{'fraction_non_alphanumeric': 0.028, 'fraction_numerical': 0.0, 'mean_word_length': 6.084905660377358, '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}}
Combined Potential-Field Surface Formulations for Resonance-Free and Low-Frequency-Stable Analyses of Three-Dimensional Closed Conductors

We present combined formulations involving the recently developed potential integral equations (PIEs) together with field formulations, particularly the magnetic-field integral equation (MFIE), for accurate, efficient, and stable analyses of three-dimensional closed conductors. This kind of combinations are required since PIEs suffer from internal resonances and are prone to numerical issues for relatively large conductors. By combining PIEs with MFIE, we obtain low-frequency-stable implementations that can be employed at both low and high frequencies without any resonance artifacts in numerical results.