Conjugate Gradient Algorithms And Finite Element Methods
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Conjugate Gradient Algorithms And Finite Element Methods
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Author : Michal Krizek
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Conjugate Gradient Algorithms And Finite Element Methods written by Michal Krizek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The position taken in this collection of pedagogically written essays is that conjugate gradient algorithms and finite element methods complement each other extremely well. Via their combinations practitioners have been able to solve complicated, direct and inverse, multidemensional problems modeled by ordinary or partial differential equations and inequalities, not necessarily linear, optimal control and optimal design being part of these problems. The aim of this book is to present both methods in the context of complicated problems modeled by linear and nonlinear partial differential equations, to provide an in-depth discussion on their implementation aspects. The authors show that conjugate gradient methods and finite element methods apply to the solution of real-life problems. They address graduate students as well as experts in scientific computing.
The Finite Element Method For Solid And Structural Mechanics
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Author : O. C. Zienkiewicz
language : en
Publisher: Elsevier
Release Date : 2005-08-09
The Finite Element Method For Solid And Structural Mechanics written by O. C. Zienkiewicz and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-09 with Technology & Engineering categories.
This is the key text and reference for engineers, researchers and senior students dealing with the analysis and modelling of structures – from large civil engineering projects such as dams, to aircraft structures, through to small engineered components. Covering small and large deformation behaviour of solids and structures, it is an essential book for engineers and mathematicians. The new edition is a complete solids and structures text and reference in its own right and forms part of the world-renowned Finite Element Method series by Zienkiewicz and Taylor. New material in this edition includes separate coverage of solid continua and structural theories of rods, plates and shells; extended coverage of plasticity (isotropic and anisotropic); node-to-surface and 'mortar' method treatments; problems involving solids and rigid and pseudo-rigid bodies; and multi-scale modelling. - Dedicated coverage of solid and structural mechanics by world-renowned authors, Zienkiewicz and Taylor - New material including separate coverage of solid continua and structural theories of rods, plates and shells; extended coverage for small and finite deformation; elastic and inelastic material constitution; contact modelling; problems involving solids, rigid and discrete elements; and multi-scale modelling
The Finite Element Method Solid Mechanics
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Author : O. C. Zienkiewicz
language : en
Publisher: Butterworth-Heinemann
Release Date : 2000
The Finite Element Method Solid Mechanics written by O. C. Zienkiewicz and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Continuum mechanics categories.
The Finite Element Method Set
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Author : O. C. Zienkiewicz
language : en
Publisher: Elsevier
Release Date : 2005-11-25
The Finite Element Method Set written by O. C. Zienkiewicz and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-25 with Technology & Engineering categories.
The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and provides self-contained reference; used together they provide a formidable resource covering the theory and the application of the universally used FEM. Written by the leading professors in their fields, the three books cover the basis of the method, its application to solid mechanics and to fluid dynamics.* This is THE classic finite element method set, by two the subject's leading authors * FEM is a constantly developing subject, and any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in these books * Fully up-to-date; ideal for teaching and reference
The Finite Element Method For Electromagnetic Modeling
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Author : Gérard Meunier
language : en
Publisher: John Wiley & Sons
Release Date : 2010-01-05
The Finite Element Method For Electromagnetic Modeling written by Gérard Meunier and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-05 with Science categories.
Written by specialists of modeling in electromagnetism, this book provides a comprehensive review of the finite element method for low frequency applications. Fundamentals of the method as well as new advances in the field are described in detail. Chapters 1 to 4 present general 2D and 3D static and dynamic formulations by the use of scalar and vector unknowns and adapted interpolations for the fields (nodal, edge, face or volume). Chapter 5 is dedicated to the presentation of different macroscopic behavior laws of materials and their implementation in a finite element context: anisotropy and hysteretic properties for magnetic sheets, iron losses, non-linear permanent magnets and superconductors. More specific formulations are then proposed: the modeling of thin regions when finite elements become misfit (Chapter 6), infinite domains by using geometrical transformations (Chapter 7), the coupling of 2D and 3D formulations with circuit equations (Chapter 8), taking into account the movement, particularly in the presence of Eddy currents (Chapter 9) and an original approach for the treatment of geometrical symmetries when the sources are not symmetric (Chapter 10). Chapters 11 to 13 are devoted to coupled problems: magneto-thermal coupling for induction heating, magneto-mechanical coupling by introducing the notion of strong and weak coupling and magneto-hydrodynamical coupling focusing on electromagnetic instabilities in fluid conductors. Chapter 14 presents different meshing methods in the context of electromagnetism (presence of air) and introduces self-adaptive mesh refinement procedures. Optimization techniques are then covered in Chapter 15, with the adaptation of deterministic and probabilistic methods to the numerical finite element environment. Chapter 16 presents a variational approach of electromagnetism, showing how Maxwell equations are derived from thermodynamic principles.
Finite Element Methods For Nonlinear Optical Waveguides
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Author : Xin-Hua Wang
language : en
Publisher: Routledge
Release Date : 2019-06-14
Finite Element Methods For Nonlinear Optical Waveguides written by Xin-Hua Wang and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-14 with Technology & Engineering categories.
This book provides researchers at the forefront of nonlinear optical technologies with robust procedures and software for the systematic investigation of the fundamental phenomena in nonlinear optical waveguide structures. A full vectorial electromagnetic formulation is adopted and the conditions under which simplification to a scalar formulation is possible are clearly indicated. The need to model the dielectric saturation properly is identified, and improved algorithms are presented for obtaining the complete power dispersion curve of structures exhibiting bistability. As the stability analysis of nonlinear modes is crucial to the development of nonlinear model methods, an effective procedure to investigate the propagation of the scalar nonlinear waves in 3D is another important feature of the book. All of the procedures described, as well as an automatic mesh generator for the finite element method, are incorporated into a software package which is included with this book.
Finite Elements Based Optimization
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Author : S. Ratnajeevan H. Hoole
language : en
Publisher: CRC Press
Release Date : 2019-07-24
Finite Elements Based Optimization written by S. Ratnajeevan H. Hoole and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-24 with Mathematics categories.
This book is intended to be a cookbook for students and researchers to understand the finite element method and optimization methods and couple them to effect shape optimization. The optimization part of the book will survey optimization methods and focus on the genetic algorithm and Powell’s method for implementation in the codes. It will contain pseudo-code for the relevant algorithms and homework problems to reinforce the theory to compile finite element programs capable of shape optimization. Features Enables readers to understand the finite element method and optimization methods and couple them to effect shape optimization Presents simple approach with algorithms for synthesis Focuses on automated computer aided design (CAD) of electromagnetic devices Provides a unitary framework involving optimization and numerical modelling Discusses how to integrate open-source mesh generators into your code Indicates how parallelization of algorithms, especially matrix solution and optimization, may be approached cheaply using the graphics processing unit (GPU) that is available on most PCs today Includes coupled problem optimization using hyperthermia as an example
Variational Methods For The Numerical Solution Of Nonlinear Elliptic Problem
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Author : Roland Glowinski
language : en
Publisher: SIAM
Release Date : 2015-11-04
Variational Methods For The Numerical Solution Of Nonlinear Elliptic Problem written by Roland Glowinski and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-04 with Mathematics categories.
Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics. This book differs from others on the topic by presenting examples of the power and versatility of operator-splitting methods; providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly nonsmooth) problems from science and engineering; and showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems. The book provides useful insights suitable for advanced graduate students, faculty, and researchers in applied and computational mathematics as well as research engineers, mathematical physicists, and systems engineers.
Unification Of Finite Element Methods
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Author : H. Kardestuncer
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Unification Of Finite Element Methods written by H. Kardestuncer and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Mathematics categories.
Unification of Finite Element Methods
Krylov Methods For Nonsymmetric Linear Systems
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Author : Gérard Meurant
language : en
Publisher: Springer Nature
Release Date : 2020-10-02
Krylov Methods For Nonsymmetric Linear Systems written by Gérard Meurant and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-02 with Mathematics categories.
This book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties. Solving systems of algebraic linear equations is among the most frequent problems in scientific computing; it is used in many disciplines such as physics, engineering, chemistry, biology, and several others. Krylov methods have progressively emerged as the iterative methods with the highest efficiency while being very robust for solving large linear systems; they may be expected to remain so, independent of progress in modern computer-related fields such as parallel and high performance computing. The mathematical properties of the methods are described and analyzed along with their behavior in finite precision arithmetic. A number of numerical examples demonstrate the properties and the behavior of the described methods. Also considered are the methods’ implementations and coding as Matlab®-like functions. Methods which became popular recently are considered in the general framework of Q-OR (quasi-orthogonal )/Q-MR (quasi-minimum) residual methods. This book can be useful for both practitioners and for readers who are more interested in theory. Together with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms. Some of the derived formulas might be useful for the design of possible new methods or for future analysis. For the more applied user, the book gives an up-to-date overview of the majority of the available Krylov methods for nonsymmetric linear systems, including well-known convergence properties and, as we said above, template codes that can serve as the base for more individualized and elaborate implementations.