Parallel-Vector Equation Solvers for Finite Element Engineering Applications

Author: Duc Thai Nguyen

Publisher: Springer Science & Business Media

ISBN: 1461513375

Category: Computers

Page: 344

View: 625

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 Methods:

Parallel-Sparse Statics and Eigen-Solutions

Author: Duc Thai Nguyen

Publisher: Springer Science & Business Media

ISBN: 9780387293301

Category: Mathematics

Page: 534

View: 7140

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.

The Finite Element Method in Engineering

Author: Singiresu S. Rao

Publisher: Butterworth-Heinemann

ISBN: 0128143649

Category: Technology & Engineering

Page: 782

View: 4259

The Finite Element Method in Engineering, Sixth Edition, provides a thorough grounding in the mathematical principles behind the Finite Element Analysis technique—an analytical engineering tool originated in the 1960's by the aerospace and nuclear power industries to find usable, approximate solutions to problems with many complex variables. Rao shows how to set up finite element solutions in civil, mechanical and aerospace engineering applications. The new edition features updated real-world examples from MATLAB, Ansys and Abaqus, and a new chapter on additional FEM topics including extended FEM (X-FEM). Professional engineers will benefit from the introduction to the many useful applications of finite element analysis. Includes revised and updated chapters on MATLAB, Ansys and Abaqus Offers a new chapter, Additional Topics in Finite Element Method Includes discussion of practical considerations, errors and pitfalls in FEM singularity elements Features a brief presentation of recent developments in FEM including extended FEM (X-FEM), augmented FEM (A-FEM) and partition of unity FEM (POUFEM) Features improved pedagogy, including the addition of more design-oriented and practical examples and problems Covers real-life applications, sample review questions at the end of most chapters, and updated references

Finite Elements for Analysis and Design

Author: J. E. Akin

Publisher: Academic Press

ISBN: 9780120476541

Category: Finite element method

Page: 548

View: 3898

The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.

Parallel Methods on Large-scale Structural Analysis and Physics Applications

Papers Presented at the Symposium on Parallel Methods on Large-Scale Structural Analysis and Physics Applications ; Held on 5-6 February 1991 at NASA Langley Research Center, Hampton, VA

Author: Olaf O. Storaasli,Edward A. Carmona

Publisher: N.A

ISBN: N.A

Category: Structural analysis (Engineering)

Page: 185

View: 7197

Finite Element Procedures

Author: Klaus-Jürgen Bathe

Publisher: Klaus-Jurgen Bathe

ISBN: 9780979004902

Category: Engineering mathematics

Page: 1037

View: 5568

Finite Element Methods for Maxwell's Equations

Author: Peter Monk

Publisher: Oxford University Press

ISBN: 9780198508885

Category: Mathematics

Page: 450

View: 1244

The emphasis in on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book.

Vector and Parallel Processing - VECPAR 2000

4th International Conference, Porto, Portugal, June 21-23, 2000, Selected Papers and Invited Talks

Author: Jose M.L.M. Palma,Jack Dongarra,Vicente Hernandez

Publisher: Springer

ISBN: 3540449426

Category: Computers

Page: 584

View: 2353

This book is the ?nal outcome of VECPAR 2000 – 4th International Meeting on Vector and Parallel Processing. VECPAR constitutes a series of conferences, which have been organized by the Faculty of Engineering of the University of Porto since 1993, with the main objective of disseminating new knowledge on parallel computing. Readership of This Book The book is aimed at an audience of researchers and graduate students in a broad range of scienti?c areas, including not only computer science, but also applied mathematics and numerical analysis, physics, and engineering. Book Plan From a total of 66 papers selected on the basis of extended abstracts for p- sentation at the conference, a subset of 34 papers were chosen during a second review process leading to their inclusion in the book, together with the invited talks. The book contains a total of 40 papers organized into 6 chapters, where each may appeal to people in di?erent but still related scienti?c areas. All ch- ters, with the exception of Chapter 6, are initiated by a short text, providing a quick overview of the organization and papers in the chapter. The 13 papers in Chapter 1 cover the aspects related to the use of multiple processors. Operating systems, languages and software tools for scheduling, and code transformation are the topics included in this chapter, initiated by the talk on computing over the Internet, entitled Grid Computing,byIan Foster.

High Performance Computing and Applications

Second International Conference, HPCA 2009, Shanghai, China, August 10-12, 2009, Revised Selected Papers

Author: Wu Zhang,Zhangxin Chen,Craig C. Douglas,Weiqin Tong

Publisher: Springer Science & Business Media

ISBN: 3642118410

Category: Computers

Page: 589

View: 8512

This book constitutes the thoroughly refereed post-conference proceedings of the Second International Conference on High Performance Computing and Applications, HPCA 2009, held in Shangahi, China, in August 2009. The 71 revised papers presented together with 10 invited presentations were carefully selected from 324 submissions. The papers cover topics such as numerical algorithms and solutions; high performance and grid computing; novel approaches to high performance computing; massive data storage and processsing; and hardware acceleration.

Automated Solution of Differential Equations by the Finite Element Method

The FEniCS Book

Author: Anders Logg,Kent-Andre Mardal,Garth Wells

Publisher: Springer Science & Business Media

ISBN: 3642230997

Category: Computers

Page: 731

View: 9293

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

One-Dimensional Finite Elements

An Introduction to the FE Method

Author: Andreas Öchsner,Markus Merkel

Publisher: Springer

ISBN: 331975145X

Category: Science

Page: 418

View: 9368

This textbook presents finite element methods using exclusively one-dimensional elements. It presents the complex methodology in an easily understandable but mathematically correct fashion. The approach of one-dimensional elements enables the reader to focus on the understanding of the principles of basic and advanced mechanical problems. The reader will easily understand the assumptions and limitations of mechanical modeling as well as the underlying physics without struggling with complex mathematics. Although the description is easy, it remains scientifically correct. The approach using only one-dimensional elements covers not only standard problems but allows also for advanced topics such as plasticity or the mechanics of composite materials. Many examples illustrate the concepts and problems at the end of every chapter help to familiarize with the topics. Each chapter also includes a few exercise problems, with short answers provided at the end of the book. The second edition appears with a complete revision of all figures. It also presents a complete new chapter special elements and added the thermal conduction into the analysis of rod elements. The principle of virtual work has also been introduced for the derivation of the finite-element principal equation.

A Collection of Technical Papers

The 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Adaptive Structures Forum ; April 19-22, 1993

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Aerodynamics

Page: 3725

View: 5325

Parallel computational methods for large-scale structural analysis and design

papers presented at the 2nd Symposium on Parallel Computational Methods for Large-Scale Structural Analysis and Design : held 24-25 February 1993, Marriott Waterside Hotel, Norfolk, VA, U.S.A.

Author: Olaf O. Storaasli,Jerrold M. Housner,Duc T. Nguyen,Langley Research Center,Lewis Research Center

Publisher: N.A

ISBN: N.A

Category: Parallel processing (Electronic Computers)

Page: 194

View: 6021

finite element methods

fifty years of the Courant element

Author: Michel Krizek,Pekka Neittaanmaki,Rolf Stenberg

Publisher: CRC Press

ISBN: 9780824792763

Category: Mathematics

Page: 536

View: 5781

These proceedings originated from a conference commemorating the 50th anniversary of the publication of Richard Courant's seminal paper, Variational Methods for Problems of Equilibrium and Vibration. These papers address fundamental questions in numerical analysis and the special problems that occur in applying the finite element method to various fields of science and engineering.

Understanding and Implementing the Finite Element Method

Author: Mark S. Gockenbach

Publisher: SIAM

ISBN: 0898716144

Category: Mathematics

Page: 363

View: 5657

The ?nite element method is the most powerful general-purpose technique for comput­ing accurate solutions to partial differential equations. Understanding and Implementing the Finite Element Method is essential reading for those interested in understanding both the theory and the implementation of the ?nite element method for equilibrium problems. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics. Understanding and Implementing the Finite Element Method includes a carefully documented collection of MATLAB® programs implementing the ideas presented in the book. Readers will bene?t from a careful explanation of data structures and speci?c coding strategies and will learn how to write a ?nite element code from scratch. Students can use the MATLAB codes to experiment with the method and extend them in various ways to learn more about programming ?nite elements. This practical book should provide an excellent foundation for those who wish to delve into advanced texts on the subject, including advanced undergraduates and beginning graduate students in mathematics, engineering, and the physical sciences.Preface; Part I: The Basic Framework for Stationary Problems. Chapter 1: Some Model PDEs; Chapter 2: The weak form of a BVP; Chapter 3: The Galerkin method; Chapter 4: Piecewise polynomials and the finite element method; Chapter 5: Convergence of the finite element method; Part II Data Structures and Implementation. Chapter 6: The mesh data structure; Chapter 7: Programming the finite element method: Linear Lagrange triangles; Chapter 8: Lagrange triangles of arbitrary degree; Chapter 9: The finite element method for general BVPs; Part III: Solving the Finite Element Equations. Chapter 10: Direct solution of sparse linear systems; Chapter 11: Iterative methods: Conjugate gradients; Chapter 12: The classical stationary iterations; Chapter 13: The multigrid method; Part IV: Adaptive Methods. Chapter 14: Adaptive mesh generation; Chapter 15: Error estimators and indicators; Bibliography; Index.