{'fraction_non_alphanumeric': 0.01589825119236884, 'fraction_numerical': 0.0, 'mean_word_length': 5.428571428571429, '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}}
Time Parallel Algorithms for Solution of Linear Parabolic PDEs

In this paper, fast time- and space-parallel algorithms for solution of parabolic PDEs are developed. It is shown that the seemingly strictly serial time-stepping procedures for solution of problem can be completely decoupled. This is achieved by developing time-parallel algorithms which allow the solution for all time steps to be computed in parallel. The time-parallel algorithms have a highly decoupled structure and hence can be efficiently implemented on emerging massively parallel MIMD architectures with minimum communication and synchronization overhead.