Research On Electromagnetic Field Integral Equation-Based Domain Decomposition Methods

With the development of information science and technology, there are more and more com-plex problems in electromagnetic field. The current electromagnetic simulation technologies do not meet all the requirements in Electromagnetic Engineering, and challenging electromagnetic problems still continue to emerge. These problems revolve large-scale, electrically large size, multiscale, inhomogeneous, etc. It is desirable for Computational Electromagnetics to pro-vide more efficient algorithms for such challenging problems. Today, fast algorithms, parallel algorithms, and domain decomposition methods (DDM) have been regarded as important ap-proaches to solve the above complex electromagnetic problems. This thesis investigates the integral equation-based domain decomposition methods, and the main results and innovation points are as follows:1. An integral equation-based non-overlapping domain decomposition method (NDDM) is proposed for analyzing EM scattering from electrically large PEC objects. The integral equation is first built on the entire PEC surface, and the RWG basis functions are used to expand the equivalent surface current on the entire surface. Then each full-RWG basis function across some boundary curve is split into two half-RWG basis functions whose unknown coefficients are constrained by the boundary current continuity (using the ex-plicit boundary condition). The convergence of the proposed NDDM is investigated the-oretically by numerical analyzing. This NDDM is especially conducive to the design of the generic simulation software.2. A hybrid algorithm of the NDDM and the MLFMA is proposed. The structural features of the local model equations are used to construct preconditioners for these local model equations, further accelerating the hybrid algorithm.3. An overlapping domain decomposition method based on the electric/magnetic current combined field integral equation formulation (JMCFTE-ODDM) is proposed for solv-ing EM scattering from homogeneous dielectric objects. Compared with the existing ODDMs, this ODDM keeps employing the RWG basis functions, and has stronger con-vergence property and lower memory requirement.4. A non-overlapping domain decomposition method based on the electric/magnetic current combined field integral equation formulation (JMCFIE-NDDM) is proposed for solving EM scattering from homogeneous dielectric objects. The JMCFIE formulation is first built on the entire surface of the object, then the RWG functions are used to expand the electric and magnetic currents on the entire surface. Then each full-RWG function across some boundary curve is split into two half-RWG functions whose unknown coef-ficients are constrained by the boundary electric and magnetic currents continuity (using the explicit boundary condition). The convergence of the proposed NDDM is investigated theoretically by numerical analyzing. This NDDM is especially conducive to the design of the generic simulation software.