## Numerical Analysis for Electromagnetic Integral EquationsImprove EM simulation efforts fast with this applications-focused resource. Bridging the gap between abstract academic treatments and the real-world needs of engineers, this timely work introduces various surface integral equation formulations, approaches to discretizing the integral equations, and measures of solution accuracy. It gives you numerical methods for 2D radiation and scattering problems, emphasizing concrete solution error bounds with exactly given constants. Moreover, the book provides techniques for higher order basis functions and 3D problems, focusing on smooth scatterers and edge singularity effects. |

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### Contents

Geometrical Singularities and the Flat Strip | |

511 Normal Operator Approximation | |

512 Discretized Operator Spectrum | |

513 Spectral Error | |

514 Spectral Error for LowOrder Basis Functions | |

515 Magic 13 Discretization | |

516 Quadrature Error | |

518 Scattering Amplitude Error | |

Surface Integral Equation Formulations and the Method of Moments | |

21 Electric Field Integral Equation | |

211 2D Scattering Problems | |

22 Magnetic Field Integral Equation | |

221 2D Scattering Problems | |

231 2D Scattering Problems | |

241 Vector Basis Functions | |

25 Number of Unknowns | |

26 Scattering Amplitude Scattering Width and Radar CrossSection | |

27 Error Measures | |

28 Basic Concepts of Modal Error Analysis | |

282 Mesh Nyquist Frequency | |

References | |

Error Analysis of the EFIE | |

31 TMEFIE with Ideal Discretizations | |

311 Discretized Operator Spectrum | |

312 Comparison of the Discretized and Exact Operator Spectra | |

313 Spectral Error | |

314 Spectral Error for LowOrder Basis Functions | |

315 Current Solution Error | |

316 Scattering Amplitude Error | |

37 Variational Principles the Moment Method and Superconvergence | |

321 Superconvergence | |

322 Idealizing Assumptions | |

33 TMEFIE with Nonideal Discretizations | |

332 Reducing Quadrature Error | |

333 Geometrical Discretization Error | |

34 TEEFIE | |

342 Spectral Error for LowOrder Basis Functions | |

343 Quadrature Error | |

344 Geometrical Discretization Error | |

35 Solution Error for Other Smooth Scatterers | |

36 Summary | |

References | |

Error Analysis of the MFIE and CFIE | |

41 TMEFIE with Ideal Discretizations | |

412 Discretized Operator Spectrum | |

413 Spectral Error | |

414 Current Solution Error | |

415 Current Error for the PointPulse Discretization | |

416 Scattering Amplitude Error | |

417 Scattering Amplitude Error for the PointPulse Discretization | |

42 Nonideal Discretizations | |

422 Single Integration Point | |

423 Geometrical Discretization Error | |

43 CFIE | |

44 Solution Error for Other Smooth Scatterers | |

45 Superconvergence and Regularization | |

451 Convergence Rates for EFIE and MFIE | |

452 Nonsuperconvergent Cases | |

453 First and SecondKind Operators | |

454 HigherOrder Basis Functions | |

46 Summary | |

References | |

521 Discretized Operator Spectrum | |

522 Spectral Error | |

523 Current Solution Error | |

524 Quadrature Error | |

53 Edge Error Analysis | |

54 Wedges | |

55 Summary | |

References | |

Resonant Structures | |

61 Resonance and the EFIE Operator Spectrum | |

611 QuasiResonant Modes | |

612 Resonance and the Method of Moments | |

63 Cavities | |

631 Resonant Case | |

632 NearResonant Case | |

633 Spectral Error | |

634 Scattering Amplitude Error | |

64 Summary | |

Error Analysis for 3D Problems | |

71 Flat Plate | |

711 Moment Matrix Spectrum | |

712 Rooftop Basis Functions | |

72 RWG Basis Functions | |

721 Nonideal Discretizations | |

72 Summary | |

HigherOrder Basis Functions | |

81 HigherOrder Basis Functions for 2D Problems | |

82 Interpolatory Polynomials | |

822 Interpolation Transfer Function | |

823 Spectral Error | |

825 Scattering Amplitude Error | |

83 Orthogonal Polynomials | |

832 Projection Transfer Function | |

833 Spectral Error | |

835 Scattering Amplitude Error | |

84 3D Problems | |

841 Numerical Results | |

85 Summary | |

References | |

Operator Spectra and Iterative Solution Methods | |

91 Krylov Subspace Algorithms | |

911 CG Algorithm | |

913 Residual Error | |

914 Condition Number | |

915 Other Krylov Subspace Methods | |

93 Condition Number Estimates | |

932 Circular Cylinder TEEFIE | |

934 Flat Strip TEEFIE | |

936 HigherOrder Basis Functions | |

937 Flat Plate 3D | |

94 LowFrequency Breakdown | |

941 Helmholtz Decomposition | |

95 Preconditioners | |

About the Author | |

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### Common terms and phrases

accuracy algorithm aliasing error approximation asymptotic basis functions cavity CFIE Chapter circular cylinder coecients computational electromagnetics condition number convergence rate curl-free current and scattering current solution error dened dierence discretization error edge eect EFIE eigenfunctions eigenvalue eigenvalue estimates error analysis error contribution evaluated exact Figure Fourier transform high-order higher-order basis functions ideal discretization IEEE incident eld integral equation integral operator internal resonance iteration kernel Lagrange polynomials linear system low-order basis functions matrix elements mesh element method of moments nite normal Nyquist frequency obtained operator eigenvalues Operator Spectrum plane wave point testing polynomial basis projection error pulse expansion functions pulse function quadrature error quadrature rule radiated RCS error relative RMS resonance frequency resonant mode rst-order scattered eld scattering amplitude error scattering problems Section singular spatial frequency spectral error superconvergence surface current testing and expansion testing functions tions TM polarization TM-EFIE triangle functions