{'fraction_non_alphanumeric': 0.01642935377875137, 'fraction_numerical': 0.0, 'mean_word_length': 5.977099236641221, '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}}
A Comparative Study of Calderón Preconditioners for PMCHWT Equations

The Calderón identities are used to precondition the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equations for wave scattering by dielectric objects. Based on the Calderón identities, several versions of preconditioners are presented and studied. The memory requirements and computational costs of different preconditioners are analyzed and discussed. The convergence properties of the iterative solutions and the solution accuracy of the Calderón preconditioned PMCHWT equations are also investigated and compared theoretically and numerically at different frequencies. With the help of the Calderón preconditioners, the convergence rate of the iterative solutions of the PMCHWT equations is significantly improved. Several numerical examples are given to show the performance of the Calderón preconditioners and to draw some conclusions.