Divide and Rule: An Efficient Strategy of Computational Electromagnetics for Complex Electromagnetic Problems

Domain Decomposition Method (DDM) is one of the most efficient and powerful methods for solving extra-large scale and intricate electromagnetic (EM) problems, fully embodying the divide-and-conquer philosophy. It provides the strategy of dealing with a computationally huge task that is not easy to be solved directly — dividing the task into a number of smaller ones, i.e. sub-tasks, each can be readily solved independently and employing appropriate transmission conditions (TCs) accounting for the interactions communication among these sub-tasks. This paper presents a comprehensive overview of DDM, highlighting its fundamental principles and wide-ranging applications in many diverse areas, such as very-large-scale integration circuits, antenna array radiation, wave scattering, and so on. In the evolution of this technology, DDM has gradually manifested its remarkable power of tackling complex EM problems through its merging with Laplace, wave, Maxwell equations, as well as surface integral-equations (IEs) and volume IEs. The advanced algorithms further evolved such as overlapped DDM and non-overlapped DDM are also reviewed. The efficiency of the DDMs depends strongly on the TCs of EM fields at the interface among adjacent sub-domains. The diversity of TCs in differential and integral equations generates a variety of DDMs. Due to the independence of sub-domains, the DDMs are inherently well-suited for parallel processing with high flexibility, making them particularly effective for EM full-wave simulations on distributed computers. Finally, a list of remaining challenging technical issues and future perspective on the fast-evolving field will be provided.