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

1. Auflage 2014
ISBN: 978-1-119-97741-4
Verlag: Wiley

Buch, Englisch, 480 Seiten, Format (B × H): 173 mm x 246 mm, Gewicht: 957 g

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.

Autoren/Hrsg.

Ergul, Ozgur

Gurel, Levent

Inhaltsverzeichnis

Preface xi

List of Abbreviations xiii

1 Basics 1

1.1 Introduction 1

1.2 Simulation Environments Based on MLFMA 2

1.3 From Maxwell’s Equations to Integro-Differential Operators 3

1.4 Surface Integral Equations 7

1.5 Boundary Conditions 9

1.6 Surface Formulations 10

1.7 Method of Moments and Discretization 12

1.7.1 Linear Functions 15

1.8 Integrals on Triangular Domains 21

1.8.1 Analytical Integrals 22

1.8.2 Gaussian Quadratures 26

1.8.3 Adaptive Integration 26

1.9 Electromagnetic Excitation 29

1.9.1 Plane-Wave Excitation 29

1.9.2 Hertzian Dipole 31

1.9.3 Complex-Source-Point Excitation 31

1.9.4 Delta-Gap Excitation 32

1.9.5 Current-Source Excitation 34

1.10 Multilevel Fast Multipole Algorithm 35

1.11 Low-Frequency Breakdown of MLFMA 39

1.12 Iterative Algorithms 41

1.12.1 Symmetric Lanczos Process 42

1.12.2 Nonsymmetric Lanczos Process 44

1.12.3 Arnoldi Process 45

1.12.4 Golub-Kahan Process 45

1.13 Preconditioning 46

1.14 Parallelization of MLFMA 50

2 Solutions of Electromagnetics Problems with Surface Integral Equations 53

2.1 Homogeneous Dielectric Objects 53

2.1.1 Surface Integral Equations 54

2.1.2 Surface Formulations 55

2.1.3 Discretizations of Surface Formulations 58

2.1.4 Direct Calculations of Interactions 60

2.1.5 General Properties of Surface Formulations 67

2.1.6 Decoupling for Perfectly Conducting Surfaces 73

2.1.7 Accuracy with Respect to Contrast 74

2.2 Low-Contrast Breakdown and Its Solution 77

2.2.1 A Combined Tangential Formulation 77

2.2.2 Nonradiating Currents 80

2.2.3 Conventional Formulations in the Limit Case 81

2.2.4 Low-Contrast Breakdown 82

2.2.5 Stabilization by Extraction 82

2.2.6 Double-Stabilized Combined Tangential Formulation 87

2.2.7 Numerical Resul

Über Autor(innen)

Dr Ozgur Ergul, Middle East Technical University, Turkey
Ozgur Ergul received B.Sc., M.S., and PhD degrees from Bilkent University, Turkey, in 2001, 2003 and 2009, respectively, all in electrical and electronic engineering.

Dr Levent Gurel, Bilkent University, Turkey
Levent Gurel received the B.Sc. degree from the Middle East Technical University, Turkey, in 1986, and the M.S. and PhD degrees from the University of Illinois at Urbana-Champaign in 1988 and 1991, respectively, all in electrical engineering.