東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Scalable algorithms for contact problems

Dostal, Zdenek.

FindBook

Google Book

Amazon

博客來

Scalable algorithms for contact problems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Scalable algorithms for contact problems/ by Zdenek Dostal ... [et al.] ; with contributions by Tomas Brzobohaty ... [et al.].
其他作者:	Dostal, Zdenek.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xxii, 443 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Contact mechanics - Mathematics. -
電子資源:	https://doi.org/10.1007/978-3-031-33580-8
ISBN:	9783031335808

Scalable algorithms for contact problems
Scalable algorithms for contact problems[electronic resource] /by Zdenek Dostal ... [et al.] ; with contributions by Tomas Brzobohaty ... [et al.]. - Second edition. - Cham :Springer International Publishing :2023. - xxii, 443 p. :ill., digital ;24 cm. - Advances in mechanics and mathematics,v. 361876-9896 ;. - Advances in mechanics and mathematics ;v. 36..

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.

ISBN: 9783031335808

Standard No.: 10.1007/978-3-031-33580-8doiSubjects--Topical Terms:

3315474
Contact mechanics
--Mathematics.

LC Class. No.: TA353

Dewey Class. No.: 620.440151

Scalable algorithms for contact problems
LDR:04041nmm a2200349 a 4500 001 2335596
003 DE-He213
005 20231028161124.0
006 m d
007 cr nn 008maaau
008 240402s2023 sz s 0 eng d
020 $a 9783031335808 $q (electronic bk.)
020 $a 9783031335792 $q (paper)
024 7 $a 10.1007/978-3-031-33580-8 $2 doi
035 $a 978-3-031-33580-8
040 $a GP $c GP
041 0 $a eng
050 4 $a TA353
072 7 $a PBKS $2 bicssc
072 7 $a MAT006000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 620.440151 $2 23
090 $a TA353 $b .S281 2023
245 0 0 $a Scalable algorithms for contact problems $h [electronic resource] / $c by Zdenek Dostal ... [et al.] ; with contributions by Tomas Brzobohaty ... [et al.].
250 $a Second edition.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xxii, 443 p. : $b ill., digital ; $c 24 cm.
490 1 $a Advances in mechanics and mathematics, $x 1876-9896 ; $v v. 36
505 0 $a 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.
520 $a 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.
650 0 $a Contact mechanics $x Mathematics. $3 3315474
650 1 4 $a Computational Mathematics and Numerical Analysis. $3 891040
650 2 4 $a Mathematical and Computational Engineering Applications. $3 3592737
650 2 4 $a Mathematics of Computing. $3 891213
700 1 $a Dostal, Zdenek. $3 1005912
700 1 $a Brzobohaty, Tomas. $3 3668132
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Advances in mechanics and mathematics ; $v v. 36. $3 3668133
856 4 0 $u https://doi.org/10.1007/978-3-031-33580-8
950 $a Mathematics and Statistics (SpringerNature-11649)