Design of microstructures with maximum permeability using FFT-based homogenization method

Despite the effectiveness of fast Fourier transform (FFT)-based methods, their application to microstructural topology optimization in fluid mechanics remains limited. With this background, this study proposes a novel framework combining FFT-based computational homogenization with gradient-based topology optimization for fluid flow problems. A detailed comparison with the finite element method (FEM) shows that the FFT-based solver achieves comparable accuracy while substantially reducing computational time and memory usage. The proposed method is applied to both two- and three-dimensional problems to investigate its feasibility and validity. The objective function is defined as the component of the homogenized permeability tensor, with sensitivities computed via the continuous adjoint method, allowing the same FFT-based scheme for forward and adjoint analyses. Characteristics of the proposed method, including iteration counts and computational time during optimization are discussed. The results confirm the effectiveness of FFT-based computational homogenization for fluidic microstructure design and provide insight into its numerical behavior. • An FFT-based microstructural design framework for fluid problems is proposed. • The framework achieves low memory consumption and fast computation. • The framework yields mechanically reasonable microstructures. • The framework handles high-resolution 3D topology optimization problems.