  The recurrence rebuild and retrieval method (R3M) is proposed in this paper
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 are 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
fully 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.
