Nonconformal FETI-DP Methods for Large-Scale Electromagnetic Simulation

Two nonconformal dual-primal finite element tearing and interconnecting (FETI-DP) methods are formulated for the finite element simulation of large-scale three-dimensional (3-D) electromagnetic problems through domain decomposition method (DDM). Both methods implement the Robin-type transmission condition at the subdomain interfaces to preserve the fast convergence of the iterative solution of the global interface problem in the high-frequency region. The first nonconformal FETI-DP method extends the conformal FETI-DP algorithm, which is based on two Lagrange multipliers, to deal with nonconformal interface and corner meshes, and the second method employs cement elements on the interface and combines the global primal unknowns with the global dual unknowns. Similar to the conformal FETI-DP method, the two methods formulate a global coarse problem related to the degrees of freedom at the subdomain corner edges to propagate the residual error to the whole computational domain in the iterative solution of the global interface equation. Numerical results for the simulation of finite antenna arrays, photonic crystal cavities, and dielectric-rod-array metamaterial slabs are presented to demonstrate the application, accuracy, efficiency, and capability of the two proposed nonconformal FETI-DP methods.