Finite Element Methods:

Parallel-Sparse Statics and Eigen-Solutions

Author: Duc Thai Nguyen

Publisher: Springer Science & Business Media

ISBN: 0387308512

Category: Mathematics

Page: 534

View: 2583

Finite element methods (FEM), and its associated computer software have been widely accepted as one of the most effective general tools for solving large-scale, practical engineering and science applications. For implicit finite element codes, it is a well-known fact that efficient equation and eigen-solvers play critical roles in solving large-scale, practical engineering/science problems. Sparse matrix technologies have been evolved and become mature enough that all popular, commercialized FEM codes have already inserted sparse solvers into their software. However, a few FEM books have detailed discussions about Lanczos eigen-solvers, or explain domain decomposition (DD) finite element formulation (including detailed hand-calculator numerical examples) for parallel computing purposes. The materials from this book have been evolved over the past several years through the author's research work, and graduate courses.

Parallel-Vector Equation Solvers for Finite Element Engineering Applications

Author: Duc T. Nguyen

Publisher: Springer Science & Business Media

ISBN: 9780306466403

Category: Computers

Page: 344

View: 6279

Despite the ample number of articles on parallel-vector computational algorithms published over the last 20 years, there is a lack of texts in the field customized for senior undergraduate and graduate engineering research. Parallel-Vector Equation Solvers for Finite Element Engineering Applications aims to fill this gap, detailing both the theoretical development and important implementations of equation-solution algorithms. The mathematical background necessary to understand their inception balances well with descriptions of their practical uses. Illustrated with a number of state-of-the-art FORTRAN codes developed as examples for the book, Dr. Nguyen's text is a perfect choice for instructors and researchers alike.

Finite Element Applications

A Practical Guide to the FEM Process

Author: Michael Okereke,Simeon Keates

Publisher: Springer

ISBN: 3319671251

Category: Mathematics

Page: 472

View: 8095

This textbook demonstrates the application of the finite element philosophy to the solution of real-world problems and is aimed at graduate level students, but is also suitable for advanced undergraduate students. An essential part of an engineer’s training is the development of the skills necessary to analyse and predict the behaviour of engineering systems under a wide range of potentially complex loading conditions. Only a small proportion of real-life problems can be solved analytically, and consequently, there arises the need to be able to use numerical methods capable of simulating real phenomena accurately. The finite element (FE) method is one such widely used numerical method. Finite Element Applications begins with demystifying the ‘black box’ of finite element solvers and progresses to addressing the different pillars that make up a robust finite element solution framework. These pillars include: domain creation, mesh generation and element formulations, boundary conditions, and material response considerations. Readers of this book will be equipped with the ability to develop models of real-world problems using industry-standard finite element packages.

Finite Element Procedures

Author: Klaus-Jürgen Bathe

Publisher: Klaus-Jurgen Bathe

ISBN: 9780979004902

Category: Engineering mathematics

Page: 1037

View: 8557

The Finite Element Method: Theory, Implementation, and Applications

Author: Mats G. Larson,Fredrik Bengzon

Publisher: Springer Science & Business Media

ISBN: 3642332870

Category: Computers

Page: 395

View: 1290

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

The Finite Element Method for Elliptic Problems

Author: Philippe G. Ciarlet

Publisher: SIAM

ISBN: 0898715148

Category: Mathematics

Page: 530

View: 8302

This is the only book available that fully analyzes the mathematical foundations of the finite element method. Not only is it valuable reference and introduction to current research, it is also a working textbook for graduate courses in numerical analysis, including useful figures and exercises of varying difficulty.

Direct Methods for Sparse Linear Systems

Author: Timothy A. Davis

Publisher: SIAM

ISBN: 0898716136

Category: Computers

Page: 217

View: 2865

The sparse backslash book. Everything you wanted to know but never dared to ask about modern direct linear solvers. Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia.Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.With a strong emphasis on MATLAB and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index.

Nonlinear Finite Element Methods

Author: Peter Wriggers

Publisher: Springer Science & Business Media

ISBN: 3540710019

Category: Mathematics

Page: 560

View: 6924

Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element discretization as well as algorithms for solving the non-linear equations. This book provides the reader with the required knowledge covering the complete field of finite element analyses in solid mechanics. It is written for advanced students in engineering fields but serves also as an introduction into non-linear simulation for the practising engineer.

Parallel supercomputing

methods, algorithms, and applications

Author: Graham F. Carey

Publisher: John Wiley & Sons

ISBN: 9780471924364

Category: Computers

Page: 287

View: 1277

Presents the state of the art in parallel processing methods applications and algorithms. Describes architectures for parallel processing and includes a wealth of examples in computational fluid dynamics, structural analysis, and other engineering applications.

Statistical Learning with Sparsity

The Lasso and Generalizations

Author: Trevor Hastie,Robert Tibshirani,Martin Wainwright

Publisher: CRC Press

ISBN: 1498712177

Category: Business & Economics

Page: 367

View: 6565

Discover New Methods for Dealing with High-Dimensional Data A sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data. Top experts in this rapidly evolving field, the authors describe the lasso for linear regression and a simple coordinate descent algorithm for its computation. They discuss the application of l1 penalties to generalized linear models and support vector machines, cover generalized penalties such as the elastic net and group lasso, and review numerical methods for optimization. They also present statistical inference methods for fitted (lasso) models, including the bootstrap, Bayesian methods, and recently developed approaches. In addition, the book examines matrix decomposition, sparse multivariate analysis, graphical models, and compressed sensing. It concludes with a survey of theoretical results for the lasso. In this age of big data, the number of features measured on a person or object can be large and might be larger than the number of observations. This book shows how the sparsity assumption allows us to tackle these problems and extract useful and reproducible patterns from big datasets. Data analysts, computer scientists, and theorists will appreciate this thorough and up-to-date treatment of sparse statistical modeling.

Finite Element Systems

A Handbook

Author: C. A. Brebbia

Publisher: Springer Science & Business Media

ISBN: 3662072297

Category: Mathematics

Page: 496

View: 9517

Iterative Methods for Linear and Nonlinear Equations

Author: C. T. Kelley

Publisher: SIAM

ISBN: 9781611970944

Category: Iterative methods (Mathematics)

Page: 166

View: 6641

Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods. Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.

Mathematica Cookbook

Building Blocks for Science, Engineering, Finance, Music, and More

Author: Sal Mangano

Publisher: "O'Reilly Media, Inc."

ISBN: 1449390765

Category: Computers

Page: 830

View: 9764

Mathematica Cookbook helps you master the application's core principles by walking you through real-world problems. Ideal for browsing, this book includes recipes for working with numerics, data structures, algebraic equations, calculus, and statistics. You'll also venture into exotic territory with recipes for data visualization using 2D and 3D graphic tools, image processing, and music. Although Mathematica 7 is a highly advanced computational platform, the recipes in this book make it accessible to everyone -- whether you're working on high school algebra, simple graphs, PhD-level computation, financial analysis, or advanced engineering models. Learn how to use Mathematica at a higher level with functional programming and pattern matching Delve into the rich library of functions for string and structured text manipulation Learn how to apply the tools to physics and engineering problems Draw on Mathematica's access to physics, chemistry, and biology data Get techniques for solving equations in computational finance Learn how to use Mathematica for sophisticated image processing Process music and audio as musical notes, analog waveforms, or digital sound samples

A Pragmatic Introduction to the Finite Element Method for Thermal and Stress Analysis

With the Matlab Toolkit SOFEA

Author: Petr Krysl

Publisher: World Scientific Publishing Company

ISBN: 9813101814

Category: Science

Page: 292

View: 1317

This textbook provides an accessible and self-contained description of the Galerkin finite element method for the two important models of continuum mechanics, transient heat conduction and elastodynamics, from formulation of the governing equations to implementation in Matlab. The coverage follows an intuitive approach: the salient features of each initial boundary value problem are reviewed, including a thorough description of the boundary conditions; the method of weighted residuals is applied to derive the discrete equations; and clear examples are introduced to illustrate the method.

Application of the Finite Element Method in Implant Dentistry

Author: Jianping Geng,Weiqi Yan,Wei Xu

Publisher: Springer Science & Business Media

ISBN: 9783540737643

Category: Technology & Engineering

Page: 137

View: 2099

This book creates the theoretical foundation that novices need to perform the finite element method in implant dentistry. It shows how both the implant dentist and the designer can benefit from finite element analysis. The authors explain the theory and math of the finite element method. Then, you get practical applications alongside discussions of the critical issues in using finite element analysis for dental implant design.