| The core of domain decomposition method (DDM) is that it decomposes the original problem domain into several non-overlapping sub-domains, and solves every sub-domain independently. In this way, the memory requirements are reduced. The DDM combined with finite element method (FEM) can solve geometrically complex and electrically large electromagnetic problems efficiently. 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.The anisotropic perfectly matched layer (PML) is introduced to this method for the analysis of electromagnetic scattering problems. The formulation is modified when the interface locates in the PML. By the numerical examples, we find that this method is not only implemented easily but also has good performance. To farther reduce the unknowns, the locally conformal PML are introduced to this method for solving electromagnetic scattering problems. For the numerical examples, we find that this method can reduce the number of unknowns and speed up the solution.When solving periodic electromagnetic problems, we make use of the structure's periodicity, and only the typical sub-domains need to be analyzed. As a result, the periodic electromagnetic problems can be solved more efficiently. At the same time, we implement this algorithm serially, so that this kind of problems can be solved quickly on single PC.Since every sub-domain is solved independently by use of direct methods and there are few data communications between subdomains, therefore, DDM is highly parallel. The parallel computing platform is constructed using 17 PCs, and the DDM is made to be a parallel algorithm on the platform. Numerical examples are given to demonstrate the accuracy and efficiency of this method. |
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