Integral Equations for Electromagnetic Scattering by Wide Scatterers

Integral equation methods for solving electromagnetic scattering problems reduce a two-dimensional problem to a one-dimensional integral equation by formulating the problem in terms of the unknown surface currents on the scattering body or bodies. Similarly, threedimensional scattering problems are reduced to two-dimensional integral equations. The unknown surface currents are approximated by a sum of basis functions times unknown coefficients. The basis functions are usually chosen to be simple piecewise constant or linear functions, although higher-order polynomials or piecewise polynomials are sometimes used. The coefficients are chosen to solve (approximately) the integral equation. The resulting electromagnetic field exactly obeys Maxwell's equations and the radiation condition, but obeys the boundary conditions on the scatterer (s) only approximately. Even if higher-order polynomial basis functions are used, the density of functions on the scatterer must be at least two per wavelength. As a rule of thumb, five to ten functions per wavelength are typical. For 1893