Hybrid Methods

Numerical methods for the computation of scattering problems can be grouped roughly into two categories: high-frequency asymptotic method, and full-wave numerical method. The physical optics method (PO), geometrical optics method (GO), geometrical theory of diffraction (GTD), physical theory of diffraction (PTD), and the shooting and bouncing ray method (SBR) are all examples of the former group. MoM, FEM and FDTD are the most popular examples of the latter group. These methods are all capable of independently solving EM problems of a particular range. However, these methods are distinct in terms of numerical performance. Each method has its own advantages and disadvantages. We usually are able to construct problem-tailored solution scheme by combining the advantage of different numerical methods, which provides both accurate and efficient result. Generally speaking, in CEM, two types of ideas exist in the hybridization. In the first type, the computational domain is decomposed into different regions and different schemes are applied to each region. The hybrid finite-element boundary-integral (FE-BI) is one of the examples. In the second type, the dimension in the EM problem is separated and we apply a different method for each dimension according to mode theory or variable separation theory. In this chapter, we present the scheme combining high-frequency asymptotic method and full-wave method in the first section, and the hybrid full-wave methods in the second one.