05393nam 22006855 450 991075507520332120251113195921.03-031-33580-510.1007/978-3-031-33580-8(MiAaPQ)EBC30832453(Au-PeEL)EBL30832453(DE-He213)978-3-031-33580-8(PPN)272914274(CKB)28572696400041(EXLCZ)992857269640004120231028d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierScalable Algorithms for Contact Problems /by Zdeněk Dostál, Tomáš Kozubek, Marie Sadowská, Vít Vondrák2nd ed. 2023.Cham :Springer International Publishing :Imprint: Springer,2023.1 online resource (447 pages)Advances in Mechanics and Mathematics,1876-9896 ;36Print version: Dostál, Zdeněk Scalable Algorithms for Contact Problems Cham : Springer International Publishing AG,c2023 9783031335792 Chapter. 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.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.Advances in Mechanics and Mathematics,1876-9896 ;36MathematicsData processingEngineering mathematicsEngineeringData processingComputer scienceMathematicsComputational Mathematics and Numerical AnalysisMathematical and Computational Engineering ApplicationsMathematics of ComputingMathematicsData processing.Engineering mathematics.EngineeringData processing.Computer scienceMathematics.Computational Mathematics and Numerical Analysis.Mathematical and Computational Engineering Applications.Mathematics of Computing.620.440151Dostál Zdeněk0Kozubek Tomás1435909Sadowská Marie1435910Vondrák Vít1435911Brzobohatý Tomás1435912Horak David1435913Říha Lubomír1435914Vlach Oldrich1435915MiAaPQMiAaPQMiAaPQBOOK9910755075203321Scalable Algorithms for Contact Problems3593962UNINA