Integral equations have proven their popularity for the electromagnetic analysis of radiation and scattering problems. The workhorse equations are the electric-field integral equation (EFIE) and the magnetic-field integral equation (MFIE) [1,2]. The development of these equations will be reviewed in the following for perfectly conducting targets and homogeneous dielectric targets. When applied to certain closed surfaces, the original equations exhibit uniqueness difficulties at frequencies where the target surface coincides with a resonant cavity [3]. In addition, the original EFIE and MFIE also fail under certain circumstances for electrically small bodies. Alternate integral equations were proposed to remedy those situations, and these will also be summarized in the following section. In addition, we describe the numerical solution of these equations and report the progress made in recent years associated with the use of hierarchical vector basis functions, and the recent use of singular basis functions.

Chapter Contents:

• 15.1 The EFIE and MFIE for perfectly conducting bodies
• 15.2 Some alternative formulations to remediate fictitious internal resonances
• 15.3 Integral equations for homogeneous dielectric bodies
• 15.4 Formulations that remediate fictitious internal resonances for dielectric targets
• 15.5 Single-source integral equations for dielectric bodies
• 15.6 Low-frequency breakdown of integral equations
• 15.7 Numerical solution of integral equations
• 15.8 Vector basis functions
• 15.9 Interpolatory and hierarchical vector basis functions
• 15.10 Singular vector basis functions
• 15.11 Summary
• References

Inspec keywords: electromagnetic wave scattering; electric field integral equations; magnetic field integral equations; integral equations; method of moments

Other keywords: hierarchical vector basis functions; electromagnetic analysis; radiation; scattering problems; numerical solution; MFIE; original equations; workhorse equations; homogeneous dielectric targets; original EFIE; electric-field integral equation; target surface; alternate integral equations

Subjects: Numerical approximation and analysis; Integral equations (numerical analysis); Electromagnetic wave propagation; Textbooks; Function theory, analysis; Electromagnetic waves: theory