Finite Elements-based Optimization: Electromagnetic Product Design and Nondestructive Evaluation [Hardback]

(Electrical and Computer Engineering Department, Michigan State University, East Lansing, USA), (ECE, University of Illinois at Urbana Champaign)
  • Formāts: Hardback, 306 pages, height x width: 235x156 mm, weight: 680 g, 164 Line drawings, black and white; 1 Halftones, black and white; 29 Tables, black and white; 165 Illustrations, black and white
  • Izdošanas datums: 31-Jul-2019
  • Izdevniecība: Productivity Press
  • ISBN-10: 1498759467
  • ISBN-13: 9781498759465
Citas grāmatas par šo tēmu:
  • Hardback
  • Cena: 197,05 €
  • Pievienot vēlmju sarakstam
  • Grāmatu piegādes laiks ir 3-4 nedēļas, ja grāmata ir uz vietas izdevniecības noliktavā. Ja izdevējam nepieciešams publicēt jaunu tirāžu, grāmatas piegāde var aizkavēties.
  • Ielikt grozā
  • Daudzums:
  • Piegādes laiks - 4-6 nedēļas
  • Bibliotēkām
  • Formāts: Hardback, 306 pages, height x width: 235x156 mm, weight: 680 g, 164 Line drawings, black and white; 1 Halftones, black and white; 29 Tables, black and white; 165 Illustrations, black and white
  • Izdošanas datums: 31-Jul-2019
  • Izdevniecība: Productivity Press
  • ISBN-10: 1498759467
  • ISBN-13: 9781498759465
Citas grāmatas par šo tēmu:

This book is intended to be a cookbook for students and researchers to understand the finite element method and optimization methods and couple them to effect shape optimization. The optimization part of the book will survey optimization methods and focus on the genetic algorithm and Powell’s method for implementation in the codes. It will contain pseudo-code for the relevant algorithms and homework problems to reinforce the theory to compile finite element programs capable of shape optimization.

Features

  • Enables readers to understand the finite element method and optimization methods and couple them to effect shape optimization
  • Presents simple approach with algorithms for synthesis
  • Focuses on automated computer aided design (CAD) of electromagnetic devices
  • Provides a unitary framework involving optimization and numerical modelling
  • Discusses how to integrate open-source mesh generators into your code
  • Indicates how parallelization of algorithms, especially matrix solution and optimization, may be approached cheaply using the graphics processing unit (GPU) that is available on most PCs today
  • Includes coupled problem optimization using hyperthermia as an example
Preface ix
Acknowledgments xi
Authors xiii
1 Analysis versus Design through Synthesis
1(16)
1.1 From Make-and-Test to Analysis and Now Synthesis
1(3)
1.2 The Power of Methods of Synthesis
4(10)
1.2.1 Examples
4(1)
1.2.2 Pole Shaping
4(2)
1.2.3 Shaping the Rotor of an Alternator
6(1)
1.2.4 Shaping a Shield
7(3)
1.2.5 Miniaturizing a Transistor
10(1)
1.2.6 Coupled Field Problems: Electroheat
10(3)
1.2.7 Nondestructive Evaluation
13(1)
1.3 What This Book Is About
14(3)
2 Analysis in Electromagnetic Product Design
17(46)
2.1 Numerical Methods
17(3)
2.2 Numerical Approximations versus Exact Methods
20(2)
2.3 Methods of Approximate Solution - Differential and Integral
22(4)
2.4 A Note on Matrix Representation of Polynomials
26(1)
2.5 The Finite Element Method
27(7)
Ingredient 1
28(1)
Ingredient 2
28(2)
Ingredient 3
30(4)
2.6 Uniqueness
34(1)
2.7 Natural Boundary Conditions
35(2)
2.8 One-Dimensional Linear Finite Elements
37(7)
2.9 Two-Dimensional Linear, Triangular Finite Elements
44(8)
2.10 Cholesky's Factorization
52(2)
2.11 A Two-Dimensional Finite Element Program through an Example
54(5)
2.12 Other Equations
59(4)
3 Optimization in Product Design - Synthesis
63(46)
3.1 An Introduction
63(1)
3.2 One-Dimensional Optimization
64(6)
3.2.1 One-Dimensional Search
64(1)
3.2.2 Bisection Search
64(1)
3.2.3 Golden Section Search
65(2)
3.2.4 The Line Search or Univariate Search
67(3)
3.3 N-Dimensional Zeroth-Order Optimization
70(15)
3.3.1 Powell's Method
70(4)
3.3.2 Genetic Algorithm
74(1)
3.3.2.1 Broad Description of the Genetic Algorithm
74(1)
3.3.2.2 Representation in the Genetic Algorithm
75(2)
3.3.2.3 Initialization
77(1)
3.3.2.4 Selection
78(1)
3.3.2.5 Cross Over and Mutation
79(2)
3.3.2.6 Termination
81(2)
3.3.2.7 The Genetic Algorithm Applied to the Ackley Function
83(1)
3.3.3 Simulated Annealing
83(2)
3.4 N-Dimensional First-Order Optimization
85(4)
3.4.1 Gradient Descent or Steepest Descent
85(3)
3.4.2 Conjugate Gradients
88(1)
3.5 A Good Test Problem from Magnetics -- The Pole Face
89(11)
3.5.1 Problem Description
89(3)
3.5.2 Expected Solution
92(1)
3.5.3 Choice of Optimization Method
93(2)
3.5.4 Preprocessing the Pole Face
95(1)
3.5.5 Powell's Method -- Special Treatment and Constraints
96(3)
3.5.6 Solution by the Genetic Algorithm
99(1)
3.6 A Test Problem from Alternator Rotor Design
100(9)
3.6.1 Problem Definition
100(4)
3.6.2 The Alternator Rotor: Problem Model
104(5)
4 Some Basic Matrix Solution Schemes
109(18)
4.1 Matrix Solution
109(1)
4.2 Matrix Solution by Gaussian Elimination
109(3)
4.3 The SOR Method
112(3)
4.4 The Cholesky-Factorization Scheme
115(2)
4.5 The Conjugate-Gradients Algorithm
117(10)
5 Matrix Computation with Sparse Matrices
127(34)
5.1 The Importance of Efficiency
127(3)
5.1.1 Seeking Efficiency
127(1)
5.1.2 Sparse Matrices
127(2)
5.1.3 Computational Time Savings
129(1)
5.2 Symmetric and Sparse Storage Schemes -- Suitable Data Structures
130(7)
5.3 Profile Storage and Fill-in: The Cholesky Scheme
137(7)
5.3.1 Data Structures for Profile Storage
137(3)
5.3.2 Cholesky's Method with Profile Storage
140(4)
5.4 Sparse Storage for SOR
144(8)
5.5 Sparse Storage and the Conjugate Gradients Algorithm
152(5)
5.6 Renumbering of Variables: The Cuthill--Mckee Algorithm
157(2)
5.7 Renumbering and Preconditioning
159(2)
6 Other Formulations, Equations and Elements
161(58)
6.1 Introduction to the Galerkin Method and Function Spaces
161(2)
6.2 The Generalized Galerkin Approach to Finite Elements
163(4)
6.3 Normal Gradient Boundary Conditions in Finite Elements -- The Neumann Condition
167(8)
6.3.1 Forced and Natural Boundary Conditions
167(5)
6.3.2 Handling Interior Line Charges in Finite Elements
172(2)
6.3.3 Natural Impedance Boundary Conditions
174(1)
6.4 A Simple Hand-Worked Example
175(7)
6.4.1 A Test Problem with an Analytical Solution
175(1)
6.4.2 Galerkin -- Strong Neumann, One Second-Order Element
176(1)
6.4.3 Collocation: Explicit Neumann, One Second-Order Element
177(1)
6.4.4 Least Squares: Strong Neumann, One Second-Order Element
177(1)
6.4.5 Galerkin: Weak Neumann, One Second-Order Element
178(1)
6.4.6 Galerkin: Weak Neumann, Two First-Order Elements
179(2)
6.4.7 Galerkin: Explicit Neumann, Two First-Order Elements
181(1)
6.4.8 Some Observations
182(1)
6.5 Higher-Order Finite Elements
182(9)
6.5.1 Higher-Order Interpolations
182(3)
6.5.2 Differentiation and Universal Matrices
185(6)
6.6 Functional Minimization
191(5)
6.7 Numerical Integration: Quadrature Formulae
196(1)
6.8 Finite Elements and Finite Differences
197(1)
6.9 Sparsity Pattern Computation
198(2)
6.10 Nonlinear Equations
200(1)
6.11 Other Equations and Methods: The Structural Beam and the Bi-Harmonic Equation
201(7)
6.12 Symbolic Algebra
208(1)
6.13 Edge Elements
209(5)
6.14 The Quadrilateral Element
214(5)
7 Parametric Mesh Generation for Optimization
219(32)
7.1 Background and Literature
219(5)
7.2 Mesh Generation
224(3)
7.2.1 Introduction
224(2)
7.2.2 Delaunay-Based Methods
226(1)
7.2.3 Delaunay Triangulation and Constrained Delaunay Triangulation
226(1)
7.3 Algorithms for Constructing a Delaunay Triangulation
227(2)
7.3.1 Speed
227(1)
7.3.2 Divide-and-Conquer Algorithm
227(1)
7.3.3 Sweep Line Algorithm
228(1)
7.3.4 Incremental Insertion Algorithm
228(1)
7.4 Mesh Refinement
229(1)
7.5 Three-Dimensional Mesh Generation
230(1)
7.6 Parameterized Mesh Generation -- A New Approach
231(1)
7.7 Data Structure and User Interface
232(19)
7.7.1 Data Structure
232(2)
7.7.2 User Interface and Defining Geometry
234(2)
7.7.3 Post-Processing of Meshing
236(1)
7.7.4 Approach to Renumbering
237(2)
7.7.5 Merge Sort
239(2)
7.7.6 Modified Form of Merge Sort for Renumbering
241(1)
Appendix 1 Sample Input File: Two-Dimensional
242(2)
Appendix 2 Sample Input File: Three-Dimensional
244(7)
8 Parallelization through the Graphics Processing Unit
251(10)
8.1 Parallelization
251(1)
8.2 Optimization with Finite Elements
252(1)
8.3 Finite Element Computation in CUDA C
253(2)
8.4 Solution of Sparse, Symmetric Finite Element Equations
255(1)
8.5 Some Issues in GPU Computation
256(3)
8.6 Conclusions
259(2)
9 Coupled Problems
261(30)
9.1 The Electrothermal Problem
261(4)
9.2 Finite Element Computation for the Electrothermal Problem
265(1)
9.3 GPU Computation for Genetic Algorithms for Electro-Heat Problems
266(2)
9.4 Shaping an Electro-Heated Conductor
268(4)
9.5 Shape Optimization of Two-Physics Systems: Gradient and Zeroth-Order Methods
272(4)
9.6 Electroheating Computation for Hyperthermia
276(2)
9.7 The Hyperthermia Model
278(5)
9.8 A Note on Electrical and Thermal Conductivity Changes
283(1)
9.8.1 Electrical Conductivity
283(1)
9.8.2 Thermal Conductivity
284(1)
9.9 The Algorithm for the Inverse Method for Electroheating
284(7)
References 291(10)
Index 301
S. Ratnajeevan H. Hoole, B.Sc. Eng. Hons Cey., M.Sc. with Mark of Distinction London, Ph.D. Carnegie Mellon, is Professor of Electrical and Computer Engineering at Michigan State University in the US. For his accomplishments in electromagnetic product synthesis the University of London awarded him its higher doctorate, the D.Sc. (Eng.) degree, in 1993, and the IEEE elevated him to the grade of Fellow in 1995 with the citation "For contributions to computational methods for design optimization of electrical devices." His paper on using his inverse problem methods from design for NDE is widely cited, as is his paper on neural networks for the same purpose. These appear in The IEEE Transactions on Magnetics (1991 and 1993, respectively). He has authored 5 engineering texts published by Elsevier, another by Elsevier now carried by Prentice Hall, Oxford, Cambridge (India) and WIT Press. Prof. Hoole has been Vice Chancellor of University of Jaffna in Sri Lanka, and as Member of the University Grants Commission there, was responsible with six others for the regulation of the administration and academic standards of all 15 Sri Lankan universities and their admissions and funding. He has contributed widely to the learned literature on Tamil studies and been a regular columnist in newspapers. Prof. Hoole has been trained in Human Rights Research and Teaching at The Rene Cassin International Institute of Human Rights, Strasbourg, France, and has pioneered teaching human rights in the engineering curriculum. Yovahn Y. Ratnajeevan Hoole is a graduate student at the University of Illinois at Urbana Champaign. He holds a B.S. in Computer Science and a B.A. in Electrical Engineering from Rice University. He is currently working towards a doctorate in Electrical Engineering. His research interests are in Optimization, Machine Learning and their applications to real world engineering problems.