Scalable Algorithms for Contact Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Scalable Algorithms for Contact Problems write by Zdeněk Dostál. This book was released on 2017-01-25. Scalable Algorithms for Contact Problems available in PDF, EPUB and Kindle. 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.
Scalable Algorithms for Contact Problems
Scalable Algorithms for Contact Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Scalable Algorithms for Contact Problems write by Zdeněk Dostál. This book was released on 2023-11-29. Scalable Algorithms for Contact Problems available in PDF, EPUB and Kindle. 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.
Scalable Algorithms for Data and Network Analysis
Scalable Algorithms for Data and Network Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Scalable Algorithms for Data and Network Analysis write by Shang-Hua Teng. This book was released on 2016. Scalable Algorithms for Data and Network Analysis available in PDF, EPUB and Kindle. 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.
Scalable Algorithms for Data and Network Analysis
Scalable Algorithms for Data and Network Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Scalable Algorithms for Data and Network Analysis write by Shang-Hua Teng. This book was released on 2016-05-04. Scalable Algorithms for Data and Network Analysis available in PDF, EPUB and Kindle. In the age of Big Data, efficient algorithms are in high demand. It is also essential that efficient algorithms should be scalable. This book surveys a family of algorithmic techniques for the design of scalable algorithms. These techniques include local network exploration, advanced sampling, sparsification, and geometric partitioning.
Optimal Quadratic Programming Algorithms
Optimal Quadratic Programming Algorithms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimal Quadratic Programming Algorithms write by Zdenek Dostál. This book was released on 2009-04-03. Optimal Quadratic Programming Algorithms available in PDF, EPUB and Kindle. 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.
