An integral equation domain decomposition method based on hybrid solvers for modeling of electromagnetic radiation

In this paper, an integral equation domain decomposition method based on hybrid solvers (HS-DDM) are developed for modeling of electromagnetic radiation problems. Based on the philosophy of `divided and conquer´, the IE-DDM divides the original multi-scale problem into many closed non-overlapping sub-domains. The Robin transmission conditions ensure the continuity of the currents across adjacent sub-domains. The meshes of different sub-domains can be allowed to be non-conformal, different basis functions based on large and small patches can be used to reduce the dimension of matrix and model the geometry properly based on its local property. Further, different fast solvers can be easily incorporated into the framework of IE-DDM to reduce the time and memory consumption according to the property of different sub-domains. Here, the multilevel fast multipole algorithm (MLFMA) and hierarchical (ℋ-) matrices method are adopted in this HS-DDM to realize efficient solution of multi-scale electromagnetic radiation problems. The MLFMA is used in large, smooth sub-domains, while ℋ-Matrices is used instead in small, dense sub-domains where the MLFMA is inefficient. Numerical results demonstrate the validity of the HS-DDM.