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The Multilevel Fast Multipole Algorithm (MLFMA) for Solving Large-Scale Computational Electromagnetics Problems

Book Description

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

  • The book will be useful for post-graduate students, researchers, and academics, studying in the areas of computational electromagnetics, numerical analysis, and computer science, and who would like to implement and develop rigorous simulation environments based on MLFMA.

    Table of Contents

    1. Cover
    2. Series Page
    3. Title Page
    4. Copyright
    5. Preface
    6. List of Abbreviations
    7. Chapter 1: Basics
      1. 1.1 Introduction
      2. 1.2 Simulation Environments Based on MLFMA
      3. 1.3 From Maxwell's Equations to Integro-Differential Operators
      4. 1.4 Surface Integral Equations
      5. 1.5 Boundary Conditions
      6. 1.6 Surface Formulations
      7. 1.7 Method of Moments and Discretization
      8. 1.8 Integrals on Triangular Domains
      9. 1.9 Electromagnetic Excitation
      10. 1.10 Multilevel Fast Multipole Algorithm
      11. 1.11 Low-Frequency Breakdown of MLFMA
      12. 1.12 Iterative Algorithms
      13. 1.13 Preconditioning
      14. 1.14 Parallelization of MLFMA
    8. Chapter 2: Solutions of Electromagnetics Problems with Surface Integral Equations
      1. 2.1 Homogeneous Dielectric Objects
      2. 2.2 Low-Contrast Breakdown and Its Solution
      3. 2.3 Perfectly Conducting Objects
      4. 2.4 Composite Objects with Multiple Dielectric and Metallic Regions
      5. 2.5 Concluding Remarks
    9. Chapter 3: Iterative Solutions of Electromagnetics Problems with MLFMA
      1. 3.1 Factorization and Diagonalization of the Green's Function
      2. 3.2 Multilevel Fast Multipole Algorithm
      3. 3.3 Lagrange Interpolation and Anterpolation
      4. 3.4 MLFMA for Hermitian Matrix-Vector Multiplications
      5. 3.5 Strategies for Building Less-Accurate MLFMA
      6. 3.6 Iterative Solutions of Surface Formulations
      7. 3.7 MLFMA for Low-Frequency Problems
      8. 3.8 Concluding Remarks
    10. Chapter 4: Parallelization of MLFMA for the Solution of Large-Scale Electromagnetics Problems
      1. 4.1 On the Parallelization of MLFMA
      2. 4.2 Parallel Computing Platforms for Numerical Examples
      3. 4.3 Electromagnetics Problems for Numerical Examples
      4. 4.4 Simple Parallelizations of MLFMA
      5. 4.5 The Hybrid Parallelization Strategy
      6. 4.6 The Hierarchical Parallelization Strategy
      7. 4.7 Efficiency Considerations for Parallel Implementations of MLFMA
      8. 4.8 Accuracy Considerations for Parallel Implementations of MLFMA
      9. 4.9 Solutions of Large-Scale Electromagnetics Problems Involving PEC Objects
      10. 4.10 Solutions of Large-Scale Electromagnetics Problems Involving Dielectric Objects
      11. 4.11 Concluding Remarks
    11. Chapter 5: Applications
      1. 5.1 Case Study: External Resonances of the Flamme
      2. 5.2 Case Study: Realistic Metamaterials Involving Split-Ring Resonators and Thin Wires
      3. 5.3 Case Study: Photonic Crystals
      4. 5.4 Case Study: Scattering from Red Blood Cells
      5. 5.5 Case Study: Log-Periodic Antennas and Arrays
      6. 5.6 Concluding Remarks
    12. Appendix
      1. A.1 Limit Part of the <img xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ibooks="http://vocabulary.itunes.apple.com/rdf/ibooks/vocabulary-extensions-1.0" src="images/b01-math-0001.png" alt="b01-math-001" style="vertical-align:middle;"></img> Operator Operator
      2. A.2 Post Processing
      3. A.3 More Details of the Hierarchical Partitioning Strategy
      4. A.4 Mie-Series Solutions
      5. A.5 Electric-Field Volume Integral Equation
      6. A.6 Calculation of Some Special Functions
    13. References
    14. Index
    15. End User License Agreement