2022/08/13 by Weiming Sun, Zimao Zhang, Sun, Weiming +1
Computer Science · Engineering · #35C10 #35G15 #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA) #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2208.06666
openalex publication_date 2022/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the fourth paper, the application of the Fourier series multiscale method to the one- and two-dimensional convection-diffusion-reaction equations is implemented, where the Fourier series multiscale solutions are derived, the convergence characteristics of the Fourier series multiscale solutions are investigated by numerical examples, the schemes for application of the Fourier series multiscale method are optimized, and the multiscale characteristics of the convection-diffusion-reaction equations are demonstrated. The preliminary study on applications verifies the effectiveness of the present Fourier series multiscale method and provides a reliable reference which can be used for persistent improvement in computational performance of other multiscale methods.