A FETI-DP Method for the Analysis of Finite Periodic Metamaterial Arrays

A domain decomposition method (DDM) combined with edge-based finite-element method, namely the dual-primal finite element tearing and interconnecting (FETI-DP), is formulated to solve the problems of finite periodic metamaterial arrays. In this method, the entire computational domain is partitioned into several non-overlapping subdomains. At the subdomain interfaces, Robin-type transmission condition is used to ensure the continuity of the electric and magnetic fields. The dual-primal idea with two Lagrange multipliers is introduced. The volume unknowns are reduced to interface unknowns by Gaussian elimination so that the computational complexity is reduced. For the finite periodic metamaterial arrays, each substructure can be treated as a subdomain, the geometrical repetition of the substructures can be full exploited to accelerate the simulation and reduce the memory requirement. Example of the analysis of a perfect metarnaterial absorber is presented. Numerical results demonstrate the accuracy and efficiency of this method.