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A FETI METHOD FOR A TDNNS DISCRETIZATION OF PLANE ELASTICITY∗
"... Abstract. In this article, we consider a hybridized tangentialdisplacement normalnormalstress (TDNNS) discretization of linear elasticity. As shown in earlier work by Joachim Schöberl and the first author, TDNNS is a stable finite element discretization that does not suffers from volume locking. ..."
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. We propose a finite element tearing and interconnecting (FETI) method in order to solve the resulting linear system iteratively. The method is analyzed thoroughly for the compressible case in two dimensions, leading to a condition number bound of C(1 + log(H/h))2, which coincides with known bounds
OVERLAPPING SCHWARZ ALGORITHMS FOR ALMOST INCOMPRESSIBLE LINEAR ELASTICITY
"... Abstract. Low order finite element discretizations of the linear elasticity system suffer increasingly from locking effects and illconditioning, when the material approaches the incompressible limit, if only the displacement variable are used. Mixed finite elements using both displacement and press ..."
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and pressure variables provide a wellknown remedy, but they yield larger and indefinite discrete systems for which the design of scalable and efficient iterative solvers is challenging. Twolevel overlapping Schwarz preconditioner for the almost incompressible system of linear elasticity, discretized by mixed
Bounds on the maximum multiplicity of some common geometric graphs
 IN: 28TH INTERNATIONAL SYMPOSIUM ON THEORETICAL ASPECTS OF COMPUTER SCIENCE, 637–648, DAGSTUHL PUBLISHING
, 2011
"... We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, nonweighted common geometric graphs drawn on n points in the plane in general position (with no three points collinear): perfect matchings, spanning trees, spanning cycles (tours), and triangulatio ..."
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Cited by 11 (6 self)
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), and triangulations. (i) We present a new lower bound construction for the maximum number of triangulations a set of n points in general position can have. In particular, we show that a generalized double chain formed by two almost convex chains admits Ω(8.65 n) different triangulations. This improves the bound Ω(8
Tight Bounds for Randomized Load Balancing . . .
, 2012
"... We consider the problem of balancing load items (tokens) on networks. Starting with an arbitrary load distribution, we allow in each round nodes to exchange tokens with their neighbors. The goal is to achieve a distribution where all nodes have nearly the same number of tokens. For the continuous ca ..."
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case where tokens are arbitrarily divisible, most load balancing schemes correspond to Markov chains whose convergence is fairly wellunderstood in terms of their spectral gap. However, in many applications load items cannot be divided arbitrarily and we need to deal with the discrete case where
Some Problems On Discrete Geometry and Combinatorics
, 2012
"... Let K be a convex body in the plane. It is known that K can never be partitioned into seven regions of equal area by three nonconcurrent lines. We will be concerned with a partition of K by three nonconcurrent lines such that the ratio of the area of smallest region to the area of biggest region i ..."
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weaker result. In the second part of the thesis, we switch to the zigzag problem. We are given a set of n points in R2 and seek the minimum number of line segments required for a polygonal chain (or a simple polygonal chain) to traverse all the points. We show an n/2 + O(n / log n) upper bound if self
Collapsing threemanifolds under a lower curvature bound
 J. Differential Geom
"... Abstract The purpose of this paper is to completely characterize the topology of threedimensional Riemannian manifolds with a uniform lower bound of sectional curvature which converges to a metric space of lower dimension. Introduction We study the topology of threedimensional Riemannian manifolds ..."
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Cited by 30 (3 self)
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diameter bound D (see Remark 4.6). Observe that ∂X × D 2 ⊂ M i collapses to ∂X. We have the following corollary of Theorem 0.3. Corollary 0.4. Let M i , X, and Seif i (X) be as in Theorem 0.3, and let g and k denote the genus of X and the number of components of ∂X respectively. Then we have the following
likelihood and the role of models in molecular phylogenetics.
 Mol. Biol. Evol.
, 2000
"... Methods such as maximum parsimony (MP) are frequently criticized as being statistically unsound and not being based on any ''model.'' On the other hand, advocates of MP claim that maximum likelihood (ML) has some fundamental problems. Here, we explore the connection between the ..."
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Cited by 70 (11 self)
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events to have very low (or zero) probability, since we only require c/(r Ϫ 1) to be an upper bound to these conditional transition probabilities. We summarize the relevant constraints on this model by the quadruple THEOREM 3. If the number of states (r) is large enough (relative to the other
The Number of Edges of Many Faces in a Line Segment Arrangement
, 1992
"... We show that the maximum number of edges bounding m faces in an arrangement of n line segments in the plane is O(m 2/3 n 2/3 +n#(n)+n log m). This improves a previous upper bound of Edelsbrunner et al. [EGS] and almost matches the best known lower bound which is # m 2/3 n 2/3 + n#(n)). In a ..."
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Cited by 6 (2 self)
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We show that the maximum number of edges bounding m faces in an arrangement of n line segments in the plane is O(m 2/3 n 2/3 +n#(n)+n log m). This improves a previous upper bound of Edelsbrunner et al. [EGS] and almost matches the best known lower bound which is # m 2/3 n 2/3 + n
1An Efficient Feedback Coding Scheme with Low Error Probability for Discrete Memoryless Channels
"... Existing feedback communication schemes are either specialized to particular channels (Schalkwijk–Kailath, Horstein), or apply to general channels but have high coding complexity (block feedback schemes) or are difficult to analyze (posterior matching). This paper introduces a feedback coding scheme ..."
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scheme that combines features from previous schemes in addition to a new randomization technique. We show that our scheme achieves the capacity for all discrete memoryless channels and establish a bound on its error exponent that approaches the sphere packing bound as the rate approaches the capacity
Ultrasonic measurements of the elastic moduli of liquid crystalline polymers
"... The five independent elastic moduli of extruded rods of two thermotropic liquid crystalline polymers, Vectra B900 and Vectra A950, and the nine independent moduli of an injectionmoulded bar of Vectra A950 have been measured by ultrasonic methods at 10 MHz. For Vectra B900, the sharp rise in the axi ..."
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the transverse shear modulus (C66) by> 50%. The mechanical anisotropy in the surface layer of the injectionmoulded bar implies that the chains lie mostly in the plane parallel to the wide surface of the bar, and preferentially along the injection direction. The weak anisotropy in the core indicates almost
Results 1  10
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146