Parallel Finite-difference Time-domain Method

The finite-difference time-domain (FTDT) method has revolutionized antenna design and electromagnetics engineering. This book raises the FDTD method to the next level by empowering it with the vast capabilities of parallel computing. It shows engineers how to exploit the natural parallel properties of FDTD to improve the existing FDTD method and to efficiently solve more complex and large problem sets. Professionals learn how to apply open source software to develop parallel software and hardware to run FDTD in parallel for their projects. The book features hands-on examples that illustrate the power of parallel FDTD and presents practical strategies for carrying out parallel FDTD. This detailed resource provides instructions on downloading, installing, and setting up the required open source software on either Windows or Linux systems, and includes a handy tutorial on parallel programming.

Preface

ix

Chapter 1 FDTD Method

1

(14)

1.1 FINITE-DIFFERENCE CONCEPT

1

(2)

1.2 INTRODUCTION TO FDTD

3

(5)

1.3 NUMERICAL DISPERSION

8

(2)

1.4 STABILITY ANALYSIS

10

(1)

1.5 NONUNIFORM MESH

11

(2)

REFERENCES

13

(2)

Chapter 2 Boundary Conditions

15

(18)

2.1 PEC AND PMC BOUNDARY CONDITIONS

16

(2)

2.2 MUR'S ABSORBING BOUNDARY CONDITION

18

(3)

2.3 UNSPLIT PML

21

(5)

2.4 STRETCHED COORDINATE PML

26

(1)

2.5 TIME CONVOLUTION PML

27

(5)

REFERENCES

32

(1)

Chapter 3 Improvement of the FDTD

33

(36)

3.1 CONFORMAL FDTD FOR PEC OBJECTS

33

(7)

3.2 CONFORMAL TECHNIQUE FOR DIELECTRIC

40

(2)

3.3 ALTERNATING DIRECTION IMPLICIT (ADI) ALGORITHM

42

(11)

3.3.1 Update for ADI Equations

43

(4)

3.3.2 PML Truncation Techniques for ADI-FDTD

47

(2)

3.3.3 Separable Backward-Central Difference

49

(4)

3.4 SIMULATION OF DISPERSIVE MEDIA

53

(7)

3.4.1 Recursive Convolution

53

(5)

3.4.2 Pole Extraction Techniques

58

(1)

3.4.3 Simulation of Double-Negative Materials

59

(1)

3.5 CIRCUIT ELEMENTS

60

(7)

REFERENCES

67

(2)

Chapter 4 Excitation Source

69

(28)

4.1 INTRODUCTION

69

(2)

4.2 TIME SIGNATURE

71

(2)

4.3 LOCAL SOURCE

73

(5)

4.4 SOURCES FOR UNIFORM TRANSMISSION LINES

78

(9)

4.5 POWER INTRODUCED BY LOCAL EXCITATION SOURCES

87

(2)

4.6 PHASE DIFFERENCE AND TIME DELAY

89

(1)

4.7 PLANE WAVE SOURCES

90

(5)

REFERENCES

95

(2)

Chapter 5 Data Collection and Post-Processing

97

(22)

5.1 TIME-FREQUENCY TRANSFORMATION

97

(3)

5.2 MODE EXTRACTION OF TIME SIGNAL

100

(3)

5.3 CIRCUIT PARAMETERS

103

(3)

5.4 NEAR-TO-FAR-FIELD TRANSFORMATION

106

(11)

5.4.1 Basic Approach

106

(3)

5.4.2 Far-Field Calculation for Planar Structures

109

(4)

5.4.3 Data Compression and Its Application

113

(4)

REFERENCES

117

(2)

Chapter 6 Introduction to Parallel Computing Systems

119

(26)

6.1 ARCHITECTURE OF THE PARALLEL SYSTEM

120

(5)

6.1.1 Symmetric Multiprocessor

121

(1)

6.1.2 Distributed Shared Memory System

122

(1)

6.1.3 Massively Parallel Processing

123

(1)

6.1.4 Beowulf PC Cluster

124

(1)

6.2 PARALLEL PROGRAMMING TECHNIQUES

125

(1)

6.3 MPICH ARCHITECTURE

126

(4)

6.4 PARALLEL CODE STRUCTURE

130

(5)

6.5 EFFICIENCY ANALYSIS OF PARALLEL FDTD

135

(8)

REFERENCES

143

(2)

Chapter 7 Parallel FDTD Method

145

(34)

7.1 INTRODUCTION TO THE MPI LIBRARY

146

(1)

7.2 DATA EXCHANGING TECHNIQUES

147

(3)

7.3 DOMAIN DECOMPOSITION TECHNIQUE

150

(2)

7.4 IMPLEMENTATION OF THE PARALLEL FDTD METHOD

152

(13)

7.4.1 Data Exchange Along the x-Direction

156

(6)

7.4.2 Data Exchange Along the y-Direction

162

(1)

7.4.3 Data Exchange Along the z-Direction

163

(2)

7.5 RESULT COLLECTION

165

(5)

7.5.1 Nonuniform Mesh Collection

165

(1)

7.5.2 Result Collection

166

(1)

7.5.3 Far-Field Collection

167

(1)

7.5.4 Surface Current Collection

167

(3)

7.6 ASSOCIATED PARALLEL TECHNIQUES

170

(4)

7.6.1 Excitation Source

170

(3)

7.6.2 Waveguide Matched Load

173

(1)

7.6.3 Subgridding Technique

173

(1)

7.7 NUMERICAL EXAMPLES

174

(4)

7.7.1 Crossed Dipole

175

(1)

7.7.2 Circular Horn Antenna

175

(1)

7.7.3 Patch Antenna Array Beam Scanning

176

(2)

REFERENCES

178

(1)

Chapter 8 Illustrative Engineering Applications

179

(14)

8.1 FINITE PATCH ANTENNA ARRAY

179

(6)

8.2 FINITE CROSSED DIPOLE ANTENNA ARRAY

185

(7)

REFERENCES

192

(1)

Chapter 9 FDTD Analysis of Bodies of Revolution

193

(22)

9.1 BOR/FDTD

193

(1)

9.2 UPDATE EQUATIONS FOR BOR/FDTD

194

(4)

9.3 PML FOR BOR/FDTD

198

(2)

9.4 NEAR-TO-FAR-FIELD TRANSFORMATION IN BOR/FDTD

200

(7)

9.5 SINGULAR BOUNDARY IN THE BOR/FDTD

207

(1)

9.6 PARTIALLY SYMMETRIC PROBLEM

208

(5)

9.6.1 Normally Incident Plane Wave

209

(1)

9.6.2 Obliquely Incident Plane Wave

210

(3)

REFERENCES

213

(2)

Chapter 10 Parallel BORJFDTD

215

(14)

10.1 INTRODUCTION TO PARALLEL BOR/FDTD

215

(1)

10.2 IMPLEMENTATION OF PARALLEL BOR/FDTD

216

(4)

10.3 EFFICIENCY ANALYSIS OF PARALLEL BOR/FDTD

220

(2)

10.4 REFLECTOR ANTENNA SYSTEM

222

(6)

10.4.1 Reflector Antenna Simulation

222

(2)

10.4.2 Combination with Reciprocity Principle

224

(2)

10.4.3 Simulation of the Reflector Antenna System

226

(2)

REFERENCES

228

(1)

Appendix A Introduction to Basic MPI Functions

229

(16)

A.1 SELECTED MPICH FUNCTIONS IN FORTRAN

229

(7)

A.2 SELECTED MPICH FUNCTIONS IN C/C++

236

(5)

A.3 MPI DATA TYPE

241

(1)

A.4 MPI OPERATOR

242

(1)

A.5 MPICH SETUP

243

(1)

A.5.1 MPICH Installation and Configuration for Windows

243

(1)

A.5.2 MPICH Installation and Configuration for Linux

243

(1)

REFERENCES

244

(1)

Appendix B PC Cluster-Building Techniques

245

(12)

B.1 SETUP OF A PC CLUSTER FOR THE LINUX SYSTEM

245

(8)

B.1.1 PC Cluster System Description

246

(1)

B.1.2 Linux Installation

246

(2)

B.1.3 Linux System Configuration

248

(3)

B.1.4 Developing Tools

251

(1)

B.1.5 MPICH

252

(1)

B.1.6 Batch Processing Systems

253

(1)

B.2 PARALLEL COMPUTING SYSTEM BASED ON WINDOWS

253

(1)

B.2.1 System Based on Windows

254

(1)

B.2.2 System Based on a Peer Network

254

(1)

B.3 USING AN EXISTING BEOWULF PC CLUSTER

254

(2)

REFERENCES

256

(1)

List of Notations

257

(2)

About the Authors

259

(2)

Index

261

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Parallel Finite-difference Time-domain Method

Summary

Table of Contents

Supplemental Materials