{'fraction_non_alphanumeric': 0.0111731843575419, 'fraction_numerical': 0.0, 'mean_word_length': 5.764150943396227, '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}}
Taking Advantages of Translatory Symmetric Parts in Electromagnetic Models

In model parts which are geometrically symmetric but in which an unsymmetric field distribution is expected, a hybrid method based on a tensor-product grid of finite elements and orthogonal polynomials is applied. The finite elements ensure a flexible approximation of all geometrical details whereas the orthogonal polynomials applied along the direction of symmetry offer a superlinear convergence of the discretisation error. The hybrid method is coupled to a standard finite-element discretisation of the remaining model parts by the Lagrange-multiplier technique. The example indicates a substantial savings of computational resources.