A multi-mesh finite element method for phase-field based photonic band structure optimization

A novel finite element method with multiple meshes is proposed, which is applied to solve the phase-field models for photonic band structures optimization. In our approach, fine meshes are used for the phase field evolution, which allows fine resolution for shape representations. The coarse meshes are adopted for the finite element analysis of the state equation. Such a multi-mesh approach could save a considerable amount of computational costs. Numerical convergence is illustrated through comparisons between our computational results and benchmarks. The efficiency and robustness of the multi-mesh approach are also shown.