{'fraction_non_alphanumeric': 0.0319634703196347, 'fraction_numerical': 0.0, 'mean_word_length': 5.388349514563107, '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 efficient linear‐precision partition of unity basis for unstructured meshless methods

We describe an approach to construct approximation basis functions for meshless methods, which is based on the concept of a partition of unity. The approach has the following properties: (i) the grid consists of scattered nodes, (ii) the basis reproduces exactly complete linear polynomials, (iii) only the values of the approximated function at the nodes are used as unknowns, (iv) the construction of the basis is only slightly more expensive than the Shepard constant-precision method, and finally, (v) the method is applicable in any number of spatial dimensions.