Scalable Algorithms for Contact Problems - Marie Sadowská

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Résumé :
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....

Biographie:
Zden?k Dost?l is a professor at the Department of Applied Mathematics and Senior Researcher at IT4Innovations National Supercomputing Center, V?B-Technical University of Ostrava. Zden?k works in Numerical Linear Algebra, Optimization, and Computational Mechanics. He published his results in more than 120 papers (Scopus). He is an author of the book 'Optimal Quadratic Programming Algorithms' (Springer 2009) and coauthor of 'Scalable Algorithms for Contact Problems' (Springer 2017) on massively parallel algorithms with theoretically supported linear (optimal) complexity. His current research concerns QP, QCQP, and generalization of the above results to H-TFETI and H-TBETI.