翻译：其次针对现有完全型区域分解合元极方法要求有限元与边界元分区匹配、有限-边界元间网格共形的局限提出一种双重非共形完全型区域分解合元极方法。其基本思想是将内部有限元求解区域和外部边界积分区域进行独立地几何分区、网格剖分和离散。在该方法中根据合元极方法的基本求解原理提出了一个通用的双重区域分解框架。有限元区域和边界元区域通过一阶Robin传输条件耦合有限元子区域之间通过完全型二阶Robin条件进行

Secondly, in response to the limitations of the existing fully decomposed hybrid finite and boundary element method, which requires matching of the finite and boundary element meshes and conformal meshing between the two, a new double non-conformal fully decomposed hybrid element method is proposed. The basic idea is to independently partition, mesh and discretize the interior finite element solving region and the exterior boundary integral solving region. In this method, a universal double region decomposition framework is proposed based on the basic solving principles of the hybrid element method. The finite element region and the boundary element region are coupled by a first-order Robin transmission condition, the finite element sub-regions are connected by a second-order fully decomposed Robin condition, and the boundary element sub-regions are connected by an internal penalty transmission condition. A new efficient Schwarz-type preconditioner for double region decomposition is proposed by sparsifying the boundary element sub-matrix. Compared with the existing fully decomposed hybrid element method, this method is more flexible and versatile. Finally, in response to the problem of large unknowns in pure finite element meshing and inefficient modeling of uniform media in traditional hybrid element methods, a new efficient mixed finite element, composite media integral equation, and multi-layer fast multipole electromagnetic modeling method is proposed, and the method is fully decomposed based on the double region decomposition framework. In this method, the internal finite element equations in the uniform media sub-regions are replaced by the media integral equations, significantly reducing the number of unknowns. Coupling factors are added to the media integral equations to improve the condition number of the final system matrix and speed up the iteration. It is more efficient in solving electromagnetic scattering problems such as antenna-multilayer media antenna enclosure integration