Introduction to Finite and Spectral Element Methods using MATLAB

Introduction to Finite and Spectral Element Methods using MATLAB

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Hardback
$146.95
ISBN 9781584885290
Cat# C5297
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Features

  • Introduces the fundamentals of finite and spectral element methods with emphasis on algorithms and computer implementation
  • Provides practical computational experience with FSELIB-a free library of MATLAB functions and codes
  • Uses the fundamentals of heat and mass transfer as a prototype, then extends the concepts to problems in mechanics
  • Includes a concise MATLAB primer in an Appendix
  • Summary

    Why another book on the finite element method? There are currently more than 200 books in print with "Finite Element Method" in their titles. Many are devoted to special topics or emphasize error analysis and numerical accuracy. Others stick to the fundamentals and do little to describe the development and implementation of algorithms for solving real-world problems.

    Introduction to Finite and Spectral Element Methods Using MATLAB provides a means of quickly understanding both the theoretical foundation and practical implementation of the finite element method and its companion spectral element method. Written in the form of a self-contained course, it introduces the fundamentals on a need-to-know basis and emphasizes algorithm development and computer implementation of the essential procedures.

    Firmly asserting the importance of simultaneous practical experience when learning any numerical method, the author provides FSELIB: a software library of user-defined MATLAB functions and complete finite and spectral element codes. FSELIB is freely available for download from http://dehesa.freeshell.org, which is also a host for the book, providing further information, links to resources, and FSELIB updates.

    The presentation is suitable for both self-study and formal course work, and its state-of-the-art review of the field make it equally valuable as a professional reference. With this book as a guide, you immediately will be able to run the codes as given and graphically display solutions to a wide variety of problems in heat transfer and solid, fluid, and structural mechanics.

    Table of Contents

    THE FINITE ELEMENT METHOD IN ONE DIMENSION
    Steady diffusion with linear elements
    Variational formulation and weighted residuals
    Steady diffusion with quadratic elements
    Unsteady diffusion in one dimension
    One-dimensional convection
    One-dimensional convection-diffusion
    Beam bending
    Beam buckling

    HIGH-ORDER AND SPECTRAL ELEMENTS IN ONE DIMENSION
    Nodal bases
    Spectral interpolation
    Lobatto interpolation and element matrices
    Spectral code for steady diffusion
    Spectral code for unsteady diffusion
    Modal expansion

    THE FINITE ELEMENT METHOD IN TWO DIMENSIONS
    Convection-diffusion in two dimensions
    3-node triangles
    Grid generation
    Code for Laplace's equation with the Dirichlet boundary condition in a disk-like domain
    Code for steady convection-diffusion with the Dirichlet boundary condition
    Code for Helmholtz's equation with the Neumann boundary condition
    Code for Laplace's equation with Dirichlet and Neumann boundary conditions
    Bilinear quadrilateral elements

    QUADRATIC AND SPECTRAL ELEMENTS IN TWO DIMENSIONS
    6-node triangular elements
    Grid generation and finite element codes
    High-order triangle expansions
    High-order node distributions
    Modal expansion on the triangle
    Surface elements
    High-order quadrilateral elements

    APPLICATIONS IN SOLID AND FLUID MECHANICS
    Plane stress-strain analysis
    Finite element methods for plane stress/strain
    Plate bending
    Hermite triangles
    Finite element methods for plate bending
    Viscous flow
    Stokes flow
    Navier-Stokes flow

    FINITE AND SPECTRAL ELEMENT METHODS IN THREE DIMENSIONS
    Convection-diffusion in three dimensions
    4-node tetrahedral elements
    High-order and spectral tetrahedral elements
    Hexahedral elements

    APPENDICES
    Function interpolation
    Orthogonal polynomials
    Linear solvers
    Mathematical supplement
    Element grid generation
    Glossary
    MATLAB primer
    References
    Index

    Editorial Reviews

    "[This book] approaches the matter from the more practical side. … It gives a broad, digestible introduction into what everybody wishing to write an FE code needs to know. …This is a hands-on book in that it presupposes the reader to work the examples in MATLAB, for which a primer is provided. The actual work is greatly facilitated by the possibility to freely download software …"
    -Monatshefte fur Mathematik, 2007

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