{'fraction_non_alphanumeric': 0.011968085106382979, 'fraction_numerical': 0.0, 'mean_word_length': 5.491379310344827, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Circulant preconditioning in the volume integral equation method for nanophotonics

Wave propagation problems arising in nanophotonics can be considered high frequency, however typically this high frequency behavior is confined to one main propagation direction. It is well known that EM solvers employing iterative methods are slow to converge for high-frequency problems and thus require effective preconditioners. Here we employ a frequency-domain volume integral equation method based on a voxelized discretization. This leads to a three-level Toeplitz system. We make a circulant approximation to this matrix along only the long dimension and show that this proves to be an extremely effective preconditioner for a range of nanophotonics problems.