Hybridization of finite methods with other techniques to solve complex problems

Summary form only given. Finite methods are well-suited for modeling complicated geometries. Hybrid methods are often used to overcome the difficulty of modeling large complicated problems. In the past, finite methods have been coupled to modal methods, integral equation methods, and high frequency or asymptotic methods with various degrees of success. The difficulty comes in coupling the two different methods in an accurate and efficient manner. The coupling can be done in many different ways. Between finite methods and integral equation methods, the coupling is straightforward. However between finite methods and high frequency methods, the choice of how to couple the two methods is not as clear. Two rigorous mechanisms to perform the coupling are to use either a generalized scattering matrix or modal expansion at the interface between the two methods. This approach produces very good solutions, but may be computatiorially expensive. Another approach is to use approximations to decouple the multiple interactions which are present between the two methods. This approach is very efficient and simple in implementation, but may be inaccurate. We review what hybrid methods have been proposed in the past and where we see the future research directions in the use of hybrid methods to solve. real-world problems of interest.