Efficient Topology Optimization of Photonic Devices Using Domain Decomposition Finite Element Method

This paper presents a domain decomposition finite element method (DD-FEM) to accelerate topology optimization of photonic devices. In the proposed approach, the structure invariant region is precomputed and transformed into a reduced boundary conditions for the design region, allowing only the design region to be reanalyzed during optimization. The applicability of the method is demonstrated through the analysis and optimal design of a matching coupler between a strip waveguide and a subwavelength-grating (SWG) waveguide, as well as a waveguide lens. Under the same optimization settings, DD-FEM reduces the computational time per-analysis by approximately a factor of 2-3 and the memory requirement to about one third of that of a standard FEM analysis, making it particularly advantageous when the design region is small relative to the overall computational domain. In addition, we investigate a thresholding method for the dense interface matrix, where small nonzero entries are discarded to further reduce the computational cost of DD-FEM. If an error of about 0.5% in transmitted-power evaluation is acceptable, the linear-system solving time can be reduced to approximately 77% of that without thresholding.