Modern Computational Methods

Herbert Koenig

• Publisher: Routledge
• Year: 2019
• Print ISBN: 9781560324683
• eBook ISBN: 9781351430609
• Topic: Technology & Engineering
• Subtopic: Computer Science General
• Index: Technology & Engineering

This book is an introduction to computational mechanics, proceeding from basic computational tools to advanced computational procedures and applications. Emphasis is placed on the numerical techniques and how they form the bases for algorithms. Numerous worked examples in structural mechanics, heat transfer, fluid flow, and biomechanics are given with the numerical codes to illustrate how the methods are applied. A concluding section addresses advanced applications in such areas as finite volume methods and biomechanics.

PART
ONE

BASIC COMPUTATIONAL TOOLS

CHAPTER
ONE

LINEAR SYSTEMS AND MATRICES

NOMENCLATURE

aij	elements of matrix A
xi,	component of the solution vector
bi, hi	right-hand-side vectors
N	number of equations
Uij	component of matrix U
Vij	component of matrix V
Tij	component of matrix T
ni	component of vector n
ti	component of vector t
∣A∣	norm of matrix A
C(A)	condition number of matrix A
I	identity matrix
E	error vector
A^−1	inverse of matrix A
Ai	component of normalized tridiagonal matrix
Bi	component of normalized tridiagonal matrix
$A_i^{\prime }$	component of manipulated tridiagonal matrix
$B_i^{\prime }$	component of manipulated tridiagonal matrix
L	lower-diagonal matrix in Cholesky decomposition
U	upper-diagonal matrix in Cholesky decomposition
y	intermediate column vector in Cholesky decomposition
ɛ	convergence tolerance
∣aij ∣	absolute value of the component aij

1-1 INTRODUCTION

The emphasis in this textbook is on computational mechanics. In the following chapters, such diverse topics as curve fitting, numerical integration, finite-difference approximations, and other numerical tools that are required by the engineer for modeling physical processes are discussed.

The eventual outcome from each of the above-mentioned numerical strategies is the need to solve systems of equations that represent ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Acknowledgment
• Part 1 Basic Computational Tools
• Part 2 Computational Tools for Applications
• Part 3 Advanced Computational Tools
• Index