{'fraction_non_alphanumeric': 0.016233766233766232, 'fraction_numerical': 0.0, 'mean_word_length': 5.494736842105263, '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}}
Schwarz waveform relaxation algorithms for semilinear reaction-diffusion equations

We introduce nonoverlapping domain decomposition algorithms of Schwarz 
waveform relaxation type for the semilinear reaction-diffusion 
equation. We define linear Robin and second 
order (or Ventcell) transmission conditions between the subdomains, which we prove to 
lead to a well defined and converging algorithm. We also propose nonlinear transmission conditions. Both types are based 
on best approximation problems for the linear equation and provide 
efficient algorithms, as the numerical results that we present here 
show.