LEADER 05381nam 22006735 450 001 9910755075203321 005 20231028161124.0 010 $a3-031-33580-5 024 7 $a10.1007/978-3-031-33580-8 035 $a(MiAaPQ)EBC30832453 035 $a(Au-PeEL)EBL30832453 035 $a(DE-He213)978-3-031-33580-8 035 $a(PPN)272914274 035 $a(EXLCZ)9928572696400041 100 $a20231028d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aScalable Algorithms for Contact Problems$b[electronic resource] /$fby Zden?k Dostál, Tomá? Kozubek, Marie Sadowská, Vít Vondrák 205 $a2nd ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (447 pages) 225 1 $aAdvances in Mechanics and Mathematics,$x1876-9896 ;$v36 311 08$aPrint version: Dostál, Zden?k Scalable Algorithms for Contact Problems Cham : Springer International Publishing AG,c2023 9783031335792 327 $aChapter. 1 Contact Problems and Their Solution -- Part. I. Basic Concepts -- Chapter. 2. Linear Algebra -- Chapter. 3. Optimization -- Chapter. 4. Analysis -- Part. II. Optimal QP and QCQP Algorithms -- Chapter. 5. Conjugate Gradients -- Chapter. 6. Gradient Projection for Separable Convex Sets -- Chapter. 7. MPGP for Separable QCQP -- Chapter. 8. MPRGP for Bound-Constrained QP -- Chapter. 9. Solvers for Separable and Equality QP/QCQP Problems -- Part. III. Scalable Algorithms for Contact Problems -- Chapter. 10. TFETI for Scalar Problems -- Chapter. 11. Frictionless Contact Problems -- Chapter. 12. Contact Problems with Friction -- Chapter. 13. Transient Contact Problems -- Chapter. 14. TBETI -- Chapter. 15. Hybrid TFETI and TBETI -- Chapter. 16. Mortars -- Chapter. 17. Preconditioning and Scaling -- Part. IV. Other Applications and Parallel Implementation -- Chapter. 18. Contact with Plasticity -- Chapter. 19. Contact Shape Optimization -- Chapter. 20. Massively Parallel Implementation -- Notation and List of Symbols. 330 $aThis book presents a comprehensive treatment of recently developed scalable algorithms for solving multibody contact problems of linear elasticity. The brand-new feature of these algorithms is their theoretically supported numerical scalability (i.e., asymptotically linear complexity) and parallel scalability demonstrated in solving problems discretized by billions of degrees of freedom. The theory covers solving multibody frictionless contact problems, contact problems with possibly orthotropic Tresca?s friction, and transient contact problems. In addition, it also covers BEM discretization, treating jumping coefficients, floating bodies, mortar non-penetration conditions, etc. This second edition includes updated content, including a new chapter on hybrid domain decomposition methods for huge contact problems. Furthermore, new sections describe the latest algorithm improvements, e.g., the fast reconstruction of displacements, the adaptive reorthogonalization of dual constraints, and an updated chapter on parallel implementation. Several chapters are extended to give an independent exposition of classical bounds on the spectrum of mass and dual stiffness matrices, a benchmark for Coulomb orthotropic friction, details of discretization, etc. The exposition is divided into four parts, the first of which reviews auxiliary linear algebra, optimization, and analysis. The most important algorithms and optimality results are presented in the third chapter. The presentation includes continuous formulation, discretization, domain decomposition, optimality results, and numerical experiments. The final part contains extensions to contact shape optimization, plasticity, and HPC implementation. Graduate students and researchers in mechanical engineering, computational engineering, and applied mathematics will find this book of great value and interest. 410 0$aAdvances in Mechanics and Mathematics,$x1876-9896 ;$v36 606 $aMathematics$xData processing 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aComputer science$xMathematics 606 $aComputational Mathematics and Numerical Analysis 606 $aMathematical and Computational Engineering Applications 606 $aMathematics of Computing 615 0$aMathematics$xData processing. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 0$aComputer science$xMathematics. 615 14$aComputational Mathematics and Numerical Analysis. 615 24$aMathematical and Computational Engineering Applications. 615 24$aMathematics of Computing. 676 $a620.440151 700 $aDostál$b Zden?k$0472333 701 $aKozubek$b Tomás$01435909 701 $aSadowská$b Marie$01435910 701 $aVondrák$b Vít$01435911 701 $aBrzobohatý$b Tomás$01435912 701 $aHorak$b David$01435913 701 $a?íha$b Lubomir$01435914 701 $aVlach$b Oldrich$01435915 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910755075203321 996 $aScalable Algorithms for Contact Problems$93593962 997 $aUNINA