Описание: Offers an introduction to the discontinuous finite element method. This book provides a review of the fundamental laws and equations governing thermal and fluid systems. It also explains mesh generation and adaptivity, parellelization algorithms and error analysis.
Описание: A knowledge of the mechanical behaviour of both naturally occurring materials, such as soils and rocks, and artificial materials such as concrete and industrial granular matter, is of fundamental importance to their proper use in engineering and scientific applications.
Описание: This book introduces the basic ideas to build discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. The presentation is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite element and finite volume viewpoints are exploited to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed.
Описание: The book analyzes a quasi-static fracture process in concrete and reinforced concrete by means of constitutive models formulated within continuum mechanics. A continuous and discontinuous modelling approach was used. Using a continuous approach, numerical analyses were performed using a finite element method and four different enhanced continuum models: isotropic elasto-plastic, isotropic damage and anisotropic smeared crack one. The models were equipped with a characteristic length of micro-structure by means of a non-local and a second-gradient theory. So they could properly describe the formation of localized zones with a certain thickness and spacing and a related deterministic size effect. Using a discontinuous FE approach, numerical results of cracks using a cohesive crack model and XFEM were presented which were also properly regularized. Finite element analyses were performed with concrete elements under monotonic uniaxial compression, uniaxial tension, bending and shear-extension. Concrete beams under cyclic loading were also simulated using a coupled elasto-plastic-damage approach. Numerical simulations were performed at macro- and meso-level of concrete. A stochastic and deterministic size effect was carefully investigated. In the case of reinforced concrete specimens, FE calculations were carried out with bars, slender and short beams, columns, corbels and tanks. Tensile and shear failure mechanisms were studied. Numerical results were compared with results from corresponding own and known in the scientific literature laboratory and full-scale tests.
Описание: the so called standard superconvergent div 6 PREFACE Contents 1 Basics 15 1.1 Meshes and shape functions ... ... .... ... .... .... ... ... 15 1.2 Spaces and approximation .... ... .... ... .... .... ... ... 19 2 Linear Diffusion I 33 3 Linear Diffusion II 67 4 Stokes Equations 89 8 CONTENTS 5 Flow Problems 105 5.1 Advection-Diffusion-ReactionEquation .. .... .... ... .... ... . 107 5.2 Oseen Equations .... ... .... ... .... .... ... .... ... . 110 5.3 Navier-Stokes Equations ... .... ... .... .... ... .... ... . 112 6 Linear Solvers 131 6.1 Krylov space methods . . . . . .... ... .... .... ... .... ... . 132 6.2 Interior Penalty . .... ... .... ... .... .... ... .... ... . 134 6.3 Local multigrid . .... ... .... ... .... .... ... .... ... . 145 6.4 LDG .... ... .... ... .... ... .... .... ... .... ... . 151 6.5 Advection Diffusion .. ... .... ... .... .... ... .... ... . 158 6.6 Stokes ... ... .... ... .... ... .... .... ... .... ... . 160 6.7 Oseen equations . .... ... .... ... .... .... ... .... ... . 162 A Example problems 167 A.1 Meshes and domains .. ... .... ... .... .... ... .... ... . 167 A.2 Poisson equation .... ... .... ... .... .... ... .... ... . 170 A.3 Advection-diffusion-reaction . .... ... .... .... ... .... ... . 171 A.4 Stokes and Oseen equations .. .... ... .... .... ... .... ... . 172 List of Figures 1.1 The set and (if ). . ... .... ... .... .... ... ... 17 1.2 The cel (dark grey) and the neighbor set (grey). Note that a common corner does not result in neighborhood. . . . . .... ... .... .... ... ... 19 2.1 Smallest eigenvalue of on a mesh of squares . .... .... ... ... 38 2.2 Eigenfunction to the smallest eigenvalue of for (left) and (right) on a mesh of squares . . . . . .... ... .... .... ... ... 39 2.3 Accuracy of the interior penalty method depending on the parameter . . ... 44 2.4 Pointwise errors on irregular meshes . . .... ... .... .... ... ... 55 2.5 Adapted mesh (level ) for the point value computation .... ... ... 60 2.6 -error over number of degrees of freedom for CG-, DG- and - elements (left) and (bi-)quadratic elements (right) .. .... .... ... ... 62
Автор: Goh Название: Discontinuous-Fibre Reinforced Composites ISBN: 1447173031 ISBN-13(EAN): 9781447173038 Издательство: Springer Рейтинг: Цена: 11359 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book provides a simple and unified approach to the mechanics of discontinuous-fibre reinforced composites, and introduces readers as generally as possible to the key concepts regarding the mechanics of elastic stress transfer, intermediate modes of stress transfer, plastic stress transfer, fibre pull-out, fibre fragmentation and matrix rupture. These concepts are subsequently applied to progressive stages of the loading process, through to the composite fractures. The book offers a valuable guide for advanced undergraduate and graduate students attending lecture courses on fibre composites. It is also intended for beginning researchers who wish to develop deeper insights into how discontinuous fibre provides reinforcement to composites, and for engineers, particularly those who wish to apply the concepts presented here to design and develop discontinuous-fibre reinforced composites.
This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem of its spurious-free approximations. Treatment of unbounded domains by Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML) is described and analyzed in a separate chapter. The two last chapters deal with time approximation including local time-stepping and with the study of some complex models, i.e. acoustics in flow, gravity waves and vibrating thin plates. Throughout, emphasis is put on the accuracy and computational efficiency of the methods, with attention brought to their practical aspects.
This monograph also covers in details the theoretical foundations and numerical analysis of these methods. As a result, this monograph will be of interest to practitioners, researchers, engineers and graduate students involved in the numerical simulation
Описание: With a pedagogic format ideal for graduate students, this text includes a wealth of examples focusing on solutions in dynamical systems theory that mirror those used in Lyapunov`s first method, tackling ordinary differential equations expressed as series form.
Автор: Avella Название: Strongly Correlated Systems ISBN: 364221830X ISBN-13(EAN): 9783642218309 Издательство: Springer Рейтинг: Цена: 14854 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The volume presents, for the very first time, an exhaustive collection of those modern theoretical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and materials science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for other researchers in the field who appreciates consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possible way, with the working details of a specific technique.
Описание: This research monograph offers an introduction to advanced quantum field theoretical techniques for many-particle systems beyond perturbation theory.
Several schemes for resummation of the Feynman diagrams are described. The resulting approximations are especially well suited for strongly correlated fermion and boson
Also considered is the crossover from BCS superconductivity to Bose--Einstein condensation in fermion systems with strong attractive interaction. In particular, a field
theoretic formulation of "bosonization" is presented; it is published here for the first time. This method is applied to the fractional quantum Hall effect, to the Coulomb plasma, and to
several exactly solvable models.
Описание: The investigation of minor solar system bodies, such as comets and asteroids, using spacecraft requires an understanding of orbital motion in strongly perturbed environments. The solutions to a wide range of complex and challenging problems in this field are reviewed in this comprehensive and authoritative work.
Описание: This book embraces the entire range of problems associated with nonstoichiometry, disorder and order in solids. Although dealing primarily with transition metal carbides, nitrides and oxides, the methods and models presented are applicable to all systems with substitutional disorder and they permit a unified approach to the structure, phase diagrams and other physical and chemical properties of these systems. This book will be useful for physicists addressing the problems of order and disorder in solids, for chemists increasingly aware that the majority of natural and synthetic materials are nonstoichiometric, and for crystallographers studying new and unusual crystal structures. Materials scientists using refractory compounds to create novel superhard and tough materials or materials for modern electronics will find essential information on the interplay between structural effects and many different properties of transition metal compounds.
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