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The recurrence rebuild and retrieval method (R3M) is proposed in this article to accelerate the electromagnetic (EM) validations of large-scale digital coding metasurfaces (DCMs). R3M aims to accelerate the EM validations of DCMs with varied codebooks, which involves the analysis of a group of similar but not identical structures. The method transforms general DCMs to rigorously periodic arrays by replacing each coding unit with the macro unit, which comprises all possible coding states. The system matrix corresponding to the rigorously periodic array is globally shared for DCMs with arbitrary codebooks via implicit retrieval. The discrepancy of the interactions for edge and corner units is precluded by the basis extension of periodic boundaries. Moreover, the hierarchical pattern exploitation (HPE) algorithm is leveraged to efficiently assemble the system matrix for further acceleration. Due to the full utilization of the rigid periodicity, the computational complexity of R3M-HPE is theoretically lower than that of    $\mathcal {H}$   -matrix within the same paradigm. Numerical results for two types of DCMs indicate that R3M-HPE is accurate in comparison with commercial software. Besides, R3M-HPE is also compatible with the preconditioning for efficient iterative solutions. The efficiency of R3M-HPE for DCMs outperforms the conventional fast algorithms in both the storage and CPU time cost.

Fast Electromagnetic Validations of Large-Scale Digital Coding Metasurfaces Accelerated by Recurrence Rebuild and Retrieval Method