Introduction to Finite and Spectral Element Methods using MATLAB
1st Edition
Published on 17. June 2005
Book
Hardback
680 pages
978-1-58488-529-0 (ISBN)
Description
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.
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.
More details
Language
English
Place of publication
United States
Publishing group
Taylor & Francis Inc
Target group
Professional and scholarly
Students in finite element method and numerical PDE courses, engineers interested in finite and spectral element methods, applied mathematicians
Illustrations
96 s/w Abbildungen, 18 s/w Tabellen
1000 equations; 18 Tables, black and white; 96 Illustrations, black and white
Dimensions
Height: 235 mm
Width: 156 mm
Weight
1111 gr
ISBN-13
978-1-58488-529-0 (9781584885290)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Constantine Pozrikidis
Introduction to Finite and Spectral Element Methods Using MATLAB
Book
06/2014
2nd Edition
Chapman & Hall/CRC
€217.50
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Content
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
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