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  • 2005-2009  (51)
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  • 1890-1899
  • 2006  (51)
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  • 2005-2009  (51)
  • 1990-1994  (2,135)
  • 1965-1969  (1,202)
  • 1925-1929
  • 1890-1899
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  • 1
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    Jahresbericht 2005 (2006)
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    Publication Date: 2019-10-24
    Keywords: ddc:000
    Language: German
    Type: annualzib , doc-type:report
    Format: application/pdf
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    OPUS
  • 2
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    Convergence of the Control Reduced Interior Point Method for PDE Constrained Optimal Control with State Constraints (2006)
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    Publication Date: 2014-02-26
    Description: We propose a variant of the control reduced interior point method for the solution of state constrained problems. We show convergence of the corresponding interior point pathfollowing algorithm in function space. Morever, we provide error bounds for the iterates.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 3
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    A Complex Mathematical Model of the Human Menstrual Cycle (2006)
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    Publication Date: 2014-02-26
    Description: This paper aims at presenting the complex coupled network of the human menstrual cycle to the interested community. Beyond the presently popular smaller models, where important network components arise only as extremely simplified source terms, we add: the GnRH pulse generator in the hypothalamus, receptor binding, and the biosynthesis in the ovaries. Simulation and parameter identification are left to a forthcoming paper.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 4
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    A continuity result for Nemyckii Operators and some applications in PDE constrained optimal control (2006)
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    Publication Date: 2014-02-26
    Description: This work explores two applications of a classical result on the continuity of Nemyckii operators to optimal control with PDEs. First, we present an alternative approach to the analysis of Newton's method for function space problems involving semi-smooth Nemyckii operators. A concise proof for superlinear convergence is presented, and sharpened bounds on the rate of convergence are derived. Second, we derive second order sufficient conditions for problems, where the underlying PDE has poor regularity properties. We point out that the analytical structure in both topics is essentially the same.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 5
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    Nash Equilibria in Online Sequential Routing Games (2006)
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    Publication Date: 2014-02-26
    Description: In this paper, we study the efficiency of Nash equilibria for a sequence of nonatomic routing games. We assume that the games are played consecutively in time in an online fashion: by the time of playing game $i$, future games $i+1,\dots,n$ are not known, and, once players of game $i$ are in equilibrium, their corresponding strategies and costs remain fixed. Given a sequence of games, the cost for the sequence of Nash equilibria is defined as the sum of the cost of each game. We analyze the efficiency of a sequence of Nash equilibria in terms of competitive analysis arising in the online optimization field. Our main result states that the online algorithm $\sl {SeqNash}$ consisting of the sequence of Nash equilibria is $\frac{4n}{2+n}$-competitive for affine linear latency functions. For $n=1$, this result contains the bound on the price of anarchy of $\frac{4}{3}$ for affine linear latency functions of Roughgarden and Tardos [2002] as a special case. Furthermore, we analyze a problem variant with a modified cost function that reflects the total congestion cost, when all games have been played. In this case, we prove an upper bound of $\frac{4n}{2+n}$ on the competitive ratio of $\sl {SeqNash}$. We further prove a lower bound of $\frac{3n-2}{n}$ of $\sl {SeqNash}$ showing that for $n=2$ our upper bound is tight.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 6
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    Adaptive, Fast and Oblivious Convolution in Evolution Equations with Memory (2006)
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    Publication Date: 2016-06-09
    Description: To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing $N$ steps requires only $O(N\log N)$ operations and $O(\log N)$ active memory, in place of $O(N^2)$ operations and $O(N)$ memory for a direct implementation. A basic feature of the fast algorithm is the reduction, via contour integral representations, to differential equations which are solved numerically with adaptive step sizes. Rather than the kernel itself, its Laplace transform is used in the algorithm. The algorithm is illustrated on three examples: a blow-up example originating from a Schrödinger equation with concentrated nonlinearity, chemical reactions with inhibited diffusion, and viscoelasticity with a fractional order constitutive law.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 7
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    Two-layer Network Design by Branch-and-Cut featuring MIP-based Heuristics (2006)
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    Publication Date: 2020-11-13
    Description: This paper deals with MIP-based primal heuristics to be used within a branch-and-cut approach for solving multi-layer telecommunication network design problems. Based on a mixed-integer programming formulation for two network layers, we present three heuristics for solving important subproblems, two of which solve a sub-MIP. On multi-layer planning instances with many parallel logical links, we show the effectiveness of our heuristics in finding good solutions early in the branch-and-cut search tree.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 8
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    Adaptive Finite Element Simulation of Ventricular Fibrillation Dynamics (2006)
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    Publication Date: 2019-05-10
    Description: The dynamics of ventricular fibrillation caused by irregular excitation is simulated in the frame of the monodomain model with an action potential model due to Aliev-Panfilov for a human 3D geometry. The numerical solution of this multiscale reaction-diffusion problem is attacked by algorithms which are fully adaptive in both space and time (code library {\sc Kardos}). The obtained results clearly demonstrate an accurate resolution of the cardiac potential during the excitation and the plateau phases (in the regular cycle) as well as after a reentrant excitation (in the irregular cycle).
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 9
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    Orbitopal Fixing (2006)
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    Publication Date: 2020-12-15
    Description: The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the permutation of the subsets of the partition is irrelevant. This kind of symmetry unnecessarily blows up the branch-and-cut tree. We present a general tool, called orbitopal fixing, for enhancing the capabilities of branch-and-cut algorithms in solving this kind of symmetric integer programming models. We devise a linear time algorithm that, applied at each node of the branch-and-cut tree, removes redundant parts of the tree produced by the above mentioned permutations. The method relies on certain polyhedra, called orbitopes, which have been investigated in (Kaibel and Pfetsch (2006)). However, it does not add inequalities to the model, and thus, it does not increase the difficulty of solving the linear programming relaxations. We demonstrate the computational power of orbitopal fixing at the example of a graph partitioning problem motivated from frequency planning in mobile telecommunication networks.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 10
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    Approximability of Unsplittable Shortest Path Routing Problems (2006)
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    Publication Date: 2014-11-10
    Description: In this paper, we discuss the relation of unsplittable shortest path routing (USPR) to other routing schemes and study the approximability of three USPR network planning problems. Given a digraph $D=(V,A)$ and a set $K$ of directed commodities, an USPR is a set of flow paths $\Phi_{(s,t)}$, $(s,t)\in K$, such that there exists a metric $\lambda=(\lambda_a)\in \mathbb{Z}^A_+$ with respect to which each $\Phi_{(s,t)}$ is the unique shortest $(s,t)$-path. In the \textsc{Min-Con-USPR} problem, we seek for an USPR that minimizes the maximum congestion over all arcs. We show that this problem is hard to approximate within a factor of $\mathcal{O}(|V|^{1-\epsilon})$, but easily approximable within min$(|A|,|K|)$ in general and within $\mathcal{O}(1)$ if the underlying graph is an undirected cycle or a bidirected ring. We also construct examples where the minimum congestion that can be obtained by USPR is a factor of $\Omega(|V|^2)$ larger than that achievable by unsplittable flow routing or by shortest multi-path routing, and a factor of $\Omega(|V|)$ larger than by unsplittable source-invariant routing. In the CAP-USPR problem, we seek for a minimum cost installation of integer arc capacities that admit an USPR of the given commodities. We prove that this problem is $\mathcal{NP}$-hard to approximate within $2-\epsilon$ (even in the undirected case), and we devise approximation algorithms for various special cases. The fixed charge network design problem \textsc{Cap-USPR}, where the task is to find a minimum cost subgraph of $D$ whose fixed arc capacities admit an USPR of the commodities, is shown to be $\mathcal{NPO}$-complete. All three problems are of great practical interest in the planning of telecommunication networks that are based on shortest path routing protocols. Our results indicate that they are harder than the corresponding unsplittable flow or shortest multi-path routing problems.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 11
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    Availability and Cost Based Evaluation of Demand-wise Shared Protection (2006)
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    Publication Date: 2014-11-11
    Description: In this paper, we investigate the connection availabilities for the new protection scheme Demand-wise Shared Protection (DSP) and describe an appropriate approach for their computation. The exemplary case study on two realistic network scenarios shows that in most cases the availabilities for DSP are comparable with that for 1+1 path protection and better than in case of shared path protection.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 12
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    THESEUS - Protein Structure Prediction at ZIB (2006)
    Details
    Publication Date: 2016-06-30
    Description: THESEUS, the ZIB threading environment, is a parallel implementation of a protein threading based on a multi-queued branch-and-bound optimal search algorithm to find the best sequence-to-structure alignment through a library of template structures. THESEUS uses a template core model based on secondary structure definition and a scoring function based on knowledge-based potentials reflecting pairwise interactions and the chemical environment, as well as pseudo energies for homology detection, loop alignment, and secondary structure matching. The threading core is implemented in C++ as a SPMD parallization architecture using MPI for communication. The environment is designed for generic testing of different scoring functions, e.g. different secondary structure prediction terms, different scoring matrices and information derived from multiple sequence alignments. A validaton of the structure prediction results has been done on the basis of standard threading benchmark sets. THESEUS successfully participated in the 6th Critical Assessment of Techniques for Protein Structure Prediction (CASP) 2004.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 13
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    On the stability of the multi-queue multi-server processor sharing with limited service (2006)
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    Publication Date: 2014-02-26
    Description: We consider a multi-queue multi-server system with $n$ servers (processors) and $m$ queues. At the system there arrives a stationary and ergodic stream of $m$ different types of requests with service requirements which are served according to the following $k$-limited head of the line processor sharing discipline: The first $k$ requests at the head of the $m$ queues are served in processor sharing by the $n$ processors, where each request may receive at most the capacity of one processor. By means of sample path analysis and Loynes' monotonicity method, a stationary and ergodic state process is constructed, and a necessary as well as a sufficient condition for the stability of the $m$ separate queues are given, which are tight within the class of all stationary ergodic inputs. These conditions lead to tight necessary and sufficient conditions for the whole system, also in case of permanent customers, generalizing an earlier result by the authors for the case of $n$=$k$=1.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 14
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    ConfJump : a fast biomolecular sampling method which drills tunnels through high mountains (2006)
    Details
    Publication Date: 2014-02-26
    Description: In order to compute the thermodynamic weights of the different metastable conformations of a molecule, we want to approximate the molecule's Boltzmann distribution in a reasonable time. This is an essential issue in computational drug design. The energy landscape of active biomolecules is generally very rough with a lot of high barriers and low regions. Many of the algorithms that perform such samplings (e.g. the hybrid Monte Carlo method) have difficulties with such landscapes. They are trapped in low-energy regions for a very long time and cannot overcome high barriers. Moving from one low-energy region to another is a very rare event. For these reasons, the distribution of the generated sampling points converges very slowly against the thermodynamically correct distribution of the molecule. The idea of ConfJump is to use $a~priori$ knowledge of the localization of low-energy regions to enhance the sampling with artificial jumps between these low-energy regions. The artificial jumps are combined with the hybrid Monte Carlo method. This allows the computation of some dynamical properties of the molecule. In ConfJump, the detailed balance condition is satisfied and the mathematically correct molecular distribution is sampled.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 15
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    Mathematik für den Volkssport (2006)
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    Publication Date: 2020-02-11
    Description: "`Volkssport Sudoku"' titelt der Stern in seiner Ausgabe vom 24. Mai2006. In der Tat traut sich derzeit kaum noch eine Zeitung, ohne Sudoku zu erscheinen. Die Begeisterung am Lösen dieser Zahlenrätsel offenbart eine unvermutete Freude am algorithmischen Arbeiten. Mathematisch kann man Sudokus als lineare diophantische Gleichungssysteme mit Nichtnegativitätsbedingungen formulieren. Solche ganzzahligen linearen Programme sind die wichtigsten Modellierungswerkzeuge in zahlreichen Anwendungsgebieten wie z.B. der Optimierung von Telekommunikations- und Verkehrsnetzen. Moderne Verfahren zur Lösung dieser Optimierungsprobleme sind durch Sudokus allerdings deutlich weniger zu beeindrucken als Zeitungsleser.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
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  • 16
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    Mathematical Methods for Physical Layout of Printed Circuit Boards: An Overview (2006)
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    Publication Date: 2020-02-11
    Description: This article surveys mathematical models and methods used for physical PCB layout, i.e., component placement and wire routing. The main concepts are briefly described together with relevant references.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 17
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    Competitive Online Multicommodity Routing (2006)
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    Publication Date: 2020-12-15
    Description: We study online multicommodity minimum cost routing problems in networks, where commodities have to be routed sequentially. Arcs are equipped with load dependent price functions defining the routing weights. We discuss an online algorithm that routes each commodity by minimizing a convex cost function that depends on the demands that are previously routed. We present a competitive analysis of this algorithm showing that for affine linear price functions this algorithm is $4K/2+K$-competitive, where $K$ is the number of commodities. For the parallel arc case this algorithm is optimal. Without restrictions on the price functions and network, no algorithm is competitive. Finally, we investigate a variant in which the demands have to be routed unsplittably.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 18
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    The extreme points of QSTAB(G) and its implications (2006)
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    Publication Date: 2021-03-16
    Description: Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations w.r.t different concepts. Perfect graphs are, e.g., characterized as precisely those graphs $G$ where the stable set polytope STAB$(G)$ coincides with the clique constraint stable set polytope QSTAB$(G)$. For all imperfect graphs STAB$(G) \subset$ QSTAB$(G)$ holds and, therefore, it is natural to measure imperfection in terms of the difference between STAB$(G)$ and QSTAB$(G)$. Several concepts have been developed in this direction, for instance the dilation ratio of STAB$(G)$ and QSTAB$(G)$ which is equivalent to the imperfection ratio imp$(G)$ of $G$. To determine imp$(G)$, both knowledge on the facets of STAB$(G)$ and the extreme points of QSTAB$(G)$ is required. The anti-blocking theory of polyhedra yields all {\em dominating} extreme points of QSTAB$(G)$, provided a complete description of the facets of STAB$(\overline G)$ is known. As this is typically not the case, we extend the result on anti-blocking polyhedra to a {\em complete} characterization of the extreme points of QSTAB$(G)$ by establishing a 1-1 correspondence to the facet-defining subgraphs of $\overline G$. We discuss several consequences, in particular, we give alternative proofs of several famous results.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 19
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    On exact algorithms for treewidth (2006)
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    Publication Date: 2014-11-10
    Description: We give experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential time algorithms using exponential space or using only polynomial space. We first report on an implementation of a dynamic programming algorithm for computing the treewidth of a graph with running time $O^\ast(2^n)$. This algorithm is based on the old dynamic programming method introduced by Held and Karp for the {\sc Tra veling Salesman} problem. We use some optimizations that do not affect the worst case running time but improve on the running time on actual instances and can be seen to be practical for small instances. However, our experiments show that the space use d by the algorithm is an important factor to what input sizes the algorithm is effective. For this purpose, we settle the problem of computing treewidth under the restriction that the space used is only polynomial. In this direction we give a simple $O^\ast(4^n)$ al gorithm that requires {\em polynomial} space. We also show that with a more complicated algorithm, using balanced separators, {\sc Treewidth} can be computed in $O^\ast(2.9512^n)$ time and polynomial space.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 20
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    Coarse Grained Molecular Kinetics (2006)
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    Publication Date: 2014-03-10
    Description: The dynamic behavior of molecules can often be described by Markov processes. From computational molecular simulations one can derive transition rates or transition probabilities between subsets of the discretized conformational space. On the basis of this dynamic information, the spatial subsets are combined into a small number of so-called metastable molecular conformations. This is done by clustering methods like the Robust Perron Cluster Analysis (PCCA+). Up to now it is an open question how this coarse graining in space can be transformed to a coarse graining of the Markov chain while preserving the essential dynamic information. In the following article we aim at a consistent coarse graining of transition probabilities or rates on the basis of metastable conformations such that important physical and mathematical relations are preserved. This approach is new because PCCA+ computes molecular conformations as linear combinations of the dominant eigenvectors of the transition matrix which does not hold for other clustering methods.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 21
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    RSWK/SWD und Faceted Browsing: neue Möglichkeiten einer inhaltlich-intuitiven Navigation (2006)
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    Publication Date: 2014-02-26
    Description: Das deutschsprachige Bibliothekswesen verfügt mit den \glqq Regeln für den Schlagwortkatalog \grqq (RSWK) unter Verwendung der \glqq Schlagwortnormdatei \grqq (SWD) über ein Instrumentarium, welches zusammen mit einem \glqq Faceted Browsing \grqq das bisher bestehende Angebot für ein Information Retrieval optimal ergänzen kann. Die Verbindung zwischen Standardvokabular (SWD) und Kettenbildung (RSWK) einerseits und eine nach Facetten-Eigenschaften gegliederte Navigation andererseits unterstützt bestmöglich eine inhaltlich bezogene Recherche. Die Stärken und Schwächen der RSWK/SWD werden erörtert und auch Klassifikationen (DDC und RVK) als mögliche Facetten diskutiert.
    Keywords: ddc:000
    Language: German
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  • 22
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    Accuracy, Stability, Convergence of Rigorous Thermodynamic Sampling Methods (2006)
    Details
    Publication Date: 2016-06-09
    Keywords: ddc:000
    Language: English
    Type: masterthesis , doc-type:masterThesis
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  • 23
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    Primal Heuristics for Mixed Integer Programs (2006)
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    Publication Date: 2022-03-14
    Description: A lot of problems arising in Combinatorial Optimization and Operations Research can be formulated as Mixed Integer Programs (MIP). Although MIP-solving is an NP-hard optimization problem, many practically relevant instances can be solved in reasonable time. In modern MIP-solvers like the branch-cut-and-price-framework SCIP, primal heuristics play a major role in finding and improving feasible solutions at the early steps of the solution process. This helps to reduce the overall computational effort, guides the remaining search process, and proves the feasibility of the MIP model. Furthermore, a heuristic solution with a small gap to optimality often is sufficient in practice. We investigate 16 different heuristics, all of which are available in SCIP. Four of them arise from the literature of the last decade, nine are specific implementations of general heuristic ideas, three have been newly developed. We present an improved version of the feasibility pump heuristic by Fischetti et al., which in experiments produced solutions with only a third of the optimality gap compared to the original version. Furthermore, we introduce two new Large Neighborhood Search (LNS) heuristics. Crossover is an LNS improvement heuristic making use of similarities of diverse MIP solutions to generate new incumbent solutions. RENS is an LNS rounding heuristic which evaluates the space of all possible roundings of a fractional LP-solution. This heuristic makes it possible to determine whether a point can be rounded to an integer solution and which is the best possible rounding. We conclude with a computational comparison of all described heuristics. It points out that a single heuristic on its own has only a slight impact on the overall performance of SCIP, but the combination of all of them reduces the running time by a factor of two compared to a version without any heuristics.
    Keywords: ddc:000
    Language: English
    Type: masterthesis , doc-type:masterThesis
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  • 24
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    A cartesian grid finite volume method for the solution of the Poisson equation with variable coefficients and embedded interfaces (2006)
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    Publication Date: 2014-02-26
    Description: We present a finite volume method for the solution of the two-dimensional Poisson equation $ \nabla\cdot( \beta( {\mbox{\boldmath $x$}}) \nabla u({\mbox{\boldmath $x$}})) = f(\mbox{\boldmath $x$}) $ with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz functions on Cartesian grids for the solution $u({\mbox{\boldmath $x$})$ resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard multigrid solver. Singularities associated with vanishing partial volumes of intersected grid cells or the dual bilinear ansatz itself are removed by a two-step asymptotic approach. The method achieves second order of accuracy in the $L^\infty$ and $L^2$ norm.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 25
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    Efficient Sampling of the Stationary Distribution of Metastable Dynamical Systems (2006)
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    Publication Date: 2014-11-11
    Description: In this article we aim at an efficient sampling of the stationary distribution of dynamical systems in the presence of metastabilities. In the past decade many sophisticated algorithms have been inven ted in this field. We do not want to simply add a further one. We address the problem that one has applied a sampling algorithm for a dynamical system many times. This leads to different samplings which more or less represent the stationary distribution partially very well, but which are still far away from ergodicity or from the global stationary distribution. We will show how these samplings can be joined together in order to get one global sampling of the stationary distribution.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 26
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    Polynomial-Time Algorithms for Linear and Convex Optimization on Jump Systems (2006)
    Details
    Publication Date: 2014-02-26
    Description: The concept of jump system, introduced by Buchet and Cunningham (1995), is a set of integer points with a certain exchange property. In this paper, we discuss several linear and convex optimization problems on jump systems and show that these problems can be solved in polynomial time under the assumption that a membership oracle for a jump system is available. We firstly present a polynomial-time implementation of the greedy algorithm for the minimization of a linear function. We then consider the minimization of a separable-convex function on a jump system, and propose the first polynomial-time algorithm for this problem. The algorithm is based on the domain reduction approach developed in Shioura (1998). We finally consider the concept of M-convex functions on constant-parity jump systems which has been recently proposed by Murota (2006). It is shown that the minimization of an M-convex function can be solved in polynomial time by the domain reduction approach.
    Keywords: ddc:000
    Language: English
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    Packing and Partitioning Orbitopes (2006)
    Details
    Publication Date: 2020-12-15
    Description: We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal subject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain insight into ways of breaking certain symmetries in integer programs by adding constraints, e.g., for a well-known formulation of the graph coloring problem. We provide a thorough polyhedral investigation of packing and partitioning orbitopes for the cases in which the group acting on the columns is the cyclic group or the symmetric group. Our main results are complete linear inequality descriptions of these polytopes by facet-defining inequalities. For the cyclic group case, the descriptions turn out to be totally unimodular, while for the symmetric group case, both the description and the proof are more involved. The associated separation problems can be solved in linear time.
    Keywords: ddc:000
    Language: English
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  • 28
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    LP-Based Local Approximation for Markov Decision Problems (2006)
    Details
    Publication Date: 2014-11-21
    Description: The standard computational methods for computing the optimal value functions of Markov Decision Problems (MDP) require the exploration of the entire state space. This is practically infeasible for applications with huge numbers of states as they arise, e.\,g., from modeling the decisions in online optimization problems by MDPs. Exploiting column generation techniques, we propose and apply an LP-based method to determine an $\varepsilon$-approximation of the optimal value function at a given state by inspecting only states in a small neighborhood. In the context of online optimization problems, we use these methods in order to evaluate the quality of concrete policies with respect to given initial states. Moreover, the tools can also be used to obtain evidence of the impact of single decisions. This way, they can be utilized in the design of policies.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 29
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    Ein gemischt-ganzzahliges lineares Optimierungsmodell für ein Laserschweißproblem im Karosseriebau (2006)
    Details
    Publication Date: 2014-11-21
    Description: Wir beschäftigen uns mit dem Problem der Betriebsplanung von Laserschweißrobotern im Karosseriebau. Gegeben ist eine Menge von Schweißnähten, die innerhalb einer Fertigungszelle an einem Karosserieteil gefertigt werden müssen. Die Schweißnähte werden durch mehrere parallel betriebene Roboter bearbeitet. Die Aufgabe besteht darin, für jeden Roboter eine Reihenfolge und eine zeitliche Koordinierung seiner Bewegungen zu finden, so dass alle Schweißnähte innerhalb der Taktzeit der Fertigungszelle bearbeitet werden und so wenig Laserquellen wie möglich eingesetzt werden. Dabei müssen einige Nebenbedingungen berücksichtigt werden. Für dieses spezielle Schweißproblem haben wir eine Formulierung als gemischt-ganzzahliges lineares Programm entwickelt, welches sich für die untersuchten praktischen Fälle sehr schnell lösen lässt.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
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  • 30
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    Software for Teaching Modeling of Integer Programming Problems (2006)
    Details
    Publication Date: 2021-08-05
    Description: Modern applications of mathematical programming must take into account a multitude of technical details, business demands, and legal requirements. Teaching the mathematical modeling of such issues and their interrelations requires real-world examples that are well beyond the toy sizes that can be tackled with the student editions of most commercial software packages. We present a new tool, which is freely available for academic use including complete source code. It consists of an algebraic modeling language and a linear mixed integer programming solver. The performance and features of the tool are in the range of current state-of-the-art commercial tools, though not in all aspects as good as the best ones. Our tool does allow the execution and analysis of large real-world instances in the classroom and can therefore enhance the teaching of problem solving issues. Teaching experience has been gathered and practical usability was tested in classes at several universities and a two week intensive block course at TU Berlin. The feedback from students and teachers has been very positive.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 31
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    On the Bottleneck Shortest Path Problem (2006)
    Details
    Publication Date: 2014-11-21
    Description: The Bottleneck Shortest Path Problem is a basic problem in network optimization. The goal is to determine the limiting capacity of any path between two specified vertices of the network. This is equivalent to determining the unsplittable maximum flow between the two vertices. In this note we analyze the complexity of the problem, its relation to the Shortest Path Problem, and the impact of the underlying machine/computation model.
    Keywords: ddc:000
    Language: English
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  • 32
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    Graph Coloring Manifolds (2006)
    Details
    Publication Date: 2014-02-26
    Description: We introduce a new and rich class of graph coloring manifolds via the Hom complex construction of Lov\´{a}sz. The class comprises examples of Stiefel manifolds, series of spheres and products of spheres, cubical surfaces, as well as examples of Seifert manifolds. Asymptotically, graph coloring manifolds provide examples of highly connected, highly symmetric manifolds.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 33
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    Polyhedra of Genus 3 with 10 Vertices and Minimal Coordinates (2006)
    Details
    Publication Date: 2014-02-26
    Description: We give coordinate-minimal geometric realizations in general position for 17 of the 20 vertex-minimal triangulations of the orientable surface of genus 3 in the 5x5x5-cube.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 34
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    ConFlow? A new space-based Application for complete Conformational Analysis of Molecules (2006)
    Details
    Publication Date: 2014-02-26
    Description: Biochemical interactions are determined by the 3D-structure of the involved components - thus the identification of conformations is a key for many applications in rational drug design. {\sf ConFlow} is a new multilevel approach to conformational analysis with main focus on completeness in investigation of conformational space. In contrast to known conformational analysis, the starting point for design is a space-based description of conformational areas. A tight integration of sampling and analysis leads to an identification of conformational areas simultaneously during sampling. An incremental decomposition of high-dimensional conformational space is used to guide the analysis. A new concept for the description of conformations and their path connected components based on convex hulls and {\em Hypercubes}is developed. The first results of the {\sf ConFlow} application constitute a 'proof of concept' and are further more highly encouraging. In comparison to conventional industrial applications, {\sf ConFlow} achieves higher accuracy and a specified degree of completeness with comparable effort.
    Keywords: ddc:000
    Language: English
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  • 35
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    Iteratively Solving Linear Inverse Problems under General Convex Contraints (2006)
    Details
    Publication Date: 2014-02-26
    Description: We consider linear inverse problems where the solution is assumed to fulfill some general homogeneous convex constraint. We develop an algorithm that amounts to a projected Landweber iteration and that provides and iterative approach to the solution of this inverse problem. For relatively moderate assumptions on the constraint we can always prove weak convergence of the iterative scheme. In certain cases, i.e. for special families of convex constraints, weak convergence implies norm convergence. The presented approach covers a wide range of problems, e.g. Besov- or BV-restoration for which we present also numerical experiments in the context of image processing.
    Keywords: ddc:000
    Language: English
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  • 36
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    Stable computation of probability densities for metastable dynamical systems (2006)
    Details
    Publication Date: 2014-03-10
    Description: Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples.
    Keywords: ddc:000
    Language: English
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  • 37
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    Facets of the (s,t)-p-path polytope (2006)
    Details
    Publication Date: 2016-02-29
    Description: \noindent We give a partial description of the $(s,t)-p$-path polytope of a directed graph $D$ which is the convex hull of the incidence vectors of simple directed $(s,t)$-paths in $D$ of length $p$. First, we point out how the $(s,t)-p$-path polytope is located in the family of path and cycle polyhedra. Next, we give some classes of valid inequalities which are very similar to inequalities which are valid for the $p$-cycle polytope, that is, the convex hull of the incidence vectors of simple cycles of length $p$ in $D$. We give necessary and sufficient conditions for these inequalities to be facet defining. Furthermore, we consider a class of inequalities that has been identifie d to be valid for $(s,t)$-paths of cardinality at most $p$. Finally, we transfer the results to related polytopes, in particular, the undirected counterpart of the $(s,t)-p$-path polytope.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 38
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    A Contact-Stabilized Newmark Method for Dynamical Contact Problems (2006)
    Details
    Publication Date: 2020-11-13
    Description: The numerical integration of dynamical contact problems often leads to instabilities at contact boundaries caused by the non-penetration condition between bodies in contact. Even a recent energy dissipative modification due to Kane et al. (1999), which discretizes the non-penetration constraints implicitly, is not able to circumvent artificial oscillations. For this reason, the present paper suggests a contact stabilization which avoids artificial oscillations at contact interfaces and is also energy dissipative. The key idea of this contact stabilization is an additional $L^2$-projection at contact interfaces, which can easily be added to any existing time integration scheme. In case of a lumped mass matrix, this projection can be carried out completely locally, thus creating only negligible additional numerical cost. For the new scheme, an elementary analysis is given, which is confirmed by numerical findings in an illustrative test example (Hertzian two body contact).
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 39
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    Implementation eines Resourcebrokers im Kontext eines Grid-Datenmanagement-Systems (2006)
    Details
    Publication Date: 2016-06-30
    Keywords: ddc:000
    Language: German
    Type: masterthesis , doc-type:masterThesis
    Format: application/pdf
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  • 40
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    Enumeration and Random Realization of Triangulated Surfaces (2006)
    Details
    Publication Date: 2014-02-26
    Description: We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can be obtained by choosing coordinates randomly.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 41
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    Note on L#-convex Function Minimization Algorithms: Comparison of Murota's and Kolmogorov's Algorithms (2006)
    Details
    Publication Date: 2014-02-26
    Description: The concept of L##-convexity is introduced by Fujishige--Murota (2000) as a discrete convexity for functions defined over the integer lattice. The main aim of this note is to understand the difference of the two algorithms for L##-convex function minimization: Murota's steepest descent algorithm (2003) and Kolmogorov's primal algorithm (2005).
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 42
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    Triangulated Manifolds with Few Vertices: Combinatorial Manifolds (2006)
    Details
    Publication Date: 2014-02-26
    Description: In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal triangulations.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 43
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    Optimizing the Landside Operation of a Container Terminal (2006)
    Details
    Publication Date: 2020-02-11
    Description: This paper concerns the problem of operating a landside container exchange area that is serviced by multiple semi-automated rail mounted gantry cranes (RMGs) that are moving on a single bi-directional traveling lane. Such a facility is being built by Patrick Corporation at the Port Botany terminal in Sydney. The gantry cranes are a scarce resource and handle the bulk of container movements. Thus, they require a sophisticated analysis to achieve near optimal utilization. We present a three stage algorithm to manage the container exchange facility, including the scheduling of cranes, the control of associated short-term container stacking, and the allocation of delivery locations for trucks and other container transporters. The key components of our approach are a time scale decomposition, whereby an integer program controls decisions across a long time horizon to produce a balanced plan that is fed to a series of short time scale online subproblems, and a highly efficient space-time divisioning of short term storage areas. A computational evaluation shows that our heuristic can find effective solutions for the planning problem; on real-world data it yields a solution at most~8\% above a lower bound on optimal RMG utilization.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 44
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    Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I (2006)
    Details
    Publication Date: 2014-02-26
    Description: We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial $d$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on $n\leq 13$ vertices. With the exception of actions of groups of small order, the enumeration is extended to 14 and 15 vertices.
    Keywords: ddc:000
    Language: English
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  • 45
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    Polyhedra of Genus 2 with 10 Vertices and Minimal Coordinates (2006)
    Details
    Publication Date: 2014-02-26
    Description: We give coordinate-minimal geometric realizations in general position of all 865 vertex-minimal triangulations of the orientable surface of genus 2 in the 4x4x4-cube.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 46
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    Combinatorial 3-Manifolds with 10 Vertices (2006)
    Details
    Publication Date: 2014-02-26
    Description: We give a complete enumeration of combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product $S^2 x S^1$ and 615 triangulations of the twisted sphere product $S^2 \underline{x} S^1$. An analysis of the 3-spheres with up to 10 vertices shows that all these spheres are shellable, but that there are 29 vertex-minimal non-shellable 3-balls with 9 vertices.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 47
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    Adaptive Linearly Implicit Methods for Linear Poroelastic Equations (2006)
    Details
    Publication Date: 2019-05-10
    Description: Adaptive numerical methods in time and space are introduced and studied for linear poroelastic models in two and three space dimensions. We present equivalent models for linear poroelasticity and choose both the {\em displacement--pressure} and the {\em stress--pressure} formulation for our computations. Their discretizations are provided by means of linearly implicit schemes in time and linear finite elements in space. Our concept of adaptivity opens a way to a fast and reliable simulation of different loading cases defined by corresponding boundary conditions. We present some examples using our code {\sf Kardos} and show that the method works efficiently. In particular, it could be used in the simulation of some bone healing models.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 48
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    A computational approach to microRNA detection (2006)
    Details
    Publication Date: 2016-06-30
    Description: During the last few years more and more functionalities of RNA have been discovered that were previously thought of being carried out by proteins alone. One of the most striking discoveries was the de tection of microRNAs, a class of noncoding RNAs that play an important role in post-transcriptional gene regulation. Large-scale analyses are needed for the still increasingly growing amount of sequen ce data derived from new experimental technologies. In this paper we present a framework for the detection of the distinctive precursor structure of microRNAS that is based on the well-known Smith-Wat erman algorithm and various filtering steps. We conducted experiments on real genomic data and we found several new putative hits for microRNA precursor structures.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 49
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    Neustart für Bibliotheken ins Informationszeitalter (2006)
    Details
    Publication Date: 2014-02-26
    Description: Wir erleben zu Beginn des aufkommenden Informationszeitalters mit dem Siegeszug von Google und anderen Internet-Technologien einen Wandel im Verhalten von Wissenschaftlern und Studenten, der mit dem Einsatz von {\sl Google Scholar} und {\sl Google Book Search} einen Paradigmenwechsel für Bibliotheken und Informationsversorger gleichkommt. Der Artikel untersucht die technischen Hintergründe für den Erfolg dieser besonderen Art des Information Retrievals: Fulltext Indexing und Citation Ranking als besondere Form des Information Minig. Er diskutiert Stärken und auch Schwächen des Google-Ansatzes. Der Autor stellt sich auch der Frage, unter welchen Bedingungen es möglich ist, ein zu {\sl Google Scholar} und der {\sl Google Book Search} konkurrenzfähiges Retrieval in der Landschaft der Bibliotheken und Bibliotheksverbünde zu entrichten. Die These ist, dass dieses unter Einsatz des {\sl Open Source} Indexierers {\sl Lucene} und des Web-Robots {\sl Nutch} möglich ist. Bibliotheken können durch gezielten Einsatz solcher Internet-Technologien dem Nutzer die Leistungen, welche Google uns mit seinen Tools im {\sl Visible Web} und mit Referenzen auf {\sl Citations} in der Welt der Literatur zur Verfügung stellt, in vergleichbarer Art auch für ihre eigenen durch Lizenzen geschützten digitalen Journale und ihre speziellen lokal verfügbaren Ressourcen, auf die Internet-Suchmaschinen keine Zugriff haben, anbieten. Es besteht die Hoffnung, dass Nutzer dann nicht - wie in einer kürzlichen Studie des OCLC konstatiert - überwiegend im Internet verbleiben, sondern bei ihrer Suche auch den Weg zu den Angeboten der örtlichen Bibliothek attraktiv finden.
    Keywords: ddc:000
    Language: German
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  • 50
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    Waiting times for M/M systems under generalized processor sharing (2006)
    Details
    Publication Date: 2014-02-26
    Description: We consider a system where the arrivals form a Poisson process and the required service times of the requests are exponentially distributed. According to the generalized processor sharing discipline, each request in the system receives a fraction of the capacity of one processor which depends on the actual number of requests in the system. We derive systems of ordinary differential equations for the LST and for the moments of the conditional waiting time of a request with given required service time as well as a stable and fast recursive algorithm for the LST of the second moment of the conditional waiting time, which in particular yields the second moment of the unconditional waiting time. Moreover, asymptotically tight upper bounds for the moments of the conditional waiting time are given. The presented numerical results for the first two moments of the sojourn times in the $M/M/m-PS$ system show that the proposed algorithms work well.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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    Domain Decomposition Method for Maxwell's Equations: Scattering off Periodic Structures (2006)
    Details
    Publication Date: 2022-07-07
    Description: We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light propagation within the multi-layer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.
    Keywords: ddc:000
    Language: English
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  • 52
    Electronic Resource
    Electronic Resource
    Introducing engineering into American secondary education (1993)
    Springer
    Journal of science education and technology 2 (1993), S. 397-406 
    Details
    ISSN: 1573-1839
    Keywords: Engineering ; technological literacy ; hands-on experiments ; active learning ; content instruction ; videotaping
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General , Technology
    Notes: Abstract Media reports indicate the decline of the technological literacy of American youth, especially that students in other countries are better prepared in science and mathematics. Our active-learning program, which consists of numerous hands-on experiments, introduces engineering applications into science and math programs, that will demonstrate to students the usefulness of the theory that they currently do not see as useful. The program, when fully developed, will make optimum use of technology, especially computers and videotapes. The hands-on experiments allow students to discover fundamental principles through data analysis and then use the principles to synthesize a solution to a technological problem. This discovery-based education will help school systems better meet performance standards such as those in the Maryland School Performance Plan. The experimental approach to science education is especially important in a technology-oriented economy where children use the new technologies without understanding the principles on which they are based.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00694528
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  • 53
    Electronic Resource
    Electronic Resource
    Computation of outflow flux for convection-dominated transport equations (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 639-647 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An a posteriori point-wise outflow flux recovery scheme which capitalizes on the hyperbolic nature of convection-dominated transport models is proposed. The scheme is seen to be robust in that it can be applied to any upwind finite-difference or finite-element approximation, and gives a superconvergent approximation to the outflow flux.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090803
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  • 54
    Electronic Resource
    Electronic Resource
    Application of iterative global/local finite-element analysis. Part 2: Geometrically non-linear analysis (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 757-766 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A geometrically non-linear global/local technique was developed and tested. This technique uses separate global and local finite-element models. Iteration is used to enforce equilibrium between the global and local models. The results of this initial study suggest that the technique can be used to reduce both computer memory and CPU requirements.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090906
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  • 55
    Electronic Resource
    Electronic Resource
    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 785-785 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090909
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    Consistent concept for line search algorithms in combination with arc-length constraints (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 773-784 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general line search concept is presented, which can be applied for the solution of non-linear equations in the presence of constraint conditions as in arc-length methods in a consistent manner.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640090908
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    Two problems with GGP generalized geometric programming algorithm (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 767-772 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The generalized geometric programming algorithm GGP has been found to be one of the better algorithms for optimizing algebraic functions subject to algebraic constraints. The paper discusses two problems with the GGP algorithm presented by Avriel et al. (1980). The first problem is that, because of the way that constraint tolerances are checked, the checks may pass even when a constraint is violated beyond the acceptable tolerance. This problem can affect an acceleration technique suggested for the algorithm. This paper presents two possible solutions to this problem. The second problem is the algorithm's weakness in handling equality constraints. This problem seems to especially affect the ‘Phase I’ part of the algorithm, which finds a feasible solution from a random starting point. While extensions have been made to get around this limitation, no discussion on why the original algorithm has problems with equality constraints has been made. This paper discusses why the problems exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090907
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091001
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  • 59
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    Matrix filter for correcting experimental data (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 797-803 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a filtering algorithm which corrects the results of measurements of certain physical quantities if any additional information about the measured values is known. The algorithm is very effective in one-dimensional as well as in two-dimensional problems where additional constraints are presented in the form of differential equations. For example, this technique can be used to correct the measurements of certain dynamic quantities if some information about motion of examined bodies is known. It can also be used to correct the strain field measurements if the conditions of continuity of strain field are included.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091003
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  • 60
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    Finite-element computer simulation of atmospheric convection with anisotropic eddys (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 805-814 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer simulation is made of cellular convection in an anisotropic atmosphere in an attempt to more closely approximate the observed values with those obtained from mathematical models. A finite-element Galerkin technique, with Taylor approximation and Crank-Nicolson, is employed and comparisons are made with the author's earlier finite-element models of isotropic convection and with finite-difference models. It is found that postulates from physics on the effect of anisotropy on cellular atmospheric convection, with its increase in the aspect ratio, are well modelled with this finite-element technique.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091004
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    Application of augmented Lagrangian techniques for non-linear constitutive laws in contact interfaces (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 815-824 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of micromechanically based constitutive equations for contact interfaces leads to technically relevant parameters to ill-conditioned finite-element equations. In the paper an augmented Lagrangian technique is employed to overcome this difficulty and to provide a good converging algorithm.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091005
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  • 62
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    Finite-element analysis of elastic contact between a shell of revolution and a rigid plate (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 883-888 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Elastic contact between a thick shell of revolution and a rigid plate in the case when the plate is brought into contact with the shell by giving a finite displacement to the plate is analysed by the finite-element method. Field-consistent higher-order strain-displacement relations with vanishing shear stresses on the surfaces are used. A finite element based on these relations is developed and used for the analysis. The contact conditions are imposed by use of the Lagrangian multipliers method, and the resulting minimization problem is solved iteratively. This procedure will lead to reduced memory requirements and computation time.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091104
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  • 63
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    Computation of isotropic tensor functions (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 889-896 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An explicit formulation and a procedure for the computation of isotropic tensor-valued tensor functions is discussed. The formulation is based on a spectral decomposition in terms of second-order eigenvalue bases, which avoids the costly computation of eigenvectors. As an important result a compact structure of the fourth-order derivatives of general second-order isotropic tensor functions is presented.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091105
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 933-935 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091110
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091201
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  • 66
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    Macro finite element using subdomain integration (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 937-949 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For some heterogeneous materials, it is not practical to model the microstructure directly using traditional finite elements. Furthermore, it is not always accurate to use homogenized properties. Macro elements have been developed which permit microstructure within a single element. These macro elements performed well in initial tests.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091202
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    Mapping of finite elements around corner singularities of the quasi-harmonic equation (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 957-974 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with the solution of the quasi-harmonic equation by the finite element method in a domain with corners on its boundary. A mapping technique, which can be used for locating the nodes of standard isoparametric elements in a subgrid (patch) of finite elements in the vicinity of a corner singularity point, is presented. The equations of the mapping are based on the analytical singular solution of the problem. Some analytical and numerical results to show the efficiency of the technique are presented.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091204
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    Arbitrary Lagrangian-Eulerian thermomechanical finite-element model of material cutting (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 975-987 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An arbitrary Lagrangian-Eulerian model is described for the prediction of metal flow in a steady-state forming process. The formulation is shown to be capable of dealing with free surface and boundary friction; the coupling with thermal effects is also considered. The numerical techniques are based on the finite elements for spatial discretization of the momentum equation and on an explicit integration scheme for discretization relative to time. The mass and energy equations are integrated by a finite-volume method. Details on the application to an orthogonal cutting process are given in the final Section of the paper.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091205
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  • 69
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    Optimization analysis of the three-level time schemes (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 951-956 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure was implemented to determine the optimum values for the two parameters of the Zienkiewicz three-level time schemes which could be utilized for the numerical solution of a system of ordinary differential equations. A multivariable search method was implemented to estimate optimum values for these parameters. The resultant optimum three-level time scheme produced very accurate results, satisfied physical reality, and did not produce any oscillations for the various problems that were investigated. The optimum values for the two parameters β and γ in the three-level scheme were β = 0·50005 and γ = 1·0007. A comparison was made between this optimum scheme and other existing three-level time schemes. The optimum scheme demonstrated superior results for all the problems that were analysed. However, the results of the optimization analysis produced a set of optimum parameters that were identical to the values that would reduce the general three-level time scheme into a central-difference two-level time scheme, i.e. β = 1/2 and γ = 1.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091203
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    New assumed natural strain formulation of the shallow shell element (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 989-1004 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new efficient formulation of the 36 degree-of-freedom conforming shallow shell element of an arbitrary triangular shape is presented. This formulation is based on natural co-ordinates and independently assumed natural strain fields, and applied to shallow shell analysis. The 3-node element incorporates the normal displacement and its first and second derivatives plus the tangential displacements and their first derivatives at each vertex. A closed form of the element stiffness matrix is achieved. The form of the stiffness matrix derived in this formulation explicitly reveals the essence of the shallow shell theory.The presented approach results in avoiding definite integrals and matrix inversions, and permits operation with lower-order numerical matrices, which are the same for all elements. The example applications presented demonstrate that accurate predictions of stresses as well as displacements are obtained with only a few elements.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091206
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    Locking-free straight beam element based on curvature (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 1005-1011 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The formulation of a straight beam element to eliminate the shear locking phenomenon is presented. The element is based on curvature so that the bending energy is fully represented, and the shear strain energy is incorporated into the formulation by the equilibrium equation. Four examples are chosen to verify the concept of the element employed and its capability of the analysis. The solutions obtained reveal that the element describes the behaviour of the straight beam quite exactly and efficiently, showing no locking and that it is also applicable to the analysis of both thin and thick straight beams.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091207
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 1013-1015 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091208
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    Computer methods in structural analysis, J. L. Meek, E. & F. N. Spon, 1991. 503 pages. Price £25.00, ISBN: 0-419-15440-X (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6 (1993), S. 167-167 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660060210
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    Circuit model for a symmetrical condensed TLM node (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6 (1993), S. 183-193 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: An equivalent circuit for a symmetrical condensed TLM node is presented. The basic circuit has twelve ports and consists of 24 1:1 ideal transformers. Three additional conductances model the conductivity of the medium. The circuit is extended with additional ideal transformers giving six ports for short-circuit and open-circuit stubs which model the permittivity and permeability of the inhomogeneous medium. The scattering matrix of the 18-port network is determined symbolically by solving a set of linear circuit equations. The matrix agrees with previously published results for a symmetrical condensed TLM node, obtained from Maxwell's equations.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660060303
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    Transmission-line matrix method for solving the multidimensional continuity equation (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6 (1993), S. 233-236 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: We have extended the one-dimensional transmission-line modelling (TLM) of diffusion, drift and recombination of charge carriers in semiconductors to multiple dimensions. Detailed TLM formulation of the continuity transport equation in a more general form is presented.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660060307
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    The hilbert space formulation of the TLM method (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6 (1993), S. 29-45 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The Hilbert space representation of the TLM method for time-domain computation of electromagnetic fields and the algebraic computation of the discrete Green's function are investigated. The complete field state is represented by a Hilbert space vector. The space and time evolution of the field state vector is governed by operator equations in Hilbert space. The discrete Green's functions may be represented by a Neumann series in space- and time-shift operators. The Hilbert space representation allows the description of the geometric structures by projection operators, too. The system of difference equations governing the time evolution of the electromagnetic field in configuration space is derived from the operator equation for the field state vector in the Hilbert space.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660060105
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    Multiport approach for the analysis of microwave non-linear networks (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6 (1993), S. 67-81 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The state and output equations of the overall networks are derived from the state and output equations of individual multiports and knowledge of the interconnections between them. A generalized lumped-distributed L/D multiport is described by its associated state, output and non-linear equations in the time domain. Any network can be considered as composed of a set of multiports and independent sources. These equations have been incorporated into a computer-aided procedure for the analysis of L/D networks. The procedure can be used for the simulation of any non-linear microwave circuit and offers the facility of developing a multiport equivalent circuit for any linear or non-linear device or subcircuit. Several examples are successfully analysed using the developed general program.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660060107
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    The efficiency of transmission-line matrix modelling - a rigorous viewpoint (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6 (1993), S. 109-126 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The difference equations of the scalar linear transmission-line matrix (TLM) routine as introduced by Johns for numerically solving the diffusion equation are shown to be isomorphic to Goldstein's correlated random walk model of diffusion. For the infinite homogeneous bar their exact solution is derived algebraically and given in the form of Jacobi polynomials. This puts the TLM algorithm on a sounder mathematical and physical basis. The accuracy in solving the diffusion equation is investigated in general form and thus its astonishing efficiency explained. Several other basic questions of this numerical technique are also discussed.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660060204
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    A comparative study of two TLM networks for the modelling of diffusion processes (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6 (1993), S. 161-164 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: A comparative study of two alternative networks for TLM modelling of diffusion processes has been undertaken. Some of their inherent advantages and disadvantages are analysed according to the ratio between the impedance of the lossless transmission lines and the lumped resistance. Their relative accuracy and utility in controlling the timestep automatically are examined.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660060208
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    A non-linear and distributed modelling procedure of fets (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6 (1993), S. 237-251 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper describes a rigorous and systematic procedure to derive a non-linear distributed FET model that can easily be implemented in CAD routines of simulators based on harmonic balance techniques. The new model is derived from a knowledge of the conventional linear lumped equivalent circuit, from non-linear current sources extracted from pulsed measurements, and from the physical dimensions of the FET.For fundamental and harmonic frequencies, the FET is modelled by N identical cells. Each cell is made up of a non-linear two-port section inserted between two linear four-port sections that simulate the coupling and the distributed effects along the electrodes of the FET in the width direction only. This non-linear distributed scaling approach to FET modelling has been applied to the analysis of a submicrometre-gate GaAs FET at millimetre-wave frequencies, and the results were compared with the non-linear lumped element approach. This approach can be applied to other transistors used in non-linear regions at microwave and millimetre-wave frequencies.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660060402
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    Electronic band structure for two-dimensional periodic lattice quantum configurations by the finite element method (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6 (1993), S. 283-297 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: A finite element method formulation is given for solving Schrodinger's wave equation for a single electron in a crystal lattice cell subject to a known periodic potential. The formulation has been implemented for a two-dimensional lattice, with an arbitrary potential profile, modelled by quadratic isoparametric elements, The FEM solver returns a specified number of electronic energy states, En, and nodal values of the complex wavefunctionψn Input data is generated by a standard FEM mesh generator. The postprocessing, given n, for reproducing a full 2-D E-k Brillouin diagram and given k, the electronic distribution, has been implemented. Tests on a 2-D generalized Kronig-Penney energy band model showed excellent agreement; between FEM results and analysis. The solver was further satisfactorily checked against published augmented plane wave calculations for a circular potential well within a square lattice. Specimen results are presented for the same circular well but with graded potential distributions and for a rectangular potential barrier set askew in a square lattice. Two-dimensional energy band solvers have application to superlattice nanostruc- tures, whilst a general, full 3-D FEM quantum solver seems feasible.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660060405
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    TLM modelling using an SIMD computer (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 6 (1993), S. 299-304 
    Details
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: A major limitation of the transmission-line matrix (TLM) method used to solve Maxwell's equations is the long computation time required. The TLM scattering calculations involved can, however, be viewed as parallel in nature. This paper describes an effort to reduce computational time by using an SIMD, DAP multiprocessor computer employed to solve a two-dimensional TLM electromagnetic field formulation. A parallel algorithm based on the TLM scattering algorithm is designed and implemented using FORTRAN- PLUS Enhanced on an AMT DAP 510 machine. Here the connectivity of the DAP is exploited to simulate the intrinsic scattering behaviour on which the TLM algorithm relies. The results show that parallel processing on an SIMD machine such as the DAP is advantageous, especially for higher-order mesh sizes.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jnm.1660060406
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  • 83
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    Masthead (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360101
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    Triangular C0 bending elements based on the Hu-Washizu principle and orthogonality conditionsDedicated to Professor Walter Wunderlich on the occasion of his sixtieth birthday anniversary. (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 181-200 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with simple and effective C0 linear triangular bending elements based on the Hu-Washizu variational principle. The following key features are inherent in the proposed formulation: extensional, flexural and transverse shear strains and the corresponding stresses are referred to the directions of the triangle sides. The independent variation of displacements, strains and stresses yields discrete approximations consistent with the continuum theory. Furthermore, a proper identification of the deformational modes and the orthogonality requirements between the assumed transverse shear forces and the undesirable strain fields lead to element formulations with important attributes: minimization of superfluous energy, properly justified assumptions, simplicity of formulation and straightforward extension to non-linear problems. Alternative approximations of strains and stresses, also presented, enhance the element performance in the case of both thick and thin plates and shells. Test examples demonstrate the characteristic properties of the proposed element formulations.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360202
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  • 85
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    Boundary element analysis of two-dimensional elastoplastic contact problems (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 221-235 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a boundary element method for two-dimensional elastoplastic stress analysis of frictional contact problems is presented. The bodies in contact are treated as separate regions. The contact conditions are used to join the different system of equations for different regions of contacted bodies and, hence, an overall system of equation is obtained. An incremental and iterative procedure can be used to find the contact load, or the contact extent and the proper contact conditions. To include the plastic deformation in the analysis, the initial strain algorithm is employed. Elastic-perfectly plastic or work-hardening material behaviour can be assumed. For the numerical analysis, an isoparametric three-noded line elements are used to represent the boundary and eight-noded quadrilateral or six-noded triangular elements are used for the interior of the domain. The displacement rates and traction rates are assumed to vary quadratically and the shape functions for the interior strain rates are also of quadratic type. As an example, the behaviour of an elastic and elastoplastic body with a smooth, circular inclusion under the increasing load is presented.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360204
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  • 86
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    Non-singular boundary integral equation implementation (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 237-254 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The basis of the boundary integral equation (BIE) development is the singular field solution for the Kelvin point load problem. The presence of the mathematical singularity in an otherwise non-singular problem has created over the years a variety of numerical coping strategies. The current paper extends some of the earlier works in a simple manner that eliminates the mathematical singularity through analytical integration of the critical terms. The resulting formulation is fully non-singular and is shown to be amenable to simple, low-order Gaussian integration. The critical class of problems involving thin sections and/or highly graded BIE meshes now can be solved without previous problems and concerns the accuracy of the numerical integrations used in creating the linear BIE equations. Extension of the formulation approach to remove hypersingular formulation problems in fracture mechanics is seen to be a future beneficiary of the semi-analytical BIE implementation reported herein.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360205
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  • 87
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    An application of preconditioned conjugate gradients to relative placement in chip design (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 255-271 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In distance geometry problems and many other applications, we are faced with the optimization of high-dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well-known preconditioning techniques for the conjugate gradient method remain applicable. Very-large-scale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. Numerical results produced by a FORTRAN 77 program illustrate the good behaviour of the algorithm.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360206
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  • 88
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    Application of block Lanczos method for analysis of cyclic symmetric structures (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 273-285 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this study the free vibration of circumferentially periodic structures has been analysed using the block Lanczos method in a semi complex domain for extracting real natural frequencies and complex mode shapes. The influence of the number of vectors in the block and also the effect of renumbering of nodes, depending on whether they are internal, adjacent or boundary nodes, on the CPU time are studied. The efficiency of the present method is compared with the subspace iteration schemes.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360207
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  • 89
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    Interpolation of curved shell geometries by low order finite elements - errors and modificationsThis contribution is dedicated to Professor Dr.-Ing. Walter Wunderlich, Lehrstuhl für Statik, Institut für Bauingenieur-wesen I, Technical University of Munich, on the occasion of his 60th birthday. (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 287-302 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Low order finite elements are of vital interest for practical applications in linear and non-linear structural analysis. The possible discretization errors, when Reissner-Mindlin shell elements with bilinear shape functions are used, and modifications to prevent these errors are presented. On some numerical examples the influence of these errors and of various modifications on the results is shown. Finally, the case of membrane locking with low order Reissner-Mindlin elements for particular assumptions concerning the base vectors and methods to prevent this locking are discussed.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360208
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  • 90
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    An efficient implementation of stress resultant plasticity in analysis of Reissner-Mindlin plates (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 303-320 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient solution procedure for elasto-plastic analysis of Reissner-Mindlin plates has been proposed in this work. The main ingredients which render efficiency are: what appears to be an optimally tuned four-node plate element with assumed shear strains and incompatible bending modes; an elasto-plastic constitutive model given directly in terms of stress resultants; and efficient computation of plastic flow which simplifies to a solution of a single scalar equation and remaining state update computation. The performance of the element has been proved very satisfying in both elastic singularity-dominated and elasto-plastic problems.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360209
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  • 91
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    Solution of the Helmholtz eigenvalue problem via the boundary element method (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 321-330 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of the Helmholtz eigenvalue problem is considered. The application of the boundary element method reduces it to that of a non-linear eigenvalue problem. Through a polynomial approximation with respect to the wavenumber, the non-linear eigenvalue problem is reduced to a standard generalized eigenvalue problem. The method is applied to the test problems of a three-dimensional sphere with an axisymmetric boundary condition and a two-dimensional square.
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360210
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  • 92
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    Announcement (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 355-355 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360212
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    Analysis of the anisotropic viscoplastic-damage response of composite laminates - continuum basis and computational algorithmsThis work is supported by NASA-Lewis Grant No. NAG3-901 (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1629-1660 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The mathematical structure underlying the rate equations of a recently-developed constitutive model for the coupled viscoplastic-damage response of anisotropic composites is critically examined. In this regard, a number of tensor projection operators have been identified, and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the Euler fully-implicit integration method. In particular, this facilitated (i) the derivation of explicit expressions of the (consistent) material tangent stiffnesses that are valid for both three-dimensional as well as subspace (e.g. plane stress) formulations, (ii) the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint, and (iii) the development of an effective time-step control strategy to ensure accuracy and convergence of the solution. In addition, the special limiting case of inviscid elastoplasticity is treated. The results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361003
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    An adaptive multigrid technique for three-dimensional elasticity (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1703-1716 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A program for finite element analysis of 3D linear elasticity problems is described. The program uses quadratic hexahedral elements. The solution process starts on an initial coarse mesh; here error estimators are determined by the standard Babuška-Rheinboldt method and local refinement is performed by partitioning of indicated elements, each hexahedron into eight new elements. Then the discrete problem is solved on the second mesh and the refinement process proceeds in the following way-on the ith mesh only the elements caused by refinement on the (i-1)th mesh can be refined. The control of refinement is the task of the user because the dimension of the discrete problem grows very rapidly in 3D. The discrete problem is being solved by the frontal solution method on the initial mesh and by a newly developed and very efficient local multigrid method on the refined meshes. The program can be successfully used for solving problems with structural singularities, such as re-entrant corners and moving boundary conditions. A numerical example shows that such problems are solved with the same efficiency as regular problems.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361006
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  • 95
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    New strategy for assumed stresses for 4-node hybrid stress membrane element (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1747-1763 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An oblique (skew) co-ordinate system defined at the origin of the isoparametric co-ordinates is introduced as the reference co-ordinate system for assumed stresses in the formulation of a 4-node hybrid membrane element. The initially uncoupled stresses in these reference co-ordinates can be constrained to satisfy the equilibrium conditions pointwise by using the procedure of Pian and Wu7, when suitable incompatible displacements are introduced. Such strategy allows the element stiffness to be formulated by using either the Hellinger-Reissner or the complementary energy functional. Numerical results show that the performances of three elements, constructed by using different sets of incompatible displacements in this paper, are practically identical and are all of slightly higher accuracy than that of the Pian-Sumihara element6.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361009
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  • 96
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    Boundary element method solutions for elastic wave scattering in 3D (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 437-455 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Time-harmonic elastic wave scattering problems such as those encountered in ultrasonic non destructive evaluation are solved by the boundary element method (BEM). Selected results for spherical and spheroidal shaped voids and inclusions are compared with analytical and other numerical solutions. Results for ellipsoids, which require a full three-dimensional formulation, are provided as a benchmark for comparison when other numerical methods would be developed for this problem class in the future. The modelling of cracklike defects with this formulation is discussed. Recent theoretical findings regarding the fictitious eigenfrequency difficulty (FED) are confirmed by a numerical study.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360306
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  • 97
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    The effect of ordering on preconditioned GMRES algorithm, for solving the compressible Navier-Stokes equations (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 457-497 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We investigate the effect of the ordering of the blocks of unknowns on the rate of convergence of a preconditioned non-linear GMRES algorithm, for solving the Navier-Stokes equations for compressible flows, using finite element methods on unstructured grids. The GMRES algorithm is preconditioned by an incomplete LDU block factorization of the Jacobian matrix associated with the non-linear problem to solve. We examine a wide range of ordering methods including minimum degree, (reverse) Cuthill-McKee and snake, and consider preconditionings without fill-in. We show empirically that there can be a significant difference in the number of iterations required by the preconditioned non-linear GMRES method and suggest a criterion for choosing a good ordering algorithm, according to the problem to solve.We also consider the effect of orderings when an incomplete factorization which allows some fill-in is performed. We consider the effect of automatically controlling the sparsity of the incomplete factorization through the level of fill-in.Finally, following the principal ideas of non-linear GMRES algorithm, we suggest other inexact Newton methods.
    Additional Material: 40 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360307
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    An algorithm for adaptive refinement of triangular element meshes (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 499-509 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple algorithm is developed for adaptive and automatic h refinement of two-dimensional triangular finite element meshes. The algorithm is based on an element refinement ratio that can be calculated from an a posteriori error indicator. The element subdivision algorithm is robust and recursive. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. Several example problems are presented to illustrate the utility of the approach.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360308
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  • 99
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    An approach to optimal design of structures with non-linear response (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 511-521 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A commonly adopted procedure to solve a structural optimum design problem is to improve the design iteratively by solving a sequence of simpler problems, where each of these is obtained as an approximation of the original problem. Considering structures with linear response, this procedure works very well and can be implemented quite straightforwardly. However, considering structures with non-linear response, the situation is more sophisticated since structural stability properties have to be taken into account.The paper presents an approach to optimal design of statically loaded structures with non-linear response. It is proposed to replace the original problem with a sequence of similar problems from which corresponding approximate problems can easily be obtained. These similar problems additionally contain an estimation of the critical load constraint while other constraints are imposed at some properly chosen load level, which is lower or at most equal to the critical load level. By this approach, the structural stability requirements are taken into account in an effective manner. The efficiency is illustrated with several examples involving kinematic as well as material non-linear effects.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360309
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    Conference diary (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 537-538 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360311
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