Parallel solution of integral equation-based EM problems in the frequency domain / Yu Zhang, Tapan K. Sarkar ; with contributions from Daniel Garcia Doñoro ... [and others].

Format:

Book

Author/Creator:

Zhang, Yu, 1978 April 20-

Contributor:

Sarkar, Tapan (Tapan K.)

Series:

Wiley series in microwave and optical engineering

Language:

English

Subjects (All):

Electromagnetism--Data processing.

Electromagnetism.

Electromagnetic fields--Mathematical models.

Electromagnetic fields.

Electromagnetic waves--Mathematical models.

Electromagnetic waves.

Parallel processing (Electronic computers).

Integral domains.

Time-domain analysis.

Physical Description:

xx, 341 pages : illustrations ; 25 cm.

Place of Publication:

Hoboken, N.J. : Wiley : IEEE Press, [2009]

Summary:

The future of computational electromagnetics is changing drastically as the new generation of computer chips evolves from single-core to multi-core. The burden now falls on software programmers to revamp existing codes and add new functionality to enable computational codes to run efficiently on this new generation of multi-core CPUs. In this book, you'll learn everything you need to know to deal with multi-core advances in chip design by employing highly efficient parallel electromagnetic code. Focusing only on the Method of Moments (MoM), the book covers:

In-Core and Out-of-Core LU Factorization for Solving a Matrix Equation

A Parallel MoM Code Using RWG Basis Functions and ScaLAPACK-Based In-Core and Out-of-Core Solvers

A Parallel MoM Code Using Higher-Order Basis Functions and ScaLAPACK-Based In-Core and Out-of-Core Solvers

Turning the Performance of a Parallel Integral Equation Solver

Refinement of the Solution Using the Conjugate Gradient Method

A Parallel MoM Code Using Higher-Order Basis Functions and PLAPACK-Based In-Core and Out-of-Core Solvers

Applications of the Parallel Frequency Domain Integral Equation Solver

Appendices are provided with detailed information on the various computer platforms used for computation; a demo shows you how to compile ScaLAPACK and PLAPACK on the Windows® operating system; and a demo parallel source code is available to solve the 2D electromagnetic scattering problems.

Parallel Solution of Integral Equation-Based EM Problems in the Frequency Domain is indispensable reading for computational code designers, computational electromagnetics researchers, graduate students, and anyone working with CEM software.

Contents:

Chapter 1 Introduction 1

1.0 Summary 1

1.1 A Brief Review of Parallel CEM 1

1.1.1 Computational Electromagnetics 1

1.1.2 Parallel Computation in Electromagnetics 3

1.2 Computer Platforms Accessed in This Book 9

1.3 Parallel Libraries Employed for the Computations 12

1.3.1 ScaLAPACK - Scalable Linear Algebra Package 13

1.3.2 PLAPACK - Parallel Linear Algebra Package 16

1.4 Conclusion 19

References 19

Chapter 2 In-Core and Out-of-Core LU Factorization for Solving a Matrix Equation 27

2.0 Summary 27

2.1 Matrix Equation from a MoM Code 28

2.2 An In-Core Matrix Equation Solver 28

2.3 Parallel Implementation of an In-Core Solver 32

2.3.1 Data Distribution for an LU Algorithm 32

2.3.2 ScaLAPACK: Two-Dimensional Block-Cyclic Matrix Distribution 36

2.3.3 PLAPACK: Physically Based Matrix Distribution 38

2.3.4 Data Distribution Comparison between ScaLAPACK and PLAPACK 40

2.4 Data Decomposition for an Out-of-Core Solver 42

2.5 Out-of-Core LU Factorization 43

2.5.1 I/O Analysis of Serial Right-Looking and Left-Looking Out-of-Core LU Algorithms 45

2.5.1.1 Right-Looking Algorithm 45

2.5.1.2 Left-Looking Algorithm 47

2.5.2 Implementation of the Serial Left-Looking Out-of-Core LU Algorithm 50

2.5.3 Design of a One-Slab Left-Looking Out-of-Core LU Algorithm 55

2.6 Parallel Implementation of an Out-of-Core LU Algorithm 61

2.6.1 Parallel Implementation of an Out-of-Core LU Algorithm Using ScaLAPACK 61

2.6.2 Parallel Implementation of an Out-of-Core LU Algorithm Using PLAPACK 64

2.6.3 Overlapping of the I/O with the Computation 65

2.6.4 Checkpointing in an Out-of-Core Solver 65

2.7 Solving a Matrix Equation Using the Out-of-Core LU Matrices 66

2.8 Conclusion 69

References 69

Chapter 3 A Parallel MoM Code Using RWG Basis Functions and ScaLAPACK-Based In-Core and Out-of-Core Solvers 71

3.0 Summary 71

3.1 Electric Field Integral Equation (EFIE) 71

3.2 Use of the Piecewise Triangular Patch (RWG) Basis Functions 74

3.3 Testing Procedure 76

3.4 Matrix Equation for MoM 78

3.5 Calculation of the Various Integrals 79

3.5.1 Evaluation of the Fundamental Integrals 79

3.5.2 Extraction of the Singularity 80

3.6 Calculation of the Fields 81

3.7 Parallel Matrix Filling-In-Core Algorithm 81

3.8 Parallel Matrix Filling-Out-of-Core Algorithm 86

3.9 Numerical Results from a Parallel In-Core MoM Solver 88

3.9.1 Numerical Results Compared with other Methods 88

3.9.1.1 A PEC Cube 88

3.9.1.2 A Combined Cube-and-Sphere PEC Model 88

3.9.2 Different Metrics Used to Assess the Degree of Parallel Efficiency 88

3.9.3 Efficiency and Portability of a Parallel MoM In-Core Solver 92

3.10 Numerical Results from a Parallel Out-of-Core MoM Solver 96

3.10.1 Parallel Out-of-Core Solver Can Be as Efficient as a Parallel In-Core Solver 96

3.10.2 Scalability and Portability of the Parallel Out-of-Core Solver 98

3.11 Conclusion 104

References 105

Chapter 4 A Parallel MoM Code Using Higher-Order Basis Functions and ScaLAPACK-Based In-Core and Out-of-Core Solvers 107

4.0 Summary 107

4.1 Formulation of the Integral Equation for Analysis of Dielectric Structures 107

4.2 A General Formulation for the Analysis of Composite Metallic and Dielectric Structures 110

4.3 Geometric Modeling of the Structures 114

4.3.1 Right-Truncated Cone to Model Wire Structures 114

4.3.2 Bilinear Surface for Modeling Arbitrarily Shaped Surfaces 116

4.4 Higher-Order Basis Functions 117

4.4.1 Current Expansion along a Thin PEC Wire 117

4.4.2 Current Expansion over a Bilinear Surface 119

4.5 Testing Procedure 124

4.5.1 Testing Procedure for Thin PEC Wires 124

4.5.2 Testing Procedure for Bilinear Surfaces 119

4.6 Parallel In-Core and Out-of-Core Matrix Filling Schemes 131

4.6.1 Parallel In-Core Matrix Filling Scheme 132

4.6.2 Parallel Out-of-Core Matrix Filling Scheme 134

4.7 Numerical Results Computed on Different Platforms 136

4.7.1 Performance Analysis for the Parallel In-Core Integral Equation Solver 136

4.7.1.1 Comparison of Numerical Results Obtained on Single-Core and Multicore Platforms 136

4.7.1.2 Numerical Results Obtained on Single-Core Platforms 141

4.7.1.2.1 Radiation from a Vivaldi Antenna Array 141

4.7.1.2.2 Scattering from a Full-Size Airplane 144

4.7.1.3 Numerical Results Obtained on Multicore Platforms 146

4.7.2 Performance Analysis for the Parallel Out-of-Core Integral Equation Solver 147

4.7.2.1 Vivaldi Antenna Array-a Large Problem Solved on Small Computer Platforms 147

4.7.2.2 Solution for a Full-Size Airplane-Parallel Out-of-Core Solver Can Be as Efficient as the Parallel In-Core 149

4.7.2.3 Solution for a Full-Size Airplane-Scalability and Portability of the Parallel Out-of-Core Solver 150

4.7.2.4 Solution for a Full-Size Airplane-a Very Large Problem Solved on Nine Nodes of CEM-4 153

4.8 Conclusion 155

References 155

Chapter 5 Tuning the Performance of a Parallel Integral Equation Solver 157

5.0 Summary 157

5.1 Anatomy of a Parallel Out-of-Core Integral Equation Solver 157

5.1.1 Various Components of a Parallel Out-of-Core Solver that Can Be Observed through Ganglia and Tuned 158

5.1.2 CPU Times of Parallel In-Core and Out-of-Core Integral Equation Solvers 161

5.1.3 Performance of a Code Varies with the Amount of Storage Used on the Hard Disk 165

5.2 Block Size 170

5.3 Shape of the Process Grid 173

5.4 Size of the In-Core Buffer Allocated to Each Process 176

5.4.1 Optimizing IASIZE for a Parallel MoM Code Using Higher-Order Basis Functions 177

5.4.1.1 Case A: Available 2 GB of RAM/Core 177

5.4.1.1.1 Overview of Wall Time with Different IASIZE 177

5.4.1.1.2 Details on Matrix Filling and Matrix Solving 181

5.4.1.2 Case B: Available 4 GB of RAM/Core 188

5.4.2 Optimizing IASIZE for a Parallel MoM Code Using RWG Basis Functions 190

5.4.3 Influence of Physical RAM Size on Performance 194

5.5 Relationship between Shape of the Process Grid and In-Core Buffer Size 197

5.6 Overall Performance of a Parallel Out-of-Core Solver on HPC Clusters 201

5.7 Conclusion 205

References 205

Chapter 6 Refinement of the Solution Using the Iterative Conjugate Gradient Method 207

6.0 Summary 207

6.1 Development of the Conjugate Gradient Method 207

6.2 The Iterative Solution of a Matrix Equation 212

6.3 Parallel Implementation of the CG Algorithm 213

6.4 A Parallel Combined LU-CG Scheme to Refine the LU Solution 215

6.5 Conclusion 216

References 217

Chapter 7 A Parallel MoM Code Using Higher-Order Basis Functions and PLAPACK-Based In-Core and Out-of-Core Solvers 219

7.0 Summary 219

7.1 Introduction 219

7.2 Factors that Affect a Parallel In-Core and Out-of-Core Matrix Filling Algorithm 220

7.3 Numerical Results 224

7.3.1 Radiation from an Array of Vivaldi Antennas 224

7.3.2 Scattering from an Electrically Large Aircraft 228

7.3.3 Discussion of the Computational FLOPS Achieved 230

7.4 Conclusion 231

References 231

Chapter 8 Applications of the Parallel Frequency-Domain Integral Equation Solver-TIDES 233

8.0 Summary 233

8.1 Performance Comparison between TIDES and a Commercial EM Analysis Software 234

8.1.1 Analysis of a Scattering Problem 234

8.1.2 Analysis of a Radiation Problem 237

8.1.3 Analysis of a Coupling Problem 241

8.2 EMC Prediction for Multiple Antennas Mounted on an Electrically Large Platform 243

8.3 Analysis of Complex Composite Antenna Array 248

8.4 Array Calibration for Direction-of-Arrival Estimation 249

8.5 Radar Cross Section (RCS) Calculation of Complex Targets 252

8.5.1 RCS Calculation of a Squadron of Tanks 252

8.5.2 RCS of the Tanks inside a Forest Environment 254

8.5.3 RCS from an Aircraft and a Formation of Aircraft 257

8.5.4 RCS Simulation with Million Level Unknowns 259

8.5.5 RCS of an Aircraft Carrier 260

8.6 Analysis of Radiation Patterns of Antennas Operating Inside a

Radome Along with the Platform on Which It Is Mounted 264

8.7 Electromagnetic Interference (EMI) Analysis of a Communication System 268

8.8 Comparison between Computations Using TIDES and Measurement data for Complex Composite Structures 271

8.9 Conclusion 273

References 273.

Notes:

Includes bibliographical references and index.

ISBN:

9780470405451

0470405457

OCLC:

277196639