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＜電子ブック＞
Scalable Algorithms for Contact Problems / by Zdeněk Dostál, Tomáš Kozubek, Marie Sadowská, Vít Vondrák
(Advances in Mechanics and Mathematics. ISSN:18769896 ; 36)

版	1st ed. 2016.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2016
本文言語	英語
大きさ	XIX, 340 p. 80 illus., 23 illus. in color : online resource
著者標目	*Dostál, Zdeněk author Kozubek, Tomáš author Sadowská, Marie author Vondrák, Vít author SpringerLink (Online service)
件　名	LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 LCSH:Computer science -- Mathematics  全ての件名で検索 FREE:Computational Mathematics and Numerical Analysis FREE:Mathematical and Computational Engineering Applications FREE:Mathematics of Computing
一般注記	1. Contact Problems and their Solution -- Part I. Basic Concepts -- 2. Linear Algebra -- 3. Optimization -- 4. Analysis -- Part II. Optimal QP and QCQP Algorithms -- 5. Conjugate Gradients -- 6. Gradient Projection for Separable Convex Sets -- 7. MPGP for Separable QCQP -- 8. MPRGP for Bound Constrained QP -- 9. Solvers for Separable and Equality QP/QCQP Problems -- Part III. Scalable Algorithms for Contact Problems -- 10. TFETI for Scalar Problems -- 11. Frictionless Contact Problems -- 12. Contact Problems with Friction -- 13. Transient Contact Problems -- 14. TBETI -- 15. Mortars -- 16. Preconditioning and Scaling -- Part IV. Other Applications and Parallel Implementation -- 17. Contact with Plasticity -- 18. Contact Shape Optimization -- 19. Massively Parallel Implementation -- Index 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 HTTP:URL=https://doi.org/10.1007/978-1-4939-6834-3

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