Computational Mathematics - Models, Methods, Analysis with MATLAB - R. White (CRC, 2004) WW.pdf

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Computational Mathematics_Models, Methods, and Analysis with MATLAB and MPI.pdf
COMPUTATIONAL
MATHEMATICS
Models, Methods, and Analysis
with MATLAB and MPI
© 2004 by Chapman & Hall/CRC
COMPUTATIONAL
MATHEMATICS
Models, Methods, and Analysis
with MATLAB and MPI
ROBERT E. WHITE
CHAPMAN & HALL/CRC
A CRC Press Company
Boca Raton London New York Washington, D.C.
© 2004 by Chapman & Hall/CRC
72341154.001.png 72341154.002.png
Library of Congress Cataloging-in-Publication Data
White, R. E. (Robert E.)
Computational mathematics : models, methods, and analysis with MATLAB and MPI /
Robert E. White.
p. cm.
Includes bibliographical references and index.
ISBN 1-58488-364-2 (alk. paper)
1. Numerical analysis. 2. MATLAB. 3. Computer interfaces. 4. Parallel programming
(Computer science) I. Title.
QA297.W495 2003
519.4—dc21
2003055207
This book contains information obtained from authentic and highly regarded sources. Reprinted material
is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable
efforts have been made to publish reliable data and information, but the author and the publisher cannot
assume responsibility for the validity of all materials or for the consequences of their use.
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© 2004 by Chapman & Hall/CRC
No claim to original U.S. Government works
International Standard Book Number 1-58488-364-2
Library of Congress Card Number 2003055207
Printed in the United States of America 1 2 3 4 5 6 7 8 9 0
Printed on acid-free paper
© 2004 by Chapman & Hall/CRC
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Computational Mathematics:
Models, Methods and Analysis
with
M ATLAB and MPI
R. E. White
Department of Mathematics
North Carolina State University
white@math.ncsu.edu
Updated on August 3, 2003
To Be Published by CRC Press in 2003
© 2004 by Chapman & Hall/CRC
Contents
List of Figures
ix
List of Tables
xi
Preface
xiii
Introduction
xv
1 Discrete Time-Space Models 1
1.1 Newton Cooling Models . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Heat Di usion in a Wire . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Di usion in a Wire with Little Insulation . . . . . . . . . . . . . 17
1.4 Flow and Decay of a Pollutant in a Stream . . . . . . . . . . . . 25
1.5 Heat and Mass Transfer in Two Directions . . . . . . . . . . . . . 32
1.6 Convergence Analysis . . . . . . . . . . . . . . . . . . . . . . . . 42
2 Steady State Discrete Models 51
2.1 Steady State and Triangular Solves . . . . . . . . . . . . . . . . . 51
2.2 Heat Di usion and Gauss Elimination . . . . . . . . . . . . . . . 59
2.3 Cooling Fin and Tridiagonal Matrices . . . . . . . . . . . . . . . 68
2.4 Schur Complement . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2.5 Convergence to Steady State . . . . . . . . . . . . . . . . . . . . 86
2.6 Convergence to Continuous Model . . . . . . . . . . . . . . . . . 91
3 Poisson Equation Models 99
3.1 Steady State and Iterative Methods . . . . . . . . . . . . . . . . 99
3.2 Heat Transfer in 2D Fin and SOR . . . . . . . . . . . . . . . . . 107
3.3 Fluid Flow in a 2D Porous Medium . . . . . . . . . . . . . . . . . 116
3.4 Ideal Fluid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.5 Deformed Membrane and Steepest Descent . . . . . . . . . . . . 130
3.6 Conjugate Gradient Method . . . . . . . . . . . . . . . . . . . . . 138
v
© 2004 by Chapman & Hall/CRC

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