The Method of Moments in Electromagnetics

Walton C. Gibson was born in Birmingham, Alabama, USA on December 9, 1975. He received the B.S. degree in electrical engineering from Auburn University in 1996, and the M.S. degree in electrical engineering from the University of Illinois Urbana-Champaign in 1998. He is a recognized authority in the area of computational electromagnetics (CEM), and has authored The Method of Moments in Electromagnetics, a textbook geared to graduate-level courses in CEM, as well as the research community and practicing professionals. He is the owner and President of Tripoint Industries, Inc., through which he has authored lucernhammer, an industry-standard suite of radar cross section solver codes implementing low and high-frequency numerical techniques. His professional interests include electromagnetic theory, computational electromagnetics, moment methods, numerical algorithms and parallel computing.

1. Computational Electromagnetics. 1.1. CEM Algorithms. 2. The Method of Moments. 2.1. Electrostatic Problems. 2.2. The Method of Moments. 2.3. Common One-Dimensional Basis Functions. 3. Radiation and Scattering. 3.1. Maxwell’s Equations. 3.2. Electromagnetic Boundary Conditions. 3.3. Formulations for Radiation. 3.4. Vector Potentials. 3.5. Near and Far Field. 3.6. Formulations for Scattering. 4. Solution of Matrix Equations. 4.1. Direct Methods. 4.2. Iterative Methods. 4.3. Software for Linear Systems. 5. Thin Wires. 5.1. Thin Wire Approximation. 5.2. Thin Wire Excitations. 5.3. Hallen’s Equation. 5.4. Pocklington’s Equation. 5.5. Thin Wires of Arbitrary Shape. 5.6. Examples. 6. Two-Dimensional Problems. 6.1. Conducting Objects. 6.2. Dielectric and Composite Objects. 7. Bodies of Revolution. 7.1. BOR Surface Description. 7.2. Expansion of Surface Currents. 7.3. EFIE. 7.4. MFIE. 7.5. Solution. 7.6. nMFIE. 7.7. Numerical Discretization. Notes on Software Implementation. Examples. 7.10. Treatment of Junctions. 8. Three-Dimensional Problems. 8.1. Modeling of Three-Dimensional Surfaces. 8.2. Expansion of Surface Currents. 8.3. EFIE. 8.4. MFIE. 8.5. nMFIE. 8.6. Enforcement of Boundary Conditions. 8.3. Software Implementation Notes. 8.8. Numerical Examples. 9. Adaptive Cross Approximation. 9.1. Rank Deficiency. 9.2. Adaptive Cross Approximation. 9.3. Clustering Techniques. 9.4. LU Factorization of ACA-Compressed Techniques. 9.5. Solutionof theACA-Compressed Matrix System. 9.6. Software Implementation Notes. 9.7. Numerical Examples. 10. Multi-Level Adaptive Cross Approximation. 10.1. MLACA Compression of Matrix Blocks. 10.2. Direct Solution of MLACA-Compressed Matrix System. 10.3. Software Implementation Notes. 10.4. Numerical Exqamples. 11. The Fast Multipole Method. 11.1 The N-Body Problem. 11.2. Matrix-Vector Product. 11.3. One-Level Fast Multipole Algorithm. 11.4. Multi-Level Fast Multipole Algorithm (MLFMA). 11.5. Preconditioners. 11.6. Software Implementation Notes. 11.7. Numerical Examples. 12. Integrations. 12.1. One-Dimensional Integration. 12.2. Integration over Triangles. A. Scattering Using Physical Optics. Index.