The Method of Moments in Electromagnetics

TLDR: In this article, the Fast Multipole Method (FMM) was used to solve the problem of two-dimensional problems with three-dimensional surfaces, and the Matrix-Vector Product Addition Theorem (MVPIT) was applied to solve it.

Abstract: PREFACE Computational Electromagnetics Computational Electromagnetics Algorithms A Brief Review of Electromagnetics Maxwell's Equations Electromagnetic Boundary Conditions Formulations for Radiation Vector Potentials Near and Far Fields Equivalent Problems Surface Integral Equations The Method of Moments Electrostatic Problems The Method of Moments Common Two-Dimensional Basis Functions Solution of Matrix Equations Thin Wires Thin Wire Approximation Thin Wire Excitations Solving Hallen's Equation Solving Pocklington's Equation Thin Wires of Arbitrary Shape Examples two-dimensional Problems Two-Dimensional EFIE Two-Dimensional MFIE Examples Bodies of Revolution BOR Surface Descriptions Surface Current Expansion on a BOR EFIE for a Conducting BOR MFIE for a Conducting BOR Notes on Software Implementation Examples three-dimensional Problems Representation of Three-Dimensional Surfaces Surface Currents on a Triangle EFIE for Three-Dimensional Conducting Surfaces MFIE for Three-Dimensional Conducting Surfaces Notes on Software Implementation Considerations for Modeling with Triangles Examples The Fast Multipole Method The Matrix-Vector Product Addition Theorem FMM Matrix Elements One-Level Fast Multipole Algorithm Multilevel Fast Multipole Algorithm Notes on Software Implementation Preconditioning Examples Integration One-Dimensional Integration Integration over Triangles INDEX References appear at the end of each chapter.