The Multilevel Fast Multipole Algorithm 1st Edition by Ozgur Ergul ,Levent Gurel ISBN 978-1-119-97741-4 111997741X
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Product details:
ISBN 10 : 111997741X
ISBN 13:978-1-119-97741-4
Author: Ozgur Ergul ,Levent Gurel
The Multilevel Fast Multipole Algorithm (MLFMA) for Solving Large-Scale Computational Electromagnetic Problems provides a detailed and instructional overview of implementing MLFMA. The book:
- Presents a comprehensive treatment of the MLFMA algorithm, including basic linear algebra concepts, recent developments on the parallel computation, and a number of application examples
- Covers solutions of electromagnetic problems involving dielectric objects and perfectly-conducting objects
- Discusses applications including scattering from airborne targets, scattering from red blood cells, radiation from antennas and arrays, metamaterials etc.
- Is written by authors who have more than 25 years experience on the development and implementation of MLFMA
Table of contents:
1.1 Introduction
1.2 Simulation Environments Based on MLFMA
1.3 From Maxwell’s Equations to Integro-Differential Operators
1.4 Surface Integral Equations
1.5 Boundary Conditions
1.6 Surface Formulations
1.7 Method of Moments and Discretization
1.7.1 Linear Functions
1.8 Integrals on Triangular Domains
1.8.1 Analytical Integrals
1.8.2 Gaussian Quadratures
1.8.3 Adaptive Integration
1.9 Electromagnetic Excitation
1.9.1 Plane-Wave Excitation
1.9.2 Hertzian Dipole
1.9.3 Complex-Source-Point Excitation
1.9.4 Delta-Gap Excitation
1.9.5 Current-Source Excitation
1.10 Multilevel Fast Multipole Algorithm
1.11 Low-Frequency Breakdown of MLFMA
1.12 Iterative Algorithms
1.12.1 Symmetric Lanczos Process
1.12.2 Nonsymmetric Lanczos Process
1.12.3 Arnoldi Process
1.12.4 Golub-Kahan Process
1.13 Preconditioning
1.14 Parallelization of MLFMA
2 Solutions of Electromagnetics Problems with Surface Integral Equations
2.1 Homogeneous Dielectric Objects
2.1.1 Surface Integral Equations
2.1.2 Surface Formulations
2.1.3 Discretizations of Surface Formulations
2.1.4 Direct Calculations of Interactions
2.1.5 General Properties of Surface Formulations
2.1.6 Decoupling for Perfectly Conducting Surfaces
2.1.7 Accuracy with Respect to Contrast
2.2 Low-Contrast Breakdown and Its Solution
2.2.1 A Combined Tangential Formulation
2.2.2 Nonradiating Currents
2.2.3 Conventional Formulations in the Limit Case
2.2.4 Low-Contrast Breakdown
2.2.5 Stabilization by Extraction
2.2.6 Double-Stabilized Combined Tangential Formulation
2.2.7 Numerical Results for Low Contrasts
2.2.8 Breakdown for Extremely Low Contrasts
2.2.9 Field-Based-Stabilized Formulations
2.2.10 Numerical Results for Extremely Low Contrasts
2.3 Perfectly Conducting Objects
2.3.1 Comments on the Integral Equations
2.3.2 Internal-Resonance Problem
2.3.3 Formulations of Open Surfaces
2.3.4 Low-Frequency Breakdown
2.3.5 Accuracy with the RWG Fuctions
2.3.6 Compatibility of the Integral Equations
2.3.7 Convergence to Minimum Achievable Error
2.3.8 Alternative Implementations of MFIE
2.3.9 Curl-Conforming Basis Functions for MFIE
2.3.10 LN-LT Type Basis Functions for MFIE and CFIE
2.3.11 Excessive Discretization Error of the Identity Operator
2.4 Composite Objects with Multiple Dielectric and Metallic Regions
2.4.1 Special Case: Homogeneous Dielectric Object
2.4.2 Special Case: Coated Dielectric Object
2.4.3 Special Case: Coated Metallic Object
2.5 Concluding Remarks
3 Iterative Solutions of Electromagnetics Problems with MLFMA
3.1 Factorization and Diagonalization of the Green’s Function
3.1.1 Addition Theorem
3.1.2 Factorization of the Translation Functions
3.1.3 Expansions
3.1.4 Diagonalization
3.2 Multilevel Fast Multipole Algorithm
3.2.1 Recursive Clustering
3.2.2 Far-Field Interactions
3.2.3 Radiation and Receiving Patterns
3.2.4 Near-Field Interactions
3.2.5 Sampling
3.2.6 Computational Requirements
3.2.7 Anterpolation
3.3 Lagrange Interpolation and Anterpolation
3.3.1 Two-Step Method
3.3.2 Virtual Extension of the θ-φ Space
3.3.3 Sampling at the Poles
3.3.4 Interpolation of Translation Operators
3.4 MLFMA for Hermitian Matrix-Vector Multiplications
3.5 Strategies for Building Less-Accurate MLFMA
3.6 Iterative Solutions of Surface Formulations
3.6.1 Hybrid Formulations of PEC Objects
3.6.2 Iterative Solutions of Normal Equations
3.6.3 Iterative Solutions of Dielectric Objects
3.6.4 Iterative Solutions of Composite Objects with Multiple Dielectric and Metallic Regions
3.7 MLFMA for Low-Frequency Problems
3.7.1 Factorization of the Matrix Elements
3.7.2 Low-Frequency MLFMA
3.7.3 Broadband MLFMA
3.7.4 Numerical Results
3.8 Concluding Remarks
4 Parallelization of MLFMA for the Solution of Large-Scale Electromagnetics Problems
4.1 On the Parallelization of MLFMA
4.2 Parallel Computing Platforms for Numerical Examples
4.3 Electromagnetics Problems for Numerical Examples
4.4 Simple Parallelizations of MLFMA
4.4.1 Near-Field Interactions
4.4.2 Far-Field Interactions
4.5 The Hybrid Parallelization Strategy
4.5.1 Aggregation Stage
4.5.2 Translation Stage
4.5.3 Disaggregation Stage
4.5.4 Communications in Hybrid Parallelizations
4.5.5 Numerical Results with the Hybrid Parallelization Strategy
4.6 The Hierarchical Parallelization Strategy
4.6.1 Hierarchical Partitioning of Tree Structures
4.6.2 Aggregation Stage
4.6.3 Translation Stage
4.6.4 Disaggregation Stage
4.6.5 Communications in Hierarchical Parallelizations
4.6.6 Irregular Partitioning of Tree Structures
4.6.7 Comparisons with Previous Parallelization Strategies
4.6.8 Numerical Results with the Hierarchical Parallelization Strategy
4.7 Efficiency Considerations for Parallel Implementations of MLFMA
4.7.1 Efficient Programming
4.7.2 System Software
4.7.3 Load Balancing
4.7.4 Memory Recycling and Optimizations
4.7.5 Parallel Environment
4.7.6 Parallel Computers
4.8 Accuracy Considerations for Parallel Implementations of MLFMA
4.8.1 Mesh Quality
4.9 Solutions of Large-Scale Electromagnetics Problems Involving PEC Objects
4.9.1 PEC Sphere
4.9.2 Other Canonical Problems
4.9.3 NASA Almond
4.9.4 Flamme
4.10 Solutions of Large-Scale Electromagnetics Problems Involving Dielectric Objects
4.11 Concluding Remarks
5 Applications
5.1 Case Study: External Resonances of the Flamme
5.2 Case Study: Realistic Metamaterials Involving Split-Ring Resonators and Thin Wires
5.3 Case Study: Photonic Crystals
5.4 Case Study: Scattering from Red Blood Cells
5.5 Case Study: Log-Periodic Antennas and Arrays
5.5.1 Nonplanar Trapezoidal-Tooth Log-Periodic Antennas
5.5.2 Circular Arrays of Log-Periodic Antennas
5.5.3 Circular-Sectoral Arrays of Log-Periodic Antennas
5.6 Concluding Remarks
Appendix 411
A.1 Limit Part of the ϰ Operator 411
A.2 Post Processing 412
A.2.1 Near-Zone Electromagnetic Fields 413
A.2.2 Far-Zone Fields 414
A.3 More Details of the Hierarchical Partitioning Strategy 423
A.3.1 Aggregation/Disaggregation Stages 423
A.3.2 Translation Stage 424
A.4 Mie-Series Solutions 425
A.4.1 Definitions
A.4.2 Debye Potentials
A.4.3 Electric and Magnetic Fields
A.4.4 Incident Fields
A.4.5 Perfectly Conducting Sphere
A.4.6 Dielectric Sphere
A.4.7 Coated Perfectly Conducting Sphere
A.4.8 Coated Dielectric Sphere
A.4.9 Far-Field Expressions
A.5 Electric-Field Volume Integral Equation
A.6 Calculation of Some Special Functions
A.6.1 Spherical Bessel Functions
A.6.2 Legendre Functions
A.6.3 Gradient of Multipole-to-Monopole Shift Functions
A.6.4 Gaunt Coefficients
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Ozgur Ergul ,Levent Gurel,The Multilevel,Algorithm