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Scalable Algorithms for Contact Problems

  • Book
  • © 2016

Overview

Authors:
  1. Zdeněk Dostál

    1. National Supercomputer Center and Department of Applied Mathematics, VŠB-Technical University of Ostrava, Ostrava, Czech Republic

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  2. Tomáš Kozubek

    1. National Supercomputer Center and Department of Applied Mathematics, VŠB-Technical University of Ostrava, Ostrava, Czech Republic

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  3. Marie Sadowská

    1. Department of Applied Mathematics, VŠB-Technical University of Ostrava, Ostrava, Czech Republic

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  4. Vít Vondrák

    1. National Supercomputer Center and Department of Applied Mathematics, VŠB-Technical University of Ostrava, Ostrava, Czech Republic

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  • This is the first monograph on theoretically supported scalable algorithms for contact problems
  • Exposition 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
  • Features algorithms tested on real world problems
  • Contains QPCQ and quadratic programming algorithms with rate of convergence
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xix
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  2. Contact Problems and Their Solution

    • Zdeněk Dostál
    Pages 1-8

  3. Basic Concepts

    1. Front Matter

      Pages 9-9
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    2. Linear Algebra

      • Zdeněk Dostál, Tomáš Kozubek
      Pages 11-27

    3. Optimization

      • Zdeněk Dostál
      Pages 29-57

    4. Analysis

      • Marie Sadowská
      Pages 59-66

  4. Optimal QP and QCQP Algorithms

    1. Front Matter

      Pages 67-67
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    2. Conjugate Gradients

      • Zdeněk Dostál
      Pages 69-82

    3. Gradient Projection for Separable Convex Sets

      • Zdeněk Dostál
      Pages 83-97

    4. MPGP for Separable QCQP

      • Zdeněk Dostál
      Pages 99-119

    5. MPRGP for Bound-Constrained QP

      • Zdeněk Dostál
      Pages 121-133

    6. Solvers for Separable and Equality QP/QCQP Problems

      • Zdeněk Dostál, Tomáš Kozubek
      Pages 135-160

  5. Scalable Algorithms for Contact Problems

    1. Front Matter

      Pages 161-161
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    2. TFETI for Scalar Problems

      • Zdeněk Dostál, Tomáš Kozubek
      Pages 163-181

    3. Frictionless Contact Problems

      • Zdeněk Dostál, Tomáš Kozubek, Vít Vondrák
      Pages 183-209

    4. Contact Problems with Friction

      • Zdeněk Dostál, Tomáš Kozubek, Vít Vondrák
      Pages 211-229

    5. Transient Contact Problems

      • Zdeněk Dostál, Tomáš Kozubek
      Pages 231-250

    6. TBETI

      • Zdenek Dostál, Tomáš Kozubek, Marie Sadowská
      Pages 251-275

    7. Mortars

      • Zdeněk Dostál, Tomáš Kozubek
      Pages 277-289

    8. Preconditioning and Scaling

      • Zdeněk Dostál, Tomáš Kozubek
      Pages 291-300
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Keywords

About this book

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.

Reviews

“The methods presented in the book can be used for solving many problems, as demonstrated by the numerical results. The book can serve as an introductory text for anybody interested in contact problems. Graduate students and researchers in mechanical engineering, computational engineering, and applied mathematics, also will find this book of big value and interest.” (V. Leontiev , zbMATH 1383.74002, 2018)

Authors and Affiliations

  • National Supercomputer Center and Department of Applied Mathematics, VŠB-Technical University of Ostrava, Ostrava, Czech Republic

    Zdeněk Dostál, Tomáš Kozubek, Vít Vondrák

  • Department of Applied Mathematics, VŠB-Technical University of Ostrava, Ostrava, Czech Republic

    Marie Sadowská

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