Periodic offshore structures are extensively utilized in coastal and offshore engineering; however, their hydrodynamic analysis poses significant challenges due to the substantial computational resources and storage required for large-scale problems. To address these challenges, an accelerated higher-order boundary element method (HOBEM) is proposed. This approach leverages the translation invariance of the Green's function to exploit the block Toeplitz structure inherent in the coefficient matrix of the discretized boundary integral equation. The dense matrix is systematically decomposed and embedded in a block circulant matrix, enabling the use of a fast Fourier transform-based iterative computational strategy. This forms a high-performance framework for matrix operations, integrating HOBEM with a fast Toeplitz-type matrix solver (FTMS), herein referred to as HOBEM-FTMS. Extensive numerical investigations demonstrate the accuracy, robustness, and computational efficiency of the proposed method. Case studies involving floating buoy arrays, hinged floating bridges, and offshore photovoltaic arrays validate their applicability to a wide range of periodic structures and elucidate the coupled effects of structural parameters, array configurations, mechanical constraints, and wave conditions. The results further indicate that resonance-prone behavior in periodic arrays can be strongly influenced—and in some cases effectively suppressed—not only by wave conditions and array geometry, but also by structural connectivity and mechanical constraints.
Cong et al. (Wed,) studied this question.