An Accelerated FETI-DPEM Method for Modeling Photonic Crystal Nanocavities

The dual-primal finite element tearing and interconnecting (FETI-DPEM) method, as an application of a nonoverlapping domain decomposition method to the finite element analysis of electromagnetic problems, is applied to the three-dimensional (3D) full-wave simulation of a high quality (Q) factor photonic crystal (PhC) nanocavity in an optically thin dielectric slab. Curvilinear tetrahedral elements and higher-order vector basis functions are employed in the FEM to accurately represent the field in the PhC nanocavity. Geometrical repetitions associated with PhCs nanocavities are fully exploited, which significantly reduces the computational complexity and memory requirement. Moreover, due to its domain decomposition nature, the FETI-DPEM method is highly parallelizable, which further accelerates the computation using parallel computing techniques. In addition, the asymptotic waveform evaluation method and the complex frequency hopping technique are implemented together with the FETI-DPEM method to obtain a fast frequency sweep by calculating the frequency responses in some automatically chosen expansion frequencies. As a result, such a method is ideally suited for the full-wave analysis of PhC nanocavities. Simulations of a high Q PhC nanocavity using the FETI-DPEM method are carried out to demonstrate the efficiency of the method. The calculated Q factors are compared with previously published data.