{'fraction_non_alphanumeric': 0.011714589989350373, 'fraction_numerical': 0.0, 'mean_word_length': 4.766871165644171, '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}}
An Adaptive Domain Partitioning Technique for Meshfree-Type Methods

An overlapping domain partitioning based on adapting nodes is 
presented for the meshless-type methods. The decomposition of the 
domain is carried out based on the distribution of the nodes produced 
rather than the geometry of the problem. A set of adaptive nodes 
is first generated using the dimension reduction and equidistributing 
along the coordinate directions with respect to arc-length monitor. The 
domain is then partitioned in such a way that the same number of nodes 
are allocated to the subdomains. A radial basis function collocation 
method is applied to each subdomain followed by assembling the global 
solution from the subproblem's solutions. A generalized thin plate spline with sufficient smoothness is used as a 
basis function in the collocation method. Some numerical results will 
be presented to show the performance of the proposed method.