A two-grid method for the phase-field model of photonic band gap optimization

A two-grid method is proposed to solve phase field models, arising from modeling the band gap optimization of photonic crystal design based on the Transverse Electric field (TE mode). In our approach, finite element methods on nested grids are used to solve different Partial Differential Equations (PDEs), say, the Hemholtz equation for the state constrain and the phase field equation for topology evolving, respectively. Dicretization on the coarse and fine grids are performed to balance the costs between the phase evolving and state equation solver. To fuse the two scheme together, additional correction step is necessary in two-grid settings. Furthermore, convergence analysis for the proposed two-grid scheme is established. Finally, numerical examples are presented to show the efficiency and robustness, and it is illustrated that the two-grid method improves the speed of computation while remain the computational accuracy.

Automated summary

A two-grid method is proposed to solve phase field models for the band gap optimization in photonic crystal design based on the TE mode. The method uses finite element methods on nested grids to solve different PDEs and achieves a balance between phase evolving and state equation solver through discretization on coarse and fine grids, along with additional correction steps. The efficiency and robustness of the method are demonstrated through numerical examples, showing improved computation speed without sacrificing accuracy.