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Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.
The purpose of this book is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDEs). These methods are widely used for numerical simulations in solid mechanics, electromagnetism, flow in porous media, etc., on parallel machines from tens to hundreds of thousands of cores. The appealing feature of domain decomposition methods is that, contrary to direct methods, they are naturally parallel. The authors focus on parallel linear solvers. The authors present all popular algorithms, both at the PDE level and at the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts. Also included is a new coarse space construction (two-level method) that adapts to highly heterogeneous problems.?
This text gives the proceedings for the fifth conference on parallel processing for scientific computing.
Computational Mechanics '91 is the Proceedings of the International Conference on Computational Engineering Science, August 12-16, 1991. Melbourne, Australia. The aim of this Conference is to become a forum for discussion of both academic & industrial research in those areas of computational engineering science & mechanics which involve & enrich the rational application of computers, numerical methods & mechanics, in modern technology. Papers that are included in Computational Mechanics '91 cover the following topics: Solid & Structural Mechanics; composite Materials; Smart Structures; constitutive Modeling; Inelastic & Finite Deformation Response; Transient Analysis; Structural Control & Optimization; Multi-Body Dynamics; Fracture Mechanics & Structural Integrity; Computational Fluid Dynamics; Compressible & Incompressible Flow; Aerodynamics; Transport Phenomena; Heat Transfer & Solidification; Electro-magnetic Field, Related Solid Mechanics & MHD; Modern Variational Methods; Biomechanics; & Off-Shore-Structural Mechanics. Among the methods to be discussed are: Finite Element & Boundary Element Methods, Spectral Methods, Finite Volume & Finite Difference Methods, Domain Decomposition Methods, Parallel Computing, etc. Also included in the proceedings are papers from: The International Assoc. for Boundary Element Methods Forum, organized by J. H. Kane (USA), G. Maier (Italy), N. Tosaka (Japan) & S. N. Atluri (USA); & The Symposium on Numerical Modeling of Composites organized by Prof. O. Ochoa (USA).
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Contact mechanics and surface effects, as well as their interaction, are important in modern engineering. The life and performance of structural components is affected by surface conditions such as wear, corrosion and, high cycle fatigue. Surface treatments that address contact conditions can reduce costs by extending the life of components. These are the subjects of a biennial conference first held in 1993, the papers from the latest of which are collected in this volume. The book discusses Computer simulation; Surface modification; Surface treatments; Surface problems in contact mechanics; Contact mechanics; Applications and case studies; Indentation and hardness; Thick and thin coatings; Corrosion problems; Nano-characterisation; Test methodology; Multiscale experiments and modelling; and Fracture fatigue and mechanics.