PARALLEL SOLUTION OF INTEGRAL EQUATION-BASED EM PROBLEMS IN THE FREQUENCY DOMAIN -- Contents -- Preface -- Acknowledgments -- Acronyms -- Chapter 1 Introduction -- 1.0 Summary -- 1.1 A Brief Review of Parallel CEM -- 1.1.1 Computational Electromagnetics -- 1.1.2 Parallel Computation in Electromagnetics -- 1.2 Computer Platforms Accessed in This Book -- 1.3 Parallel Libraries Employed for the Computations -- 1.3.1 ScaLAPACK - Scalable Linear Algebra Package -- 1.3.2 PLAPACK - Parallel Linear Algebra Package -- 1.4 Conclusion -- References -- Chapter 2 In-Core and Out-of-Core LU Factorization for Solving a Matrix Equation -- 2.0 Summary -- 2.1 Matrix Equation from a MoM Code -- 2.2 An In-Core Matrix Equation Solver -- 2.3 Parallel Implementation of an In-Core Solver -- 2.3.1 Data Distribution for an LU Algorithm -- 2.3.2 ScaLAPACK: Two-Dimensional Block-Cyclic Matrix Distribution -- 2.3.3 PLAPACK: Physically Based Matrix Distribution -- 2.3.4 Data Distribution Comparison between ScaLAPACK and PLAPACK -- 2.4 Data Decomposition for an Out-of-Core Solver -- 2.5 Out-of-Core LU Factorization -- 2.5.1 I/O Analysis of Serial Right-Looking and Left-Looking Out-of-Core LU Algorithms -- 2.5.1.1 Right-Looking Algorithm -- 2.5.1.2 Left-Looking Algorithm -- 2.5.2 Implementation of the Serial Left-Looking Out-of-Core LU Algorithm -- 2.5.3 Design of a One-Slab Left-Looking Out-of-Core LU Algorithm -- 2.6 Parallel Implementation of an Out-of-Core LU Algorithm -- 2.6.1 Parallel Implementation of an Out-of-Core LU Algorithm Using ScaLAPACK -- 2.6.2 Parallel Implementation of an Out-of-Core LU Algorithm Using PLAPACK -- 2.6.3 Overlapping of the I/O with the Computation -- 2.6.4 Checkpointing in an Out-of-Core Solver -- 2.7 Solving a Matrix Equation Using the Out-of-Core LU Matrices -- 2.8 Conclusion -- References.

Chapter 3 A Parallel MoM Code Using RWG Basis Functions and ScaLAPACK-Based In-Core and Out-of-Core Solvers -- 3.0 Summary -- 3.1 Electric Field Integral Equation (EFIE) -- 3.2 Use of the Piecewise Triangular Patch (RWG) Basis Functions -- 3.3 Testing Procedure -- 3.4 Matrix Equation for MoM -- 3.5 Calculation of the Various Integrals -- 3.5.1 Evaluation of the Fundamental Integrals -- 3.5.2 Extraction of the Singularity -- 3.6 Calculation of the Fields -- 3.7 Parallel Matrix Filling - In-Core Algorithm -- 3.8 Parallel Matrix Filling - Out-of-Core Algorithm -- 3.9 Numerical Results from a Parallel In-Core MoM Solver -- 3.9.1 Numerical Results Compared with other Methods -- 3.9.1.1 A PEC Cube -- 3.9.1.2 A Combined Cube-and-Sphere PEC Model -- 3.9.2 Different Metrics Used to Assess the Degree of Parallel Efficiency -- 3.9.3 Efficiency and Portability of a Parallel MoM In-Core Solver -- 3.10 Numerical Results from a Parallel Out-of-Core MoM Solver -- 3.10.1 Parallel Out-of-Core Solver Can Be as Efficient as a Parallel In-Core Solver -- 3.10.2 Scalability and Portability of the Parallel Out-of-Core Solver -- 3.11 Conclusion -- References -- Chapter 4 A Parallel MoM Code Using Higher-Order Basis Functions and ScaLAPACK-Based In-Core and Out-of-Core Solvers -- 4.0 Summary -- 4.1 Formulation of the Integral Equation for Analysis of Dielectric Structures -- 4.2 A General Formulation for the Analysis of Composite Metallic and Dielectric Structures -- 4.3 Geometric Modeling of the Structures -- 4.3.1 Right-Truncated Cone to Model Wire Structures -- 4.3.2 Bilinear Surface for Modeling Arbitrarily Shaped Surfaces -- 4.4 Higher-Order Basis Functions -- 4.4.1 Current Expansion along a Thin PEC Wire -- 4.4.2 Current Expansion over a Bilinear Surface -- 4.5 Testing Procedure -- 4.5.1 Testing Procedure for Thin PEC Wires.

4.5.2 Testing Procedure for Bilinear Surfaces -- 4.6 Parallel In-Core and Out-of-Core Matrix Filling Schemes -- 4.6.1 Parallel In-Core Matrix Filling Scheme -- 4.6.2 Parallel Out-of-Core Matrix Filling Scheme -- 4.7 Numerical Results Computed on Different Platforms -- 4.7.1 Performance Analysis for the Parallel In-Core Integral Equation Solver -- 4.7.1.1 Comparison of Numerical Results Obtained on Single-Core and Multicore Platforms -- 4.7.1.2 Numerical Results Obtained on Single-Core Platforms -- 4.7.1.2.1 Radiation from a Vivaldi Antenna Array -- 4.7.1.2.2 Scattering from a Full-Size Airplane -- 4.7.1.3 Numerical Results Obtained on Multicore Platforms -- 4.7.2 Performance Analysis for the Parallel Out-of-Core Integral Equation Solver -- 4.7.2.1 Vivaldi Antenna Array - a Large Problem Solved on Small Computer Platforms -- 4.7.2.2 Solution for a Full-Size Airplane - Parallel Out-of core Solver Can Be as Efficient as the Parallel In-Core -- 4.7.2.3 Solution for a Full-Size Airplane - Scalability and Portability of the Parallel Out-of-Core Solver -- 4.7.2.4 Solution for a Full- Size Airplane - a Very Large Problem Solved on Nine Nodes of CEM-4 -- 4.8 Conclusion -- References -- Chapter 5 Tuning the Performance of a Parallel Integral Equation Solver -- 5.0 Summary -- 5.1 Anatomy of a Parallel Out-of-Core Integral Equation Solver -- 5.1.1 Various Components of a Parallel Out-of-Core Solver that Can Be Observed through Ganglia and Tuned -- 5.1.2 CPU Times of Parallel In-Core and Out-of-Core Integral Equation Solvers -- 5.1.3 Performance of a Code Varies with the Amount of Storage Used on the Hard Disk -- 5.2 Block Size -- 5.3 Shape of the Process Grid -- 5.4 Size of the In-Core Buffer Allocated to Each Process -- 5.4.1 Optimizing IASIZE for a Parallel MoM Code Using Higher-Order Basis Functions -- 5.4.1.1 Case A: Available 2 GB of RAM/Core.

5.4.1.1.1 Overview of Wall Time with Different IASIZE -- 5.4.1.1.2 Details on Matrix Filling and Matrix Solving -- 5.4.1.2 Case B: Available 4 GB of RAM/Core -- 5.4.2 Optimizing IASIZE for a Parallel MoM Code Using RWG Basis Functions -- 5.4.3 Influence of Physical RAM Size on Performance -- 5.5 Relationship between Shape of the Process Grid and In-Core Buffer Size -- 5.6 Overall Performance of a Parallel Out-of-Core Solver on HPC Clusters -- 5.7 Conclusion -- References -- Chapter 6 Refinement of the Solution Using the Iterative Conjugate Gradient Method -- 6.0 Summary -- 6.1 Development of the Conjugate Gradient Method -- 6.2 The Iterative Solution of a Matrix Equation -- 6.3 Parallel Implementation of the CG Algorithm -- 6.4 A Parallel Combined LU-CG Scheme to Refine the LU Solution -- 6.5 Conclusion -- References -- Chapter 7 A Parallel MoM Code Using Higher-Order Basis Functions and PLAPACK-Based In-Core and Out-of-Core Solvers -- 7.0 Summary -- 7.1 Introduction -- 7.2 Factors that Affect a Parallel In-Core and Out-of-Core Matrix Filling Algorithm -- 7.3 Numerical Results -- 7.3.1 Radiation from an Array of Vivaldi Antennas -- 7.3.2 Scattering from an Electrically Large Aircraft -- 7.3.3 Discussion of the Computational FLOPS Achieved -- 7.4 Conclusion -- References -- Chapter 8 Applications of the Parallel Frequency-Domain Integral Equation Solver - TIDES -- 8.0 Summary -- 8.1 Performance Comparison between TIDES and a Commercial EM Analysis Software -- 8.1.1 Analysis of a Scattering Problem -- 8.1.2 Analysis of a Radiation Problem -- 8.1.3 Analysis of a Coupling Problem -- 8.2 EMC Prediction for Multiple Antennas Mounted on an Electrically Large Platform -- 8.3 Analysis of Complex Composite Antenna Array -- 8.4 Array Calibration for Direction-of-Arrival Estimation -- 8.5 Radar Cross Section (RCS) Calculation of Complex Targets.

8.5.1 RCS Calculation of a Squadron of Tanks -- 8.5.2 RCS of the Tanks inside a Forest Environment -- 8.5.3 RCS from an Aircraft and a Formation of Aircraft -- 8.5.4 RCS Simulation with Million Level Unknowns, -- 8.5.5 RCS of an Aircraft Carrier -- 8.6 Analysis of Radiation Patterns of Antennas Operating Inside a Radome Along with the Platform on Which It Is Mounted -- 8.7 Electromagnetic Interference (EMI) Analysis of a Communication System -- 8.8 Comparison between Computations Using TIDES and Measurement data for Complex Composite Structures -- 8.9 Conclusion -- References -- Appendix A A Summary of the Computer Platforms Used in This Book -- A.0 Summary -- A.1 Description of the Platforms Used in This Book -- A.2 Conclusion -- References -- Appendix B An Efficient Cross-Platform Compilation of the ScaLAPACK and PLAPACK Routines -- B.0 Summary -- B.1 Tools for Compiling both ScaLAPACK and PLAPACK -- B.2 Generating the ScaLAPACK Library -- B.2.1 Source Codes for Compiling ScaLAPACK -- B.2.2 Steps for Compiling ScaLAPACK -- B.2.3 Script Files for 32-bit Windows Operating System -- B.2.3.1 Script Files for BLAS -- B.2.3.2 Script Files for BLACS -- B.2.3.3 Script Files for ScaLAPACK -- B.2.4 Script Files for 64-bit Windows Operating System -- B.3 Generating the PLAPACK Library -- B.3.1 Source Codes for Compiling PLAPACK -- B.3.2 Script Files for PLAPACK -- B.4 Tuning the Performance by Turning on Proper Flags -- B.5 Conclusion -- References -- Appendix C An Example of a Parallel MoM Source Code for Analysis of 2D EM Scattering -- C.0 Summary -- C.1 Introduction of MoM -- C.2 Solution of a Two-Dimensional Scattering Problem -- C.2.1 Development of the Integral Equation and the MoM Solution -- C.2.2 Evaluation of the Parameter of Interest -- C.3 Implementation of a Serial MoM Code -- C.3.1 Flowchart and Results of a Serial MoM Code.

C.3.2 A Serial MoM Source Code for the 2D Scattering Problem.