Parallel Solution of Integral Equation-Based EM Problems in the Frequency Domain

by Zhang, Y.; Sarkar, T. K.

• ISBN13: 9780470405451
• ISBN10: 0470405457
• Edition: 1st
• Format: Hardcover
• Copyright: 2009-06-22
• Publisher: Wiley-IEEE Press

Summary

Method of Moments (MoM) remains one of the most powerful numerical methods of the past several decades and a powerful weapon for the solution of current complex Electromagnetic field problems. Parallel Solution of EM Problems in the Frequency Domain provides complete coverage of parallel electromagnetic simulation techniques for Method of Moments. Presenting research that illustrates how to take the shortest route to highly efficient parallel electromagnetic (EM) code, this roadmap for computational code designers and chip designers demonstrates how to navigate through the multi-core advancements in chip design.

Author Biography

Yu Zhang is an Associate Professor?at Xidian University and currently works at Syracuse University. He authored the book Parallel Computation in Electromagnetics as well as over seventy journal papers and thirty conference papers. His research is focused on computational electromagnetics with an interest in antenna design, EMC simulation, and signal processing.

Tapan K. Sarkar is a Professor in the Department of Electrical and Computer Engineering at Syracuse University. His current research interests deal with numerical solutions of operator equations arising in electromagnetics and signal processing with applications in system design. He has authored or coauthored more than 300 journal articles, numerous conference papers, and thirty-two book chapters. He is the author of fifteen books, including Smart Antennas, History of Wireless, and Physics of Multiantenna Systems and Broadband Processing (all published by Wiley).

Table of Contents

Preface	p. xiii
Acknowledgments	p. xvii
Acronyms	p. xix
Introduction	p. 1
Summary	p. 1
A Brief Review of Parallel CEM	p. 1
Computational Electromagnetics	p. 1
Parallel Computation in Electromagnetics	p. 3
Computer Platforms Accessed in This Book	p. 9
Parallel Libraries Employed for the Computations	p. 12
ScaLAPACK - Scalable Linear Algebra Package	p. 13
PLAPACK - Parallel Linear Algebra Package	p. 16
Conclusion	p. 19
References	p. 19
In-Core and Out-of-Core LU Factorization for Solving a Matrix Equation	p. 27
Summary	p. 27
Matrix Equation from a MoM Code	p. 28
An In-Core Matrix Equation Solver	p. 28
Parallel Implementation of an In-Core Solver	p. 32
Data Distribution for an LU Algorithm	p. 32
ScaLAPACK: Two-Dimensional Block-Cyclic Matrix Distribution	p. 36
PLAPACK: Physically Based Matrix Distribution	p. 38
Data Distribution Comparison between ScaLAPACK and PLAPACK	p. 40
Data Decomposition for an Out-of-Core Solver	p. 42
Out-of-Core LU Factorization	p. 43
I/O Analysis of Serial Right-Looking and Left-Looking Out-of-Core LU Algorithms	p. 45
Right-Looking Algorithm	p. 45
Left-Looking Algorithm	p. 47
Implementation of the Serial Left-Looking Out-of-Core LU Algorithm	p. 50
Design of a One-Slab Left-Looking Out-of-Core LU Algorithm	p. 55
Parallel Implementation of an Out-of-Core LU Algorithm	p. 61
Parallel Implementation of an Out-of-Core LU Algorithm Using ScaLAPACK	p. 61
Parallel Implementation of an Out-of-Core LU Algorithm Using PLAPACK	p. 64
Overlapping of the I/O with the Computation	p. 65
Checkpointing in an Out-of-Core Solver	p. 65
Solving a Matrix Equation Using the Out-of-Core LU Matrices	p. 66
Conclusion	p. 69
References	p. 69
A Parallel MoM Code Using RWG Basis Functions and ScaLAPACK-Based In-Core and Out-of-Core Solvers	p. 71
Summary	p. 71
Electric Field Integral Equation (EFIE)	p. 71
Use of the Piecewise Triangular Patch (RWG) Basis Functions	p. 74
Testing Procedure	p. 76
Matrix Equation for MoM	p. 78
Calculation of the Various Integrals	p. 79
Evaluation of the Fundamental Integrals	p. 79
Extraction of the Singularity	p. 80
Calculation of the Fields	p. 81
Parallel Matrix Filling-In-Core Algorithm	p. 81
Parallel Matrix Filling-Out-of-Core Algorithm	p. 86
Numerical Results from a Parallel In-Core MoM Solver	p. 88
Numerical Results Compared with other Methods	p. 88
A PEC Cube	p. 88
A Combined Cube-and-Sphere PEC Model	p. 88
Different Metrics Used to Assess the Degree of Parallel Efficiency	p. 88
Efficiency and Portability of a Parallel MoM In-Core Solver	p. 92
Numerical Results from a Parallel Out-of-Core MoM Solver	p. 96
Parallel Out-of-Core Solver Can Be as Efficient as a Parallel In-Core Solver	p. 96
Scalability and Portability of the Parallel Out-of-Core Solver	p. 98
Conclusion	p. 104
References	p. 105
A Parallel MoM Code Using Higher-Order Basis Functions and ScaLAPACK-Based In-Core and Out-of-Core Solvers	p. 107
Summary	p. 107
Formulation of the Integral Equation for Analysis of Dielectric Structures	p. 107
A General Formulation for the Analysis of Composite Metallic and Dielectric Structures	p. 110
Geometric Modeling of the Structures	p. 114
Right-Truncated Cone to Model Wire Structures	p. 114
Bilinear Surface for Modeling Arbitrarily Shaped Surfaces	p. 116
Higher-Order Basis Functions	p. 117
Current Expansion along a Thin PEC Wire	p. 117
Current Expansion over a Bilinear Surface	p. 119
Testing Procedure	p. 124
Testing Procedure for Thin PEC Wires	p. 124
Testing Procedure for Bilinear Surfaces	p. 119
Parallel In-Core and Out-of-Core Matrix Filling Schemes	p. 131
Parallel In-Core Matrix Filling Scheme	p. 132
Parallel Out-of-Core Matrix Filling Scheme	p. 134
Numerical Results Computed on Different Platforms	p. 136
Performance Analysis for the Parallel In-Core Integral Equation Solver	p. 136
Comparison of Numerical Results Obtained on Single-Core and Multicore Platforms	p. 136
Numerical Results Obtained on Single-Core Platforms	p. 141
Radiation from a Vivaldi Antenna Array	p. 141
Scattering from a Full-Size Airplane	p. 144
Numerical Results Obtained on Multicore Platforms	p. 146
Performance Analysis for the Parallel Out-of-Core Integral Equation Solver	p. 147
Vivaldi Antenna Array-a Large Problem Solved on Small Computer Platforms	p. 147
Solution for a Full-Size Airplane-Parallel Out-of-Core Solver Can Be as Efficient as the Parallel In-Core	p. 149
Solution for a Full-Size Airplane-Scalability and Portability of the Parallel Out-of-Core Solver	p. 150
Solution for a Full-Size Airplane-a Very Large Problem Solved on Nine Nodes of CEM-4	p. 153
Conclusion	p. 155
References	p. 155
Tuning the Performance of a Parallel Integral Equation Solver	p. 157
Summary	p. 157
Anatomy of a Parallel Out-of-Core Integral Equation Solver	p. 157
Various Components of a Parallel Out-of-Core Solver that Can Be Observed through Ganglia and Tuned	p. 158
CPU Times of Parallel In-Core and Out-of-Core Integral Equation Solvers	p. 161
Performance of a Code Varies with the Amount of Storage Used on the Hard Disk	p. 165
Block Size	p. 170
Shape of the Process Grid	p. 173
Size of the In-Core Buffer Allocated to Each Process	p. 176
Optimizing IASIZE for a Parallel MoM Code Using Higher-Order Basis Functions	p. 177
Case A: Available 2 GB of RAM/Core	p. 177
Overview of Wall Time with Different IASIZE	p. 177
Details on Matrix Filling and Matrix Solving	p. 181
Case B: Available 4 GB of RAM/Core	p. 188
Optimizing IASIZE for a Parallel MoM Code Using RWG Basis Functions	p. 190
Influence of Physical RAM Size on Performance	p. 194
Relationship between Shape of the Process Grid and In-Core Buffer Size	p. 197
Overall Performance of a Parallel Out-of-Core Solver on HPC Clusters	p. 201
Conclusion	p. 205
References	p. 205
Refinement of the Solution Using the Iterative Conjugate Gradient Method	p. 207
Summary	p. 207
Development of the Conjugate Gradient Method	p. 207
The Iterative Solution of a Matrix Equation	p. 212
Parallel Implementation of the CG Algorithm	p. 213
A Parallel Combined LU-CG Scheme to Refine the LU Solution	p. 215
Conclusion	p. 216
References	p. 217
A Parallel MoM Code Using Higher-Order Basis Functions and PLAPACK-Based In-Core and Out-of-Core Solvers	p. 219
Summary	p. 219
Introduction	p. 219
Factors that Affect a Parallel In-Core and Out-of-Core Matrix Filling Algorithm	p. 220
Numerical Results	p. 224
Radiation from an Array of Vivaldi Antennas	p. 224
Scattering from an Electrically Large Aircraft	p. 228
Discussion of the Computational FLOPS Achieved	p. 230
Conclusion	p. 231
References	p. 231
Applications of the Parallel Frequency-Domain Integral Equation Solver-TIDES	p. 233
Summary	p. 233
Performance Comparison between TIDES and a Commercial EM Analysis Software	p. 234
Analysis of a Scattering Problem	p. 234
Analysis of a Radiation Problem	p. 237
Analysis of a Coupling Problem	p. 241
EMC Prediction for Multiple Antennas Mounted on an Electrically Large Platform	p. 243
Analysis of Complex Composite Antenna Array	p. 248
Array Calibration for Direction-of-Arrival Estimation	p. 249
Radar Cross Section (RCS) Calculation of Complex Targets	p. 252
RCS Calculation of a Squadron of Tanks	p. 252
RCS of the Tanks inside a Forest Environment	p. 254
RCS from an Aircraft and a Formation of Aircraft	p. 257
RCS Simulation with Million Level Unknowns	p. 259
RCS of an Aircraft Carrier	p. 260
Analysis of Radiation Patterns of Antennas Operating Inside a Radome Along with the Platform on Which It Is Mounted	p. 264
Electromagnetic Interference (EMI) Analysis of a Communication System	p. 268
Comparison between Computations Using TIDES and Measurement data for Complex Composite Structures	p. 271
Conclusion	p. 273
References	p. 273
A Summary of the Computer Platforms Used in This Book	p. 275
Summary	p. 275
Description of the Platforms Used in This Book	p. 275
Conclusion	p. 284
References	p. 285
An Efficient Cross-Platform Compilation of the ScaLAPACK and PLAPACK Routines	p. 287
Summary	p. 287
Tools for Compiling both ScaLAPACK and PLAPACK	p. 287
Generating the ScaLAPACK Library	p. 288
Source Codes for Compiling ScaLAPACK	p. 288
Steps for Compiling ScaLAPACK	p. 288
Script Files for 32-bit Windows Operating System	p. 289
Script Files for BLAS	p. 289
Script Files for BLACS	p. 293
Script Files for ScaLAPACK	p. 296
Script Files for 64-bit Windows Operating System	p. 297
Generating the PLAPACK Library	p. 298
Source Codes for Compiling PLAPACK	p. 298
Script Files for PLAPACK	p. 298
Tuning the Performance by Turning on Proper Flags	p. 300
Conclusion	p. 301
References	p. 301
An Example of a Parallel MoM Source Code for Analysis of 2D EM Scattering	p. 303
Summary	p. 303
Introduction of MoM	p. 303
Solution of a Two-Dimensional Scattering Problem	p. 305
Development of the Integral Equation and the MoM Solution	p. 305
Evaluation of the Parameter of Interest	p. 308
Implementation of a Serial MoM Code	p. 309
Flowchart and Results of a Serial MoM Code	p. 309
A Serial MoM Source Code for the 2D Scattering Problem	p. 312
Implementation of a Parallel MoM Code	p. 313
Flowchart and Results of a Parallel MoM Code	p. 313
A Parallel MoM Source Code Using ScaLAPACK for the 2D Scattering Problem	p. 318
Compilation and Execution of the Parallel Code	p. 331
Conclusion	p. 333
References	p. 333
Index	p. 335
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