Scalable Algorithms for Contact Problems

Description

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 Front Matter....Pages i-xix Contact Problems and Their Solution....Pages 1-8 Front Matter....Pages 9-9 Linear Algebra....Pages 11-27 Optimization....Pages 29-57 Analysis....Pages 59-66 Front Matter....Pages 67-67 Conjugate Gradients....Pages 69-82 Gradient Projection for Separable Convex Sets....Pages 83-97 MPGP for Separable QCQP....Pages 99-119 MPRGP for Bound-Constrained QP....Pages 121-133 Solvers for Separable and Equality QP/QCQP Problems....Pages 135-160 Front Matter....Pages 161-161 TFETI for Scalar Problems....Pages 163-181 Frictionless Contact Problems....Pages 183-209 Contact Problems with Friction....Pages 211-229 Transient Contact Problems....Pages 231-250 TBETI....Pages 251-275 Mortars....Pages 277-289 Preconditioning and Scaling....Pages 291-300 Front Matter....Pages 301-301 Contact with Plasticity....Pages 303-309 Contact Shape Optimization....Pages 311-318 Massively Parallel Implementation....Pages 319-333 Back Matter....Pages 335-340