de tous ces schémas sont examinées sur plusieurs cas tests utilisant des maillages polyédriques tridimensionnels
This thesis analyzes, at the continuous and at the discrete level on polyhedral meshes, the scalar and the vector transport problems in three-dimensional domains. These problems are composed of a diffusive term, an advective term, and a reactive term. In the context of Friedrichs systems, the continuous problems are analyzed in Lebesgue graph spaces. The classical positivity assumption on the Friedrichs tensor is generalized so as to consider the case of practical interest where this tensor takes null or slightly negative values. A new scheme converging at the order 3/2 is devised for the scalar advection-reaction problem using scalar degrees of freedom attached to mesh vertices. Two new schemes considering as well scalar degrees of freedom attached to mesh vertices are devised for the scalar transport problem and are robust with respect to the dominant regime. The first scheme converges at the order 1/2 when advection effects are dominant and at the order 1 when diffusion effects are dominant. The second scheme improves the accuracy by converging at the order 3/2 when advection effects are dominant. Finally, a new scheme converging at the order 1/2 is devised for the vector advection-reaction problem considering only one scalar degree of freedom per mesh edge. The accuracy and the efficiency of all these schemes are assessed on various test cases using three-dimensional polyhedral meshes
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McDonald, Terry Lynn. "Piecewise polynomial functions on a planar region: boundary constraints and polyhedral subdivisions." Texas A&M University, 2003. http://hdl.handle.net/1969.1/3915.

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Splines are piecewise polynomial functions of a given order of smoothness r on a triangulated region (or polyhedrally subdivided region) of Rd. The set of splines of degree at most k forms a vector space Crk() Moreover, a nice way to study Cr k()is to embed n Rd+1, and form the cone b of with the origin. It turns out that the set of splines on b is a graded module Cr b() over the polynomial ring R[x1; : : : ; xd+1], and the dimension of Cr k() is the dimension o This dissertation follows the works of Billera and Rose, as well as Schenck and Stillman, who each approached the study of splines from the viewpoint of homological and commutative algebra. They both defined chain complexes of modules such that Cr(b) appeared as the top homology module. First, we analyze the effects of gluing planar simplicial complexes. Suppose 1, 2, and = 1 [ 2 are all planar simplicial complexes which triangulate pseudomanifolds. When 1 \ 2 is also a planar simplicial complex, we use the Mayer-Vietoris sequence to obtain a natural relationship between the spline modules Cr(b), Cr (c1), Cr(c2), and Cr( \ 1 \ 2). Next, given a simplicial complex , we study splines which also vanish on the boundary of. The set of all such splines is denoted by Cr(b). In this case, we will discover a formula relating the Hilbert polynomials of Cr(cb) and Cr (b). Finally, we consider splines which are defined on a polygonally subdivided region of the plane. By adding only edges to to form a simplicial subdivision , we will be able to find bounds for the dimensions of the vector spaces Cr k() for k 0. In particular, these bounds will be given in terms of the dimensions of the vector spaces Cr k() and geometrical data of both and . This dissertation concludes with some thoughts on future research questions and an appendix describing the Macaulay2 package SplineCode, which allows the study of the Hilbert polynomials of the spline modules.
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Schulz, Henrik. "Polyhedral Surface Approximation of Non-Convex Voxel Sets and Improvements to the Convex Hull Computing Method." Forschungszentrum Dresden, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:d120-qucosa-27865.

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In this paper we introduce an algorithm for the creation of polyhedral approximations for objects represented as strongly connected sets of voxels in three-dimensional binary images. The algorithm generates the convex hull of a given object and modifies the hull afterwards by recursive repetitions of generating convex hulls of subsets of the given voxel set or subsets of the background voxels. The result of this method is a polyhedron which separates object voxels from background voxels. The objects processed by this algorithm and also the background voxel components inside the convex hull of the objects are restricted to have genus 0. The second aim of this paper is to present some improvements to our convex hull algorithm to reduce computation time.
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Schulz, Henrik. "Polyhedral Surface Approximation of Non-Convex Voxel Sets and Improvements to the Convex Hull Computing Method." Forschungszentrum Dresden-Rossendorf, 2009. https://hzdr.qucosa.de/id/qucosa%3A21613.

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In this paper we introduce an algorithm for the creation of polyhedral approximations for objects represented as strongly connected sets of voxels in three-dimensional binary images. The algorithm generates the convex hull of a given object and modifies the hull afterwards by recursive repetitions of generating convex hulls of subsets of the given voxel set or subsets of the background voxels. The result of this method is a polyhedron which separates object voxels from background voxels. The objects processed by this algorithm and also the background voxel components inside the convex hull of the objects are restricted to have genus 0. The second aim of this paper is to present some improvements to our convex hull algorithm to reduce computation time.
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Wang, Jiaxi. "PARAMETRIZATION AND SHAPE RECONSTRUCTION TECHNIQUES FOR DOO-SABIN SUBDIVISION SURFACES." UKnowledge, 2008. http://uknowledge.uky.edu/gradschool_theses/509.

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This thesis presents a new technique for the reconstruction of a smooth surface from a set of 3D data points. The reconstructed surface is represented by an everywhere -continuous subdivision surface which interpolates all the given data points. And the topological structure of the reconstructed surface is exactly the same as that of the data points. The new technique consists of two major steps. First, use an efficient surface reconstruction method to produce a polyhedral approximation to the given data points. Second, construct a Doo-Sabin subdivision surface that smoothly passes through all the data points in the given data set. A new technique is presented for the second step in this thesis. The new technique iteratively modifies the vertices of the polyhedral approximation 1CM until a new control meshM, whose Doo-Sabin subdivision surface interpolatesM, is reached. It is proved that, for any mesh M with any size and any topology, the iterative process is always convergent with Doo-Sabin subdivision scheme. The new technique has the advantages of both a local method and a global method, and the surface reconstruction process can reproduce special features such as edges and corners faithfully.
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Paradinas, Salsón Teresa. "Simplification, approximation and deformation of large models." Doctoral thesis, Universitat de Girona, 2011. http://hdl.handle.net/10803/51293.

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The high level of realism and interaction in many computer graphic applications requires techniques for processing complex geometric models. First, we present a method that provides an accurate low-resolution approximation from a multi-chart textured model that guarantees geometric fidelity and correct preservation of the appearance attributes. Then, we introduce a mesh structure called Compact Model that approximates dense triangular meshes while preserving sharp features, allowing adaptive reconstructions and supporting textured models. Next, we design a new space deformation technique called *Cages based on a multi-level system of cages that preserves the smoothness of the mesh between neighbouring cages and is extremely versatile, allowing the use of heterogeneous sets of coordinates and different levels of deformation. Finally, we propose a hybrid method that allows to apply any deformation technique on large models obtaining high quality results with a reduced memory footprint and a high performance.
L’elevat nivell de realisme i d’interacció requerit en múltiples aplicacions gràfiques fa que siguin necessàries tècniques pel processament de models geomètrics complexes. En primer lloc, presentem un mètode de simplificació que proporciona una aproximació precisa de baixa resolució d'un model texturat que garanteix fidelitat geomètrica i una correcta preservació de l’aparença. A continuació, introduïm el Compact Model, una nova estructura de dades que permet aproximar malles triangulars denses preservant els trets més distintius del model, permetent reconstruccions adaptatives i suportant models texturats. Seguidament, hem dissenyat *Cages, un esquema de deformació basat en un sistema de caixes multi-nivell que conserva la suavitat de la malla entre caixes veïnes i és extremadament versàtil, permetent l'ús de conjunts heterogenis de coordenades i diferents nivells de deformació. Finalment, proposem un mètode híbrid que permet aplicar qualsevol tècnica de deformació sobre models complexes obtenint resultats d’alta qualitat amb una memòria reduïda i un alt rendiment.
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Schulz, Henrik. "Polyedrisierung dreidimensionaler digitaler Objekte mit Mitteln der konvexen Hülle." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1225887695624-97002.

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Für die Visualisierung dreidimensionaler digitaler Objekte ist im Allgemeinen nur ihre Oberfläche von Interesse. Da von den bildgebenden Verfahren das gesamte räumliche Objekt in Form einer Volumenstruktur digitalisiert wird, muss aus den Daten die Oberfläche berechnet werden. In dieser Arbeit wird ein Algorithmus vorgestellt, der die Oberfläche dreidimensionaler digitaler Objekte, die als Menge von Voxeln gegeben sind, approximiert und dabei Polyeder erzeugt, die die Eigenschaft besitzen, die Voxel des Objektes von den Voxeln des Hintergrundes zu trennen. Weiterhin werden nicht-konvexe Objekte klassifiziert und es wird untersucht, für welche Klassen von Objekten die erzeugten Polyeder die minimale Flächenanzahl und den minimalen Oberflächeninhalt besitzen.
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Wang, Guanglei. "Relaxations in mixed-integer quadratically constrained programming and robust programming." Thesis, Evry, Institut national des télécommunications, 2016. http://www.theses.fr/2016TELE0026/document.

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De nombreux problèmes de la vie réelle sont exprimés sous la forme de décisions à prendre à l’aide de l’information accessible dans le but d’atteindre certains objectifs. La programmation numérique a prouvé être un outil efficace pour modéliser et résoudre une grande variété de problèmes de ce type. Cependant, de nombreux problèmes en apparence faciles sont encore durs à résoudre. Et même des problèmes faciles de programmation linéaire deviennent durs avec l’incertitude de l’information disponible. Motivés par un problème de télécommunication où l’on doit associer des machines virtuelles à des serveurs tout en minimisant les coûts, nous avons employé plusieurs outils de programmation mathématique dans le but de résoudre efficacement le problème, et développé de nouveaux outils pour des problèmes plus généraux. Dans l’ensemble, résumons les principaux résultats de cette thèse comme suit. Une formulation exacte et plusieurs reformulations pour le problème d’affectation de machines virtuelles dans le cloud sont données. Nous utilisons plusieurs inégalités valides pour renforcer la formulation exacte, accélérant ainsi l’algorithme de résolution de manière significative. Nous donnons en outre un résultat géométrique sur la qualité de la borne lagrangienne montrant qu’elle est généralement beaucoup plus forte que la borne de la relaxation continue. Une hiérarchie de relaxation est également proposée en considérant une séquence de couverture de l’ensemble de la demande. Ensuite, nous introduisons une nouvelle formulation induite par les symétries du problème. Cette formulation permet de réduire considérablement le nombre de termes bilinéaires dans le modèle, et comme prévu, semble plus efficace que les modèles précédents. Deux approches sont développées pour la construction d’enveloppes convexes et concaves pour l’optimisation bilinéaire sur un hypercube. Nous établissons plusieurs connexions théoriques entre différentes techniques et nous discutons d’autres extensions possibles. Nous montrons que deux variantes de formulations pour approcher l’enveloppe convexe des fonctions bilinéaires sont équivalentes. Nous introduisons un nouveau paradigme sur les problèmes linéaires généraux avec des paramètres incertains. Nous proposons une hiérarchie convergente de problèmes d’optimisation robuste – approche robuste multipolaire, qui généralise les notions de robustesse statique, de robustesse d’affinement ajustable, et de robustesse entièrement ajustable. En outre, nous montrons que l’approche multipolaire peut générer une séquence de bornes supérieures et une séquence de bornes inférieures en même temps et les deux séquences convergent vers la valeur robuste des FARC sous certaines hypothèses modérées
Many real life problems are characterized by making decisions with current information to achieve certain objectives. Mathematical programming has been developed as a successful tool to model and solve a wide range of such problems. However, many seemingly easy problems remain challenging. And some easy problems such as linear programs can be difficult in the face of uncertainty. Motivated by a telecommunication problem where assignment decisions have to be made such that the cloud virtual machines are assigned to servers in a minimum-cost way, we employ several mathematical programming tools to solve the problem efficiently and develop new tools for general theoretical problems. In brief, our work can be summarized as follows. We provide an exact formulation and several reformulations on the cloud virtual machine assignment problem. Then several valid inequalities are used to strengthen the exact formulation, thereby accelerating the solution procedure significantly. In addition, an effective Lagrangian decomposition is proposed. We show that, the bounds providedby the proposed Lagrangian decomposition is strong, both theoretically and numerically. Finally, a symmetry-induced model is proposed which may reduce a large number of bilinear terms in some special cases. Motivated by the virtual machine assignment problem, we also investigate a couple of general methods on the approximation of convex and concave envelopes for bilinear optimization over a hypercube. We establish several theoretical connections between different techniques and prove the equivalence of two seeming different relaxed formulations. An interesting research direction is also discussed. To address issues of uncertainty, a novel paradigm on general linear problems with uncertain parameters are proposed. This paradigm, termed as multipolar robust optimization, generalizes notions of static robustness, affinely adjustable robustness, fully adjustable robustness and fills the gaps in-between. As consequences of this new paradigms, several known results are implied. Further, we prove that the multipolar approach can generate a sequence of upper bounds and a sequence of lower bounds at the same time and both sequences converge to the robust value of fully adjustable robust counterpart under some mild assumptions
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Schulz, Henrik. "Polyedrisierung dreidimensionaler digitaler Objekte mit Mitteln der konvexen Hülle." Doctoral thesis, Technische Universität Dresden, 2007. https://tud.qucosa.de/id/qucosa%3A23659.

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Für die Visualisierung dreidimensionaler digitaler Objekte ist im Allgemeinen nur ihre Oberfläche von Interesse. Da von den bildgebenden Verfahren das gesamte räumliche Objekt in Form einer Volumenstruktur digitalisiert wird, muss aus den Daten die Oberfläche berechnet werden. In dieser Arbeit wird ein Algorithmus vorgestellt, der die Oberfläche dreidimensionaler digitaler Objekte, die als Menge von Voxeln gegeben sind, approximiert und dabei Polyeder erzeugt, die die Eigenschaft besitzen, die Voxel des Objektes von den Voxeln des Hintergrundes zu trennen. Weiterhin werden nicht-konvexe Objekte klassifiziert und es wird untersucht, für welche Klassen von Objekten die erzeugten Polyeder die minimale Flächenanzahl und den minimalen Oberflächeninhalt besitzen.
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Books on the topic "Polyhedral approximation"

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Finite Frame Theory: A Complete Introduction to Overcompleteness. American Mathematical Society, 2016.

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Book chapters on the topic "Polyhedral approximation"

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Ayala, D., P. Brunet, R. Joan-Arinyo, and I. Navazo. "Multiresolution Approximation of Polyhedral Solids." In CAD Systems Development, 327–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60718-9_23.

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Goodman, T. N. T. "Shape Preserving Approximation by Polyhedral Splines." In Multivariate Approximation Theory III, 198–205. Basel: Birkhäuser Basel, 1985. http://dx.doi.org/10.1007/978-3-0348-9321-3_19.

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Simanchev, R. Yu, I. V. Urazova, and Yu A. Kochetov. "Polyhedral Attack on the Graph Approximation Problem." In Mathematical Optimization Theory and Operations Research, 255–65. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-33394-2_20.

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Guo, Xijuan, Lei Xie, and Yongliang Gao. "Optimal Accurate Minkowski Sum Approximation of Polyhedral Models." In Lecture Notes in Computer Science, 179–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-87442-3_23.

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Maréchal, Alexandre, Alexis Fouilhé, Tim King, David Monniaux, and Michael Périn. "Polyhedral Approximation of Multivariate Polynomials Using Handelman’s Theorem." In Lecture Notes in Computer Science, 166–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-49122-5_8.

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Bärmann, Andreas. "Polyhedral Approximation of Second-Order Cone Robust Counterparts." In Solving Network Design Problems via Decomposition, Aggregation and Approximation, 163–77. Wiesbaden: Springer Fachmedien Wiesbaden, 2016. http://dx.doi.org/10.1007/978-3-658-13913-1_12.

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Mahmudov, Elimhan N. "Approximation and Optimization of Polyhedral Discrete and Differential Inclusions." In Communications in Computer and Information Science, 364–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31724-8_38.

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del Campo, Miguel Vázquez-Martin, Hermilo Sánchez-Cruz, César Omar Jiménez-Ibarra, and Mario Alberto Rodríguez-Díaz. "Polyhedral Approximation for 3D Objects by Dominant Point Detection." In Advances in Computer Vision and Computational Biology, 189–204. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-71051-4_14.

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Cangiani, Andrea, Zhaonan Dong, Emmanuil H. Georgoulis, and Paul Houston. "Inverse Estimates and Polynomial Approximation on Polytopic Meshes." In hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes, 23–37. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67673-9_3.

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Lotov, Alexander V., Vladimir A. Bushenkov, and Georgy K. Kamenev. "Theory of Iterative Methods for Polyhedral Approximation of Convex Bodies." In Interactive Decision Maps, 237–61. Boston, MA: Springer US, 2004. http://dx.doi.org/10.1007/978-1-4419-8851-5_8.

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Conference papers on the topic "Polyhedral approximation"

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Francis, Schmitt, and Gholizadeh Behrouz. "Adaptative Polyhedral Approximation Of Digitized Surfaces." In 1985 International Technical Symposium/Europe, edited by Olivier D. Faugeras and Robert B. Kelley. SPIE, 1986. http://dx.doi.org/10.1117/12.952249.

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Kalvin, Alan D., and Russell H. Taylor. "Superfaces: polyhedral approximation with bounded error." In Medical Imaging 1994, edited by Yongmin Kim. SPIE, 1994. http://dx.doi.org/10.1117/12.173991.

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Kim, Young J., Gokul Varadhan, Ming C. Lin, and Dinesh Manocha. "Fast swept volume approximation of complex polyhedral models." In the eighth ACM symposium. New York, New York, USA: ACM Press, 2003. http://dx.doi.org/10.1145/781606.781613.

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Nicu, Theodor-Gabriel, Florin Stoican, and Ionela Prodan. "Smooth approximation of polyhedral potential field in NMPC for obstacle avoidance." In 2023 European Control Conference (ECC). IEEE, 2023. http://dx.doi.org/10.23919/ecc57647.2023.10178410.

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Lundell, Andreas, and Jan Kronqvist. "Integration of polyhedral outer approximation algorithms with MIP solvers through callbacks and lazy constraints." In PROCEEDINGS LEGO – 14TH INTERNATIONAL GLOBAL OPTIMIZATION WORKSHOP. Author(s), 2019. http://dx.doi.org/10.1063/1.5089979.

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Rashid, Mark M., Mili Selimotic, and Tarig Dinar. "General Polyhedral Finite Elements for Rapid Nonlinear Analysis." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49248.

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An analysis system for solid mechanics applications is described in which a new finite element method that can accommodate general polyhedral elements is exploited. The essence of the method is direct polynomial approximation of the shape functions on the physical element, without transformation to a canonical element. The main motive is elimination of the requirement that all elements be similar to a canonical element via the usual isoparametric mapping. It is this topological restriction that largely drives the design of mesh-generation algorithms, and ultimately leads to the considerable human effort required to perform complex analyses. An integrated analysis system is described in which the flexibility of the polyhedral element method is leveraged via a robust computational geometry processor. The role of the latter is to perform rapid Boolean intersection operations between hex meshes and surface representations of the body to be analyzed. A typical procedure is to create a space-filling structured hex mesh that contains the body, and then extract a polyhedral mesh of the body by intersecting the hex mesh and the body’s surface. The result is a mesh that is directly usable in the polyhedral finite element method. Some example applications are: 1) simulation on very complex geometries; 2) rapid geometry modification and re-analysis; and 3) analysis of material-removal process steps following deformation processing. This last class of problems is particularly challenging for the conventional FE methodology, because the element boundaries are, in general, not aligned with the cutting geometry following the deformation (e.g. forging) step.
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Shovkun, Igor, and Hamdi A. Tchelepi. "A Cut-Cell Polyhedral Finite Element Model for Coupled Fluid Flow and Mechanics in Fractured Reservoirs." In SPE Reservoir Simulation Conference. SPE, 2021. http://dx.doi.org/10.2118/203958-ms.

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Abstract Mechanical deformation induced by injection and withdrawal of fluids from the subsurface can significantly alter the flow paths in naturally fractured reservoirs. Modeling coupled fluid-flow and mechanical deformation in fractured reservoirs relies on either sophisticated gridding techniques, or enhancing the variables (degrees-of-freedom) that represent the physics in order to describe the behavior of fractured formation accurately. The objective of this study is to develop a spatial discretization scheme that cuts the "matrix" grid with fracture planes and utilizes traditional formulations for fluid flow and geomechanics. The flow model uses the standard low-order finite-volume method with the Compartmental Embedded fracture Model (cEDFM). Due to the presence of non-standard polyhedra in the grid after cutting/splitting, we utilize numerical harmonic shape functions within a Polyhedral finite-element (PFE) formulation for mechanical deformation. In order to enforce fracture-contact constraints, we use a penalty approach. We provide a series of comparisons between the approach that uses conforming Unstructured grids and a Discrete Fracture Model (Unstructured DFM) with the new cut-cell PFE formulation. The manuscript analyzes the convergence of both methods for linear elastic, single-fracture slip, and Mandel’s problems with tetrahedral, Cartesian, and PEBI-grids. Finally, the paper presents a fully-coupled 3D simulation with multiple inclined intersecting faults activated in shear by fluid injection, which caused an increase in effective reservoir permeability. Our approach allows for great reduction in the complexity of the (gridded) model construction while retaining the solution accuracy together with great saving in the computational cost compared with UDFM. The flexibility of our model with respect to the types of grid polyhedra allows us to eliminate mesh artifacts in the solution of the transport equations typically observed when using tetrahedral grids and two-point flux approximation.
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Höhner, Dominik, Siegmar Wirtz, and Viktor Scherer. "Experimental and Numerical Investigation on the Discharge of Wood Pellets From a Hopper With the Discrete Element Method." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-87406.

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In this study hopper discharge experiments with wood pellets were conducted. The experimental bulk density, flow behavior and discharge rate were compared to corresponding 3-dimensional discrete element simulations with both multi-sphere and polyhedral approximations of the pellet geometry. Additionally a numerical sensitivity analysis for the particle-wall friction was made in order to evaluate the influence of this parameter on hopper discharge in the context of different particle geometries. In the past comparisons of experimentally and numerically obtained results demonstrated the adequacy of the discrete element method for predicting the general discharge behavior of a hopper. Nevertheless, in this study, comparing two different particle shape-approximations, significant differences in terms of bulk density, discharge rate, flow profile and dependency on the particle-wall friction coefficient between both investigated particle-shape approximation schemes could be observed. As a result, particle shape-representation must be considered a significant parameter in DEM-simulations.
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Kustova, Natalia V., Alexander V. Konoshonkin, Anatoli G. Borovoi, and Kirill S. Salnikov. "Verification of the physical optics approximation for the calculation of the light scattering matrixes on polyhedral Platonic bodies." In XXIX International Symposium "Atmospheric and Ocean Optics, Atmospheric Physics", edited by Oleg A. Romanovskii. SPIE, 2023. http://dx.doi.org/10.1117/12.2690718.

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Dong, Rencheng, Faruk O. Alpak, and Mary F. Wheeler. "Accurate Multi-Phase Flow Simulation in Faulted Reservoirs Using Mimetic Finite Difference Methods on Polyhedral Cells." In SPE Annual Technical Conference and Exhibition. SPE, 2021. http://dx.doi.org/10.2118/206298-ms.

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Abstract Faulted reservoirs are commonly modeled by corner-point grids. Since the two-point flux approximation (TPFA) method is not consistent on non-orthogonal grids, multi-phase flow simulation using TPFA on corner-point grids may have significant discretization errors if grids are not K-orthogonal. To improve the simulation accuracy, we developed a novel method where the faults are modeled by polyhedral cells, and mimetic finite difference (MFD) methods are used to solve flow equations. We use a cut-cell approach to build the mesh for faulted reservoirs. A regular orthogonal grid is first constructed,and then fault planes are added by dividing cells at fault planes. Most cells remain orthogonal while irregular non-orthogonal polyhedral cells can be formed with multiple cell divisions. We investigated three spatial discretization methods for solving the pressure equation on general polyhedral grids, including the TPFA, MFD and TPFA-MFD hybrid methods. In the TPFA-MFD hybrid method, the MFD method is only applied to part of the domain while the TPFA method is applied to rest of the domain. We compared flux accuracy between TPFA and MFD methods by solving a single-phase flow problem. The reference solution is obtained on a rectangular grid while the same problem is solved by TPFA and MFD methods on a grid with distorted cells near a fault. Fluxes computed using TPFA exhibit larger errors in the vicinity of the fault while fluxes computed using MFD are still as accurate as the reference solution. We also compared saturation accuracy of two-phase (oil and water) flow in faulted reservoirs when the pressure equation is solved by different discretization methods. Compared with the reference saturation solution, saturation exhibits non-physical errors near the fault when pressure equation is solved by the TPFA method. Since the MFD method yields accurate fluxes over general polyhedral grids, the resulting saturation solutions match the reference saturation solutions with an enhanced accuracy when the pressure equation is solved by the MFD method. Based on the results of our simulation studies, the accuracy of the TPFA-MFD hybrid method is very close to the accuracy of the MFD method while the TPFA-MFD hybrid method is computationally cheaper than the MFD method.
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