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Scalable Algorithms For Contact Problems

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Scalable Algorithms For Contact Problems

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Author : Zdeněk Dostál
language : en
Publisher: Springer Nature
Release Date : 2023-10-28

Scalable Algorithms For Contact Problems written by Zdeněk Dostál and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-28 with Mathematics categories.

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 Contact Problems

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Author : Zdeněk Dostál
language : en
Publisher: Springer
Release Date : 2023-10-29

Scalable Algorithms For Contact Problems written by Zdeněk Dostál and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-29 with Mathematics categories.

Numerical Methods For Strong Nonlinearities In Mechanics

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Author : Jacques Besson
language : en
Publisher: John Wiley & Sons
Release Date : 2025-01-09

Numerical Methods For Strong Nonlinearities In Mechanics written by Jacques Besson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-09 with Mathematics categories.

Numerical Methods for Strong Nonlinearities in Mechanics deals with recent advances in the numerical treatment of contact/friction and damage phenomena. Although physically distinct, these phenomena both lead to a strong nonlinearity in the mechanical problem, therefore limiting the regularity of the problem, which is now non-differentiable. This has two direct consequences: on the one hand, the mathematical characteristics of the problem deviate from wellestablished forms, requiring innovative discretization schemes; on the other hand, the low regularity makes it particularly difficult to solve the corresponding large-scale algebraic systems robustly and efficiently. In addition, neither the uniqueness, nor the existence of solutions, remain assured, resulting in bifurcation points, limit loads and structural instabilities, which are always tricky to overcome numerically.

Optimal Quadratic Programming Algorithms

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Author : Zdenek Dostál
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03

Optimal Quadratic Programming Algorithms written by Zdenek Dostál and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Mathematics categories.

Solving optimization problems in complex systems often requires the implementation of advanced mathematical techniques. Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. QP problems arise in fields as diverse as electrical engineering, agricultural planning, and optics. Given its broad applicability, a comprehensive understanding of quadratic programming is a valuable resource in nearly every scientific field. Optimal Quadratic Programming Algorithms presents recently developed algorithms for solving large QP problems. The presentation 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. The reader is required to have a basic knowledge of calculus in several variables and linear algebra.

Domain Decomposition Methods In Science And Engineering Xvii

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Author : Ulrich Langer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-02

Domain Decomposition Methods In Science And Engineering Xvii written by Ulrich Langer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-02 with Mathematics categories.

Domain decomposition is an active, interdisciplinary research field concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models. This volume contains selected papers presented at the 17th International Conference on Domain Decomposition Methods in Science and Engineering. It presents the newest domain decomposition techniques and examines their use in the modeling and simulation of complex problems.

High Performance Structures And Materials Vi

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Author : Willy Patrick Wilde
language : en
Publisher: WIT Press
Release Date : 2012

High Performance Structures And Materials Vi written by Willy Patrick Wilde and has been published by WIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Technology & Engineering categories.

Containing the edited papers presented at the Sixth International Conference on High Performance Structures and Materials, High Performance Structures and Materials VI addresses the issues involved with advanced types of structures, particularly those based on new concepts or new materials. Contributions will highlight the latest developments in design, optimisation, manufacturing and experimentation in these areas.The use of novel materials and new structural concepts nowadays is not restricted to highly technical areas like aerospace, aeronautical applications or the automotive industry, but affects all engineering fields including those such as civil engineering and architecture. Most high performance structures require the development of a generation of new materials, which can more easily resist a range of external stimuli or react in a non-conventional manner.The book will cover such topics as: Composite materials and structures, Lightweight structures, Nanocomposites, High performance concretes, Concrete fibres, Automotive composites, Steel structures, Natural fibre composites, Timber structures, Material characterisation, Experiments and numerical analysis, Damage and fracture mechanics, Computational intelligence, Adaptable and mobile structures, Environmentally friendly structures.

Domain Decomposition Methods In Science And Engineering

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Author : Ralf Kornhuber
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Domain Decomposition Methods In Science And Engineering written by Ralf Kornhuber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Mathematics categories.

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.

High Performance Computing In Science And Engineering

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Author : Tomáš Kozubek
language : en
Publisher: Springer
Release Date : 2018-07-16

High Performance Computing In Science And Engineering written by Tomáš Kozubek and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-16 with Computers categories.

This book constitutes the thoroughly refereed post-conference proceedings of the Third International Conference on High Performance Computing in Science and Engineering, HPCSE 2017, held in Karolinka, Czech Republic, in May 2017. The 15 papers presented in this volume were carefully reviewed and selected from 20 submissions. The conference provides an international forum for exchanging ideas among researchers involved in scientific and parallel computing, including theory and applications, as well as applied and computational mathematics. The focus of HPCSE 2017 was on models, algorithms, and software tools which facilitate efficient and convenient utilization of modern parallel and distributed computing architectures, as well as on large-scale applications.

Large Scale Nonlinear Optimization

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Author : Gianni Pillo
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-03

Large Scale Nonlinear Optimization written by Gianni Pillo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-03 with Mathematics categories.

Large-Scale Nonlinear Optimization reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. The chapters of the book, authored by some of the most active and well-known researchers in nonlinear optimization, give an updated overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.

Uncertainty Quantification In Variational Inequalities

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Author : Joachim Gwinner
language : en
Publisher: CRC Press
Release Date : 2021-12-21

Uncertainty Quantification In Variational Inequalities written by Joachim Gwinner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-21 with Mathematics categories.

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

Scalable Algorithms For Contact Problems

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