{'fraction_non_alphanumeric': 0.036619718309859155, 'fraction_numerical': 0.0018779342723004694, 'mean_word_length': 5.580246913580247, '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}}
Preconditioned sparse-matrix/canonical grid algorithm for fast analysis of microstrip structure

In this paper, the sparse-matrix/canonical grid (SMCG) is used to analyze large-scale planar structures. Discretization of the corresponding integral equations by method of moment (MoM) with Rao-Wilton-Glisson (RWG) basis functions can model arbitrarily shaped planar structures, but usually leads to a fully populated matrix. The integral equation is solved by the sparse-matrix/canonical grid (SMCG) with fast Fourier transforms technique (FFT) to accelerate the matrix-vector multiplication. It reduces the memory requirement from O(N2) to O(N) and the operation complexity from O(N2) to O(N log N), where N is the number of unknowns. The resultant equations are then solved by the generalized minimal residual method (GMRES) with several preconditioning techniques employed to enhance its computational efficiency. Microstrip antenna arrays are analyzed and the numerical results show that the preconditioned GMRES can converge much faster than conventional GMRES.