Overview
- Neatly presents efficient domain decomposition methods and a comprehensive description of parallel implementation
- Describes finite and boundary element domain decomposition methods in a unified form
- Contains QPCQ and quadratic programming algorithms with rate of convergence
Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 36)
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Table of contents (20 chapters)
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Front Matter
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Basic Concepts
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Front Matter
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Optimal QP and QCQP Algorithms
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Front Matter
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Scalable Algorithms for Contact Problems
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Front Matter
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Keywords
About this book
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.
Authors and Affiliations
About the authors
Tomáš Kozubek is a professor of applied mathematics at IT4Innovations National Supercomputing Center, VŠB–Technical University of Ostrava, specialising in developing scalable algorithms for massively parallel solutions ofengineering problems. He is a scientific director at IT4Innovations. He is also the author or coauthor of over 60 articles (concerning WoS) published in conference proceedings and journals. He is/was PI for the Czech Republic of the project FP7-ICT EXA2CT (Exascale Algorithms and Advanced Computational Techniques), H2020-MSCA-ITN EXPERTISE (models, Experiments and high PERformance computing for Turbine mechanical Integrity and Structural dynamics in Europe), H2020-JTI-EuroHPC Hercules (Hpc EuRopean ConsortiUm Leading Education activitieS), and ERASMUS+ SCTrain. He participates in activities of the H2020 Centre of Excellence in HPC project SPACE focused on computational astrophysics, and the European Digital Innovation Hub Ostrava focused on supporting industry and public organisations in HPC, artificial intelligence, and advanced data analysis. He is a guarantor of the doctoral study programme Computational Sciences at VSB–Technical University of Ostrava, a member of university scientific boards and programming committees of conferences, and a leading organiser of the HPCSE (HPC in Science and Engineering Conference). He is also the primary coordinator of the national Doctoral School for Education in Mathematical Methods and Tools in HPC.
Marie Sadowská works as an assistant professor at the Department of Applied Mathematics, closely cooperating with IT4Innovations National Supercomputing Center, both at VŠB-Technical University of Ostrava. She has been interested in boundary element methods in combination with domain decomposition approaches with applications to computational mechanics.
Vít Vondrák has been working at VŠB–Technical University of Ostrava since 1993, with the longest period spent at the Department of Applied Mathematics at the Faculty of Electrical Engineering and Computer Science, where he received the title of associate professor in 2007. His professional focus is on numerical linear algebra, optimisation methods including design optimisation, domain decomposition methods, highperformance computing and their applications in structural mechanics, biomechanics, hydrological and traffic simulations. From 1997 to 2007, he spent 2 years at Aalborg University, Denmark, as part of several research stays, and in 2004 and 2006, he stayed in the USA at the University of Colorado at Boulder and Stanford University, California. He was one of the founders of IT4Innovations National Supercomputing Center in the Czech Republic, of which he has been the Managing Director since 2017. As part of his scientific career, he has led or participated in leading a number of research projects, including international EU projects. He was the principal investigator of the Intel Parallel Computing Centre funded by Intel corp., the CzeBaCCA project for cooperation between the Czech Republic and Bavaria in the field of supercomputing applications, and the project to support large infrastructures in the Czech Republic.
Bibliographic Information
Book Title: Scalable Algorithms for Contact Problems
Authors: Zdeněk Dostál, Tomáš Kozubek, Marie Sadowská, Vít Vondrák
Series Title: Advances in Mechanics and Mathematics
DOI: https://doi.org/10.1007/978-3-031-33580-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-33579-2Published: 29 October 2023
Softcover ISBN: 978-3-031-33582-2Due: 29 November 2023
eBook ISBN: 978-3-031-33580-8Published: 28 October 2023
Series ISSN: 1571-8689
Series E-ISSN: 1876-9896
Edition Number: 2
Number of Pages: XXII, 443
Number of Illustrations: 75 b/w illustrations, 29 illustrations in colour
Topics: Computational Mathematics and Numerical Analysis, Mathematical and Computational Engineering, Mathematics of Computing