There have been intense efforts in fullwave inverse design of large-scale metasurface with potentially broad-bandwidth / multi-frequency and multi-functional performance. However, conventional simulation tools used in the design process show poor scalability in accuracy and efficiency with size (thickness and diameter). Fast direct solvers based on volume integral equation (VIE) can reach linear scalability but are very difficult to implement, especially beyond two-dimensional settings. Here, we use the Duan-Rokhlin method, a convenient VIE solver, to simulate large structures with near-optimal time complexity O(NlogN). We demonstrate its high efficiency and accuracy in large-scale simulation and inverse design process.
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