Scalable Algorithms for Contact Problems

  • Zdeněk Dostál
  • Tomáš Kozubek
  • Marie Sadowská
  • Vít Vondrák

Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 36)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Zdeněk Dostál
    Pages 1-8
  3. Basic Concepts

    1. Front Matter
      Pages 9-9
    2. Zdeněk Dostál, Tomáš Kozubek
      Pages 11-27
    3. Zdeněk Dostál
      Pages 29-57
    4. Marie Sadowská
      Pages 59-66
  4. Optimal QP and QCQP Algorithms

    1. Front Matter
      Pages 67-67
    2. Zdeněk Dostál
      Pages 69-82
    3. Zdeněk Dostál
      Pages 83-97
    4. Zdeněk Dostál
      Pages 99-119
    5. Zdeněk Dostál
      Pages 121-133
    6. Zdeněk Dostál, Tomáš Kozubek
      Pages 135-160
  5. Scalable Algorithms for Contact Problems

    1. Front Matter
      Pages 161-161
    2. Zdeněk Dostál, Tomáš Kozubek
      Pages 163-181
    3. Zdeněk Dostál, Tomáš Kozubek, Vít Vondrák
      Pages 183-209
    4. Zdeněk Dostál, Tomáš Kozubek, Vít Vondrák
      Pages 211-229
    5. Zdeněk Dostál, Tomáš Kozubek
      Pages 231-250
    6. Zdenek Dostál, Tomáš Kozubek, Marie Sadowská
      Pages 251-275
    7. Zdeněk Dostál, Tomáš Kozubek
      Pages 277-289
    8. Zdeněk Dostál, Tomáš Kozubek
      Pages 291-300

About this book

Introduction

This 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.

Keywords

Contact problems of elasticity Domain decomposition Parallel algorithms Scalable algorithms Sobolev spaces variational inequalities multibody frictionless contact problems parallel scalability Tresca's friction transient contact problems BEM discretization

Authors and affiliations

  • Zdeněk Dostál
    • 1
  • Tomáš Kozubek
    • 2
  • Marie Sadowská
    • 3
  • Vít Vondrák
    • 4
  1. 1.National Supercomputer Center and Department of Applied MathematicsVŠB-Technical University of OstravaOstravaCzech Republic
  2. 2.National Supercomputer Center and Department of Applied MathematicsVŠB-Technical University of OstravaOstravaCzech Republic
  3. 3.Department of Applied MathematicsVŠB-Technical University of OstravaOstravaCzech Republic
  4. 4.National Supercomputer Center and Department of Applied MathematicsVŠB-Technical University of OstravaOstravaCzech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-6834-3
  • Copyright Information Springer Science+Business Media LLC 2016
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-6832-9
  • Online ISBN 978-1-4939-6834-3
  • Series Print ISSN 1571-8689
  • Series Online ISSN 1876-9896
  • About this book