| This dissertation presents a domain decomposition method as an effective and efficient preconditioner for frequency domain FEM solution of geometrically complex and electrically large electromagnetic problems. The method reduces memory requirements by decomposing the original problem domain into several non-overlapping and possibly repeatable sub-domains. At the heart of this research are the Robin-to-Robin map, the "cement" finite element coupling of non-conforming grids and the concept of duality paring. The Robin's transmission condition is employed on interfaces between adjacent sub-domains to enforce continuity of electromagnetic fields and to ensure the sub-domain problems are well-posed. Through the introduction of cement variables, the meshes at the interface could be non-conformal which significantly relaxes the meshing procedures. By following the spirit of duality paring a symmetric system is obtained to better reflect physical nature of the problem. These concepts in conjunction with the so-called finite element tearing and interconnecting algorithm form the basic modules of the present domain decomposition method. To enhance the convergence of DDM solver, the Krylov solvers instead of classical stationary solvers are employed and studied.; In order to account the radiation condition exactly thus eliminating spurious reflection, a boundary element formulation is hybridized with the present DD method, also through the aforementioned novel concepts. One of the special cases of present hybridization is the well known hybrid finite element and boundary element method. It will be shown that the proposed hybrid offers simultaneously: (1) symmetry, (2) modularity, (3) non-conformity between FEM and BEM domains, (4) free of internal resonance, and (5) natural and effective preconditioning scheme that guarantees spectral radius less or equal to one.; Lastly this dissertation presents a DDM solution scheme for analyzing electromagnetic problems involving multiple separable scatterers. The method first decomposes the original problem into several disjoint sub-regions. In each sub-region, the domain decomposition method is further applied rendering geometrically complicated and electrically large sub-region problems tractable. The sub-regions communicate through the near-field Green's function. To overcome the vast computational costs required in exchanging information between electrically large sub-regions, the adaptive cross approximation algorithm is adopted to expedite the process. |
