Download or read book Scalable Algorithms for Contact Problems written by Zdeněk Dostál and published by Springer. This book was released on 2017-01-25 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive and self-contained treatment of the authors’ newly developed scalable algorithms for the solutions of multibody contact problems of linear elasticity. The brand new feature of these algorithms is theoretically supported numerical scalability and parallel scalability demonstrated on problems discretized by billions of degrees of freedom. The theory supports solving multibody frictionless contact problems, contact problems with possibly orthotropic Tresca’s friction, and transient contact problems. It covers BEM discretization, jumping coefficients, floating bodies, mortar non-penetration conditions, etc. The exposition is divided into four parts, the first of which reviews appropriate facets of linear algebra, optimization, and analysis. The most important algorithms and optimality results are presented in the third part of the volume. The presentation is complete, including continuous formulation, discretization, decomposition, optimality results, and numerical experiments. The final part includes extensions to contact shape optimization, plasticity, and HPC implementation. Graduate students and researchers in mechanical engineering, computational engineering, and applied mathematics, will find this book of great value and interest.

Download or read book Scalable Algorithms for Contact Problems written by Zdeněk Dostál and published by Springer Nature. This book was released on 2023-11-29 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive treatment of recently developed scalable algorithms for solving multibody contact problems of linear elasticity. The brand-new feature of these algorithms is their theoretically supported numerical scalability (i.e., asymptotically linear complexity) and parallel scalability demonstrated in solving problems discretized by billions of degrees of freedom. The theory covers solving multibody frictionless contact problems, contact problems with possibly orthotropic Tresca’s friction, and transient contact problems. In addition, it also covers BEM discretization, treating jumping coefficients, floating bodies, mortar non-penetration conditions, etc. This second edition includes updated content, including a new chapter on hybrid domain decomposition methods for huge contact problems. Furthermore, new sections describe the latest algorithm improvements, e.g., the fast reconstruction of displacements, the adaptive reorthogonalization of dual constraints, and an updated chapter on parallel implementation. Several chapters are extended to give an independent exposition of classical bounds on the spectrum of mass and dual stiffness matrices, a benchmark for Coulomb orthotropic friction, details of discretization, etc. The exposition is divided into four parts, the first of which reviews auxiliary linear algebra, optimization, and analysis. The most important algorithms and optimality results are presented in the third chapter. The presentation includes continuous formulation, discretization, domain decomposition, optimality results, and numerical experiments. The final part contains extensions to contact shape optimization, plasticity, and HPC implementation. Graduate students and researchers in mechanical engineering, computational engineering, and applied mathematics will find this book of great value and interest.

Download or read book Scalable Algorithms for Data and Network Analysis written by Shang-Hua Teng and published by . This book was released on 2016 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the age of Big Data, efficient algorithms are now in higher demand more than ever before. While Big Data takes us into the asymptotic world envisioned by our pioneers, it also challenges the classical notion of efficient algorithms: Algorithms that used to be considered efficient, according to polynomial-time characterization, may no longer be adequate for solving today's problems. It is not just desirable, but essential, that efficient algorithms should be scalable. In other words, their complexity should be nearly linear or sub-linear with respect to the problem size. Thus, scalability, not just polynomial-time computability, should be elevated as the central complexity notion for characterizing efficient computation. In this tutorial, I will survey a family of algorithmic techniques for the design of provably-good scalable algorithms. These techniques include local network exploration, advanced sampling, sparsification, and geometric partitioning. They also include spectral graph-theoretical methods, such as those used for computing electrical flows and sampling from Gaussian Markov random fields. These methods exemplify the fusion of combinatorial, numerical, and statistical thinking in network analysis. I will illustrate the use of these techniques by a few basic problems that are fundamental in network analysis, particularly for the identification of significant nodes and coherent clusters/communities in social and information networks. I also take this opportunity to discuss some frameworks beyond graph-theoretical models for studying conceptual questions to understand multifaceted network data that arise in social influence, network dynamics, and Internet economics.

Download or read book Optimal Quadratic Programming Algorithms written by Zdenek Dostál and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic programming (QP) is one advanced mathematical technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This book presents recently developed algorithms for solving large QP problems and focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming.

Download or read book Recent Advances in Contact Mechanics written by Georgios E. Stavroulakis and published by Springer Science & Business Media. This book was released on 2012-10-19 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contact mechanics is an active research area with deep theoretical and numerical roots. The links between nonsmooth analysis and optimization with mechanics have been investigated intensively during the last decades, especially in Europe. The study of complementarity problems, variational -, quasivariational- and hemivariational inequalities arising in contact mechanics and beyond is a hot topic for interdisciplinary research and cooperation. The needs of industry for robust solution algorithms suitable for large scale applications and the regular updates of the respective elements in major commercial computational mechanics codes, demonstrate that this interaction is not restricted to the academic environment. The contributions of this book have been selected from the participants of the CMIS 2009 international conference which took place in Crete and continued a successful series of specialized contact mechanics conferences.

Download or read book Contact in Structural Mechanics written by Anh Le van and published by John Wiley & Sons. This book was released on 2024-06-04 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contact in Structural Mechanics treats the problem of contact in the context of large deformations and the Coulomb friction law. The proposed formulation is based on a weak form that generalizes the classical principle of virtual powers in the sense that the weak form also encompasses all the contact laws. This formulation is thus a weighted residue method and has the advantage of being amenable to a standard finite element discretization. This book provides the reader with a detailed description of contact kinematics and the variation calculus of kinematic quantities, two essential subjects for any contact study. The numerical resolution is carried out in statics and dynamics. In both cases, the derivation of the contact tangent matrix – an essential ingredient for iterative calculation – is explained in detail. Several numerical examples are presented to illustrate the efficiency of the method.

Download or read book Domain Decomposition Methods in Science and Engineering written by Ralf Kornhuber and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.

Download or read book Uncertainty Quantification in Variational Inequalities written by Joachim Gwinner and published by CRC Press. This book was released on 2021-12-21 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature

Download or read book Computer Graphics through Key Mathematics written by Huw Jones and published by Springer Science & Business Media. This book was released on 2001-04-27 with total page 1078 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the mathematical concepts that underpin computer graphics. It is written in an approachable way, without burdening readers with the skills of ow to do'things. The author discusses those aspects of mathematics that relate to the computer synthesis of images, and so gives users a better understanding of the limitations of computer graphics systems. Users of computer graphics who have no formal training and wish to understand the essential foundations of computer graphics systems will find this book very useful, as will mathematicians who want to understand how their subject is used in computer image synthesis. '

Download or read book A Parallel Algorithm for Contact in a Finite Element Hydrocode written by Timothy G. Pierce and published by . This book was released on 2003 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parallel Computing in Optimization written by A. Migdalas and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last three decades, breakthroughs in computer technology have made a tremendous impact on optimization. In particular, parallel computing has made it possible to solve larger and computationally more difficult prob lems. This volume contains mainly lecture notes from a Nordic Summer School held at the Linkoping Institute of Technology, Sweden in August 1995. In order to make the book more complete, a few authors were invited to contribute chapters that were not part of the course on this first occasion. The purpose of this Nordic course in advanced studies was three-fold. One goal was to introduce the students to the new achievements in a new and very active field, bring them close to world leading researchers, and strengthen their competence in an area with internationally explosive rate of growth. A second goal was to strengthen the bonds between students from different Nordic countries, and to encourage collaboration and joint research ventures over the borders. In this respect, the course built further on the achievements of the "Nordic Network in Mathematical Programming" , which has been running during the last three years with the support ofthe Nordic Council for Advanced Studies (NorFA). The final goal was to produce literature on the particular subject, which would be available to both the participating students and to the students of the "next generation" .

Download or read book Scalable Algorithms for Misinformation Prevention in Social Networks written by Michael Simpson and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis investigates several problems in social network analysis on misinformation prevention with an emphasis on finding solutions that can scale to massive online networks. In particular, it considers two problem formulations related to the spread of misinformation in a network that cover the elimination of existing misinformation and the prevention of future dissemination of misinformation. Additionally, a comprehensive comparison of several algorithms for the feedback arc set (FAS) problem is presented in order to identify an approach that is both scalable and computes a lightweight solution. The feedback arc set problem is of particular interest since several notable problems in social network analysis, including the elimination of existing misinformation, crucially rely on computing a small FAS as a preliminary. The elimination of existing misinformation is modelled as a graph searching game. The problem can be summarized as constructing a search strategy that will leave the graph clear of any misinformation at the end of the searching process in as few steps as possible. Despite the problem being NP-hard, even on directed acyclic graphs, this thesis presents an efficient approximation algorithm and provides new experimental results that compares the performance of the approximation algorithm to the lower bound on several large online networks. In particular, new scalability goals are achieved through careful algorithmic engineering and a highly optimized pre-processing step. The minimum feedback arc set problem is an NP-hard problem on graphs that seeks a minimum set of arcs which, when removed from the graph, leave it acyclic. A comprehensive comparison of several approximation algorithms for computing a minimum feedback arc set is presented with the goal of comparing the quality of the solutions and the running times. Additionally, careful algorithmic engineering is applied for multiple algorithms in order to improve their scalability. In particular, two approaches that are optimized (one greedy and one randomized) result in simultaneously strong performance for both feedback arc set size and running time. The experiments compare the performance of a wide range of algorithms on a broad selection of large online networks and reveal that the optimized greedy and randomized implementations outperform the other approaches by simultaneously computing a feedback arc set of competitive size and scaling to web-scale graphs with billions of vertices and tens of billions of arcs. Finally, the algorithms considered are extended to the probabilistic case in which arcs are realized with some fixed probability and a detailed experimental comparison is provided. \sloppy Finally, the problem of preventing the spread of misinformation propagating through a social network is considered. In this problem, a ``bad'' campaign starts propagating from a set of seed nodes in the network and the notion of a limiting (or ``good'') campaign is used to counteract the effect of misinformation. The goal is to identify a set of $k$ users that need to be convinced to adopt the limiting campaign so as to minimize the number of people that adopt the ``bad'' campaign at the end of both propagation processes. \emph{RPS} (Reverse Prevention Sampling), an algorithm that provides a scalable solution to the misinformation prevention problem, is presented. The theoretical analysis shows that \emph{RPS} runs in $O((k + l)(n + m)(\frac{1}{1 - \gamma}) \log n / \epsilon^2 )$ expected time and returns a $(1 - 1/e - \epsilon)$-approximate solution with at least $1 - n^{-l}$ probability (where $\gamma$ is a typically small network parameter). The time complexity of \emph{RPS} substantially improves upon the previously best-known algorithms that run in time $\Omega(m n k \cdot POLY(\epsilon^{-1}))$. Additionally, an experimental evaluation of \emph{RPS} on large datasets is presented where it is shown that \emph{RPS} outperforms the state-of-the-art solution by several orders of magnitude in terms of running time. This demonstrates that misinformation prevention can be made practical while still offering strong theoretical guarantees.

Download or read book Algorithms and Data Structures written by Frank Dehne and published by Springer Science & Business Media. This book was released on 1993-07-28 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume were presented at the Third Workshop on Algorithmsand Data Structures (WADS '93), held in Montreal, Canada, August 1993. The volume opens with five invited presentations: "Computing the all-pairs longest chains in the plane" by M.J. Atallah and D.Z. Chen, "Towards a better understanding of pure packet routing" by A. Borodin, "Tolerating faults in meshes and other networks" (abstract) by R. Cole, "A generalization of binary search" by R.M. Karp, and "Groups and algebraic complexity" (abstract) by A.C. Yao. The volume continues with 52 regular presentations selected from 165 submissions, each of which was evaluated by at least three program committee members, many of whom called upon additional reviewers.

Download or read book Geographically Weighted Regression written by A. Stewart Fotheringham and published by John Wiley & Sons. This book was released on 2003-02-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geographical Weighted Regression (GWR) is a new local modelling technique for analysing spatial analysis. This technique allows local as opposed to global models of relationships to be measured and mapped. This is the first and only book on this technique, offering comprehensive coverage on this new 'hot' topic in spatial analysis. * Provides step-by-step examples of how to use the GWR model using data sets and examples on issues such as house price determinants, educational attainment levels and school performance statistics * Contains a broad discussion of and basic concepts on GWR through to ideas on statistical inference for GWR models * uniquely features accompanying author-written software that allows users to undertake sophisticated and complex forms of GWR within a user-friendly, Windows-based, front-end (see book for details).

Download or read book Nonlinear Structural Dynamics and Damping written by Juan Carlos Jauregui and published by Springer. This book was released on 2019-03-14 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book compiles recent research in the field of nonlinear dynamics, vibrations and damping applied to engineering structures. It addresses the modeling of nonlinear vibrations in beams, frames and complex mechanical systems, as well as the modeling of damping systems and viscoelastic materials applied to structural dynamics. The book includes several chapters related to solution techniques and signal analysis techniques. Last but not least, it deals with the identification of nonlinear responses applied to condition monitoring systems.

Download or read book Scalable Fuzzy Algorithms for Data Management and Analysis Methods and Design written by Laurent, Anne and published by IGI Global. This book was released on 2009-10-31 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents up-to-date techniques for addressing data management problems with logic and memory use"--Provided by publisher.

Download or read book High Performance Algorithms for Structured Matrix Problems written by Peter Arbenz and published by Nova Publishers. This book was released on 1998 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprises 10 contributions that summarize the state of the art in the areas of high performance solutions of structured linear systems and structured eigenvalue and singular-value problems. Topics covered range from parallel solvers for sparse or banded linear systems to parallel computation of eigenvalues and singular values of tridiagonal and bidiagonal matrices. Specific paper topics include: the stable parallel solution of general narrow banded linear systems; efficient algorithms for reducing banded matrices to bidiagonal and tridiagonal form; a numerical comparison of look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems; and parallel CG-methods automatically optimized for PC and workstation clusters. Annotation copyrighted by Book News, Inc., Portland, OR