LEADER 04638nam 22006375 450 001 9910162852003321 005 20200703034007.0 010 $a1-4939-6834-3 024 7 $a10.1007/978-1-4939-6834-3 035 $a(CKB)3710000001041177 035 $a(MiAaPQ)EBC4793459 035 $a(DE-He213)978-1-4939-6834-3 035 $a(PPN)198338333 035 $a(EXLCZ)993710000001041177 100 $a20170128d2016 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aScalable Algorithms for Contact Problems /$fby Zden?k Dostál, Tomá? Kozubek, Marie Sadowská, Vít Vondrák 205 $a1st ed. 2016. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2016. 215 $a1 online resource (341 pages) $cillustrations 225 1 $aAdvances in Mechanics and Mathematics,$x1571-8689 ;$v36 311 $a1-4939-6832-7 320 $aIncludes bibliographical references and index. 327 $a1. 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. 330 $aThis book presents a comprehensive and self-contained treatment of the authors? newly developed scalable algorithms for the solutions of multibody contact problems of linear elasticity. The brand new feature of these algorithms is theoretically supported numerical scalability and parallel scalability demonstrated on problems discretized by billions of degrees of freedom. The theory supports solving multibody frictionless contact problems, contact problems with possibly orthotropic Tresca?s friction, and transient contact problems. It covers BEM discretization, jumping coefficients, floating bodies, mortar non-penetration conditions, etc. The exposition is divided into four parts, the first of which reviews appropriate facets of linear algebra, optimization, and analysis. The most important algorithms and optimality results are presented in the third part of the volume. The presentation is complete, including continuous formulation, discretization, decomposition, optimality results, and numerical experiments. The final part includes extensions to contact shape optimization, plasticity, and HPC implementation. Graduate students and researchers in mechanical engineering, computational engineering, and applied mathematics, will find this book of great value and interest. 410 0$aAdvances in Mechanics and Mathematics,$x1571-8689 ;$v36 606 $aComputer mathematics 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aComputer science?Mathematics 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 606 $aMathematics of Computing$3https://scigraph.springernature.com/ontologies/product-market-codes/I17001 615 0$aComputer mathematics. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 0$aComputer science?Mathematics. 615 14$aComputational Mathematics and Numerical Analysis. 615 24$aMathematical and Computational Engineering. 615 24$aMathematics of Computing. 676 $a620.105 700 $aDostál$b Zden?k$4aut$4http://id.loc.gov/vocabulary/relators/aut$0472333 702 $aKozubek$b Tomá?$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSadowská$b Marie$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aVondrák$b Vít$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910162852003321 996 $aScalable algorithms for contact problems$91749414 997 $aUNINA