Enhanced Fourier modal analysis for water-wave diffractions induced by submerged periodic blocks with arbitrary cross sections.

This article presents an enhanced Fourier modal analysis method for modeling water wave diffractions caused by submerged periodic planar blocks with large thicknesses or arbitrary-shaped cross sections. The approach improves computational stability by reformulating the boundary matching matrix as a Thomson–Haskell propagator and applying an enhanced transmission matrix (T-matrix) method, reducing precision loss by about 16 digits compared to conventional matrix inversion techniques. For complex block geometries, the method discretizes arbitrary cross sections into finite rectangular elements and introduces two computational approximations to balance accuracy and numerical stability. Numerical validations demonstrate the method's robustness and precision, making it suitable for applications such as designing coastal breakwaters and ocean wave energy converter arrays, while acknowledging limitations related to geometric symmetry and computational trade-offs.