{'fraction_non_alphanumeric': 0.009259259259259259, 'fraction_numerical': 0.0, 'mean_word_length': 5.7625, '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}}
Multigrid Methods for Anisotropic Edge Refinement

A finite element method with optimal convergence on nonsmooth three dimensional domains requires anisotropic mesh refinement towards the edges. Multigrid methods for anisotropic tensor product meshes are available and are based either on line (or plane) smoothers or on semicoarsening strategies. In this paper we suggest and analyze a new multigrid scheme combining semicoarsening and line smoothers to obtain a solver of optimal algorithmic complexity for anisotropic meshes along edges.