Integral Equations and Other Field Representations

Integral Equations and Other Field Representations

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The field integral representations given in the previous chapter, although of sufficient generality, are often inconvenient and possibly inefficient for specific applications. Also, their integrands are highly singular, requiring special treatment when the observation point is in the source region. This difficulty cannot be eliminated, but any reduction in the integrand's singularity is desirable for achieving higher accuracies in numerical computations involving such integrals. Obviously, a variety of field representations, integral equations, and formal solutions could be derived, many of which can be applicable only to a specific situation. This chapter will consider some alternative field representations to construct integral equations that are among the most frequently used. First, we shall develop three-dimensional representations. Many of the two-dimensional representations can then be reduced from the three-dimensional ones. However, for scattering applications a larger variety of two-dimensional representations is available primarily because the topic has been extensively studied.

Chapter Contents:

  • 3.1 Three-Dimensional Integral Equations
  • 3.2 Two-Dimensional Representations
  • Problems
  • Bibliography

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

Other keywords: integral equation; three-dimensional representation; two-dimensional representation; field integral representation; numerical computation; integrand singularity; scattering application

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

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