Authors:
- This is the first monograph on theoretically supported scalable algorithms for contact problems
- Exposition neatly presents efficient domain decomposition methods and a comprehensive description of parallel implementation
- Describes finite and boundary element domain decomposition methods in a unified form
- Features algorithms tested on real world problems
- Contains QPCQ and quadratic programming algorithms with rate of convergence
- Includes supplementary material: sn.pub/extras
Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 36)
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Table of contents (19 chapters)
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Other Applications and Parallel Implementation
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Front Matter
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Back Matter
About this book
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.Reviews
Authors and Affiliations
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National Supercomputer Center and Department of Applied Mathematics, VŠB-Technical University of Ostrava, Ostrava, Czech Republic
Zdeněk Dostál, Tomáš Kozubek, Vít Vondrák
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Department of Applied Mathematics, VŠB-Technical University of Ostrava, Ostrava, Czech Republic
Marie Sadowská
Bibliographic Information
Book Title: Scalable Algorithms for Contact Problems
Authors: Zdeněk Dostál, Tomáš Kozubek, Marie Sadowská, Vít Vondrák
Series Title: Advances in Mechanics and Mathematics
DOI: https://doi.org/10.1007/978-1-4939-6834-3
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media LLC 2016
Softcover ISBN: 978-1-4939-8312-4Published: 12 July 2018
eBook ISBN: 978-1-4939-6834-3Published: 25 January 2017
Series ISSN: 1571-8689
Series E-ISSN: 1876-9896
Edition Number: 1
Number of Pages: XIX, 340
Number of Illustrations: 57 b/w illustrations, 23 illustrations in colour
Topics: Computational Mathematics and Numerical Analysis, Mathematical and Computational Engineering, Mathematics of Computing