Inward-looking and outward-looking formulations for scattering from penetrable objects

A number of approaches for solving the problem of scattering from two-dimensional penetrable objects using the finite-element method or other differential-equation-based solutions are reviewed. Different ways of joining the numerical solution on a finite domain to a field representation that satisfies the Sommerfield radiation condition in the infinite exterior domain are also reviewed within the paradigm of the equivalence principle of electromagnetics. Depending on the region where the solution is deduced first in an inherently sequential process, these approaches can often be classified as either inward-looking or outward-looking. Although inward-looking formulations may exhibit computational advantages, outward-looking formulations appear preferable for electrically large domains because of internal resonance difficulties that may arise when solving the isolated interior problem first in an inward-looking formulation.>