Parallel Solution of Integral Equation-Based EM Problems in the Frequency Domain (Wiley Series in Microwave and Optical Engineering)

PARALLEL SOLUTION OF INTEGRAL EQUATION-BASED EM PROBLEMS IN THE FREQUENCY DOMAIN......Page 9
Contents......Page 11
Preface......Page 19
Acknowledgments......Page 23
Acronyms......Page 25
1.1.1 Computational Electromagnetics......Page 27
1.1.2 Parallel Computation in Electromagnetics......Page 29
1.2 Computer Platforms Accessed in This Book......Page 35
1.3 Parallel Libraries Employed for the Computations......Page 38
1.3.1 ScaLAPACK — Scalable Linear Algebra Package......Page 39
1.3.2 PLAPACK — Parallel Linear Algebra Package......Page 42
References......Page 45
2.0 Summary......Page 53
2.2 An In-Core Matrix Equation Solver......Page 54
2.3.1 Data Distribution for an LU Algorithm......Page 58
2.3.2 ScaLAPACK: Two-Dimensional Block-Cyclic Matrix Distribution......Page 62
2.3.3 PLAPACK: Physically Based Matrix Distribution......Page 64
2.3.4 Data Distribution Comparison between ScaLAPACK and PLAPACK......Page 66
2.4 Data Decomposition for an Out-of-Core Solver......Page 68
2.5 Out-of-Core LU Factorization......Page 69
2.5.1.1 Right-Looking Algorithm......Page 71
2.5.1.2 Left-Looking Algorithm......Page 73
2.5.2 Implementation of the Serial Left-Looking Out-of-Core LU Algorithm......Page 76
2.5.3 Design of a One-Slab Left-Looking Out-of-Core LU Algorithm......Page 81
2.6.1 Parallel Implementation of an Out-of-Core LU Algorithm Using ScaLAPACK......Page 87
2.6.2 Parallel Implementation of an Out-of-Core LU Algorithm Using PLAPACK......Page 90
2.6.4 Checkpointing in an Out-of-Core Solver......Page 91
2.7 Solving a Matrix Equation Using the Out-of-Core LU Matrices......Page 92
References......Page 95
3.1 Electric Field Integral Equation (EFIE)......Page 97
3.2 Use of the Piecewise Triangular Patch (RWG) Basis Functions......Page 100
3.3 Testing Procedure......Page 102
3.4 Matrix Equation for MoM......Page 104
3.5.1 Evaluation of the Fundamental Integrals......Page 105
3.5.2 Extraction of the Singularity......Page 106
3.7 Parallel Matrix Filling — In-Core Algorithm......Page 107
3.8 Parallel Matrix Filling — Out-of-Core Algorithm......Page 112
3.9.2 Different Metrics Used to Assess the Degree of Parallel Efficiency......Page 114
3.9.3 Efficiency and Portability of a Parallel MoM In-Core Solver......Page 118
3.10.1 Parallel Out-of-Core Solver Can Be as Efficient as a Parallel In-Core Solver......Page 122
3.10.2 Scalability and Portability of the Parallel Out-of-Core Solver......Page 124
3.11 Conclusion......Page 130
References......Page 131
4.1 Formulation of the Integral Equation for Analysis of Dielectric Structures......Page 133
4.2 A General Formulation for the Analysis of Composite Metallic and Dielectric Structures......Page 136
4.3.1 Right-Truncated Cone to Model Wire Structures......Page 140
4.3.2 Bilinear Surface for Modeling Arbitrarily Shaped Surfaces......Page 142
4.4.1 Current Expansion along a Thin PEC Wire......Page 143
4.4.2 Current Expansion over a Bilinear Surface......Page 145
4.5.1 Testing Procedure for Thin PEC Wires......Page 150
4.5.2 Testing Procedure for Bilinear Surfaces......Page 154
4.6 Parallel In-Core and Out-of-Core Matrix Filling Schemes......Page 157
4.6.1 Parallel In-Core Matrix Filling Scheme......Page 158
4.6.2 Parallel Out-of-Core Matrix Filling Scheme......Page 160
4.7.1.1 Comparison of Numerical Results Obtained on Single-Core and Multicore Platforms......Page 162
4.7.1.2.1 Radiation from a Vivaldi Antenna Array......Page 167
4.7.1.2.2 Scattering from a Full-Size Airplane......Page 170
4.7.1.3 Numerical Results Obtained on Multicore Platforms......Page 172
4.7.2.1 Vivaldi Antenna Array — a Large Problem Solved on Small Computer Platforms......Page 173
4.7.2.2 Solution for a Full-Size Airplane — Parallel Out-of core Solver Can Be as Efficient as the Parallel In-Core......Page 175
4.7.2.3 Solution for a Full-Size Airplane — Scalability and Portability of the Parallel Out-of-Core Solver......Page 176
4.7.2.4 Solution for a Full- Size Airplane — a Very Large Problem Solved on Nine Nodes of CEM-4......Page 179
References......Page 181
5.1 Anatomy of a Parallel Out-of-Core Integral Equation Solver......Page 183
5.1.1 Various Components of a Parallel Out-of-Core Solver that Can Be Observed through Ganglia and Tuned......Page 184
5.1.2 CPU Times of Parallel In-Core and Out-of-Core Integral Equation Solvers......Page 187
5.1.3 Performance of a Code Varies with the Amount of Storage Used on the Hard Disk......Page 191
5.2 Block Size......Page 196
5.3 Shape of the Process Grid......Page 199
5.4 Size of the In-Core Buffer Allocated to Each Process......Page 202
5.4.1.1.1  Overview of Wall Time with Different IASIZE......Page 203
5.4.1.1.2  Details on Matrix Filling and Matrix Solving......Page 207
5.4.1.2 Case B: Available 4 GB of RAM/Core......Page 214
5.4.2 Optimizing IASIZE for a Parallel MoM Code Using RWG Basis Functions......Page 216
5.4.3 Influence of Physical RAM Size on Performance......Page 220
5.5 Relationship between Shape of the Process Grid and In-Core Buffer Size......Page 223
5.6 Overall Performance of a Parallel Out-of-Core Solver on HPC Clusters......Page 227
References......Page 231
6.1 Development of the Conjugate Gradient Method......Page 233
6.2 The Iterative Solution of a Matrix Equation......Page 238
6.3 Parallel Implementation of the CG Algorithm......Page 239
6.4 A Parallel Combined LU-CG Scheme to Refine the LU Solution......Page 241
6.5 Conclusion......Page 242
References......Page 243
7.1 Introduction......Page 245
7.2 Factors that Affect a Parallel In-Core and Out-of-Core Matrix Filling Algorithm......Page 246
7.3.1 Radiation from an Array of Vivaldi Antennas......Page 250
7.3.2 Scattering from an Electrically Large Aircraft......Page 254
7.3.3 Discussion of the Computational FLOPS Achieved......Page 256
References......Page 257
8.0 Summary......Page 259
8.1.1 Analysis of a Scattering Problem......Page 260
8.1.2 Analysis of a Radiation Problem......Page 263
8.1.3 Analysis of a Coupling Problem......Page 267
8.2 EMC Prediction for Multiple Antennas Mounted on an Electrically Large Platform......Page 269
8.3 Analysis of Complex Composite Antenna Array......Page 274
8.4 Array Calibration for Direction-of-Arrival Estimation......Page 275
8.5.1 RCS Calculation of a Squadron of Tanks......Page 278
8.5.2 RCS of the Tanks inside a Forest Environment......Page 280
8.5.3 RCS from an Aircraft and a Formation of Aircraft......Page 283
8.5.4 RCS Simulation with Million Level Unknowns,......Page 285
8.5.5 RCS of an Aircraft Carrier......Page 286
8.6 Analysis of Radiation Patterns of Antennas Operating Inside a Radome Along with the Platform on Which It Is Mounted......Page 290
8.7 Electromagnetic Interference (EMI) Analysis of a Communication System......Page 294
8.8 Comparison between Computations Using TIDES and Measurement data for Complex Composite Structures......Page 297
References......Page 299
A.1 Description of the Platforms Used in This Book......Page 301
A.2 Conclusion......Page 310
References......Page 311
B.1 Tools for Compiling both ScaLAPACK and PLAPACK......Page 313
B.2.2 Steps for Compiling ScaLAPACK......Page 314
B.2.3.1  Script Files for BLAS......Page 315
B.2.3.2  Script Files for BLACS......Page 319
B.2.3.3  Script Files for ScaLAPACK......Page 322
B.2.4 Script Files for 64-bit Windows Operating System......Page 323
B.3.2 Script Files for PLAPACK......Page 324
B.4 Tuning the Performance by Turning on Proper Flags......Page 326
References......Page 327
C.1 Introduction of MoM......Page 329
C.2.1 Development of the Integral Equation and the MoM Solution......Page 331
C.2.2 Evaluation of the Parameter of Interest......Page 334
C.3.1 Flowchart and Results of a Serial MoM Code......Page 335
C.3.2 A Serial MoM Source Code for the 2D Scattering Problem......Page 338
C.4.1 Flowchart and Results of a Parallel MoM Code......Page 339
C.4.2 A Parallel MoM Source Code Using ScaLAPACK for the 2D Scattering Problem......Page 344
C.5 Compilation and Execution of the Parallel Code......Page 357
References......Page 359
Index......Page 361