Fig. 2: Benchmarks on a large-scale disordered system.
From: Fast multi-source nanophotonic simulations using augmented partial factorization

a, The system considered consists of 30,000 randomly positioned cylindrical scatterers in air, each with refractive index of 2.0 and diameter between 0.3λ and 0.8λ, where λ is the wavelength. A periodic boundary condition is used in the y direction, and perfectly matched layers (PMLs) are used in the ±x directions as outgoing boundaries. We compute the scattering matrix with up to 2W/λ = 1,000 plane-wave inputs from either the left or right and with all of the \(M^{\prime} =\) 2,000 outgoing plane waves. b, Computing time versus the number M of input angles using APF and other methods: conventional FDFD method using MaxwellFDFD with direct40 or iterative41 solvers for the full-basis solutions, RCWA using S4 (ref. 43) and the RGF method42. Open symbols are extrapolated from smaller M or smaller systems. The two ‘FDFD direct’ curves correspond to an unmodified version of MaxwellFDFD (blue squares) and one modified to have the LU factors reused for different inputs (black circles). c, Memory usage of different methods; grey-edged bars are extrapolated from smaller systems. d, Breakdown of the APF computing time into time used in building the matrix K, analysing and reordering it, and partially factorizing it.