Mathematical Models and Numerical Simulations Based on High Precision Multiscale Algorithms
Guiping Shen · Procedia Computer Science · 2025
In view of the challenges of multi-scale problems in high-precision numerical simulation, this paper introduces a mathematical model based on a high-precision multi-scale algorithm, aiming to improve the accuracy and computational efficiency of simulation results and solve the shortcomings of traditional algorithms in multi-scale modeling. First, a mathematical model suitable for multi-scale problems is constructed, which fully considers the interaction of physical phenomena at different scales. Then, high-precision numerical methods, such as high-order finite element method and spectral method, are used to discretize the model to ensure the transfer accuracy between fine scale and coarse scale. Finally, adaptive grid encryption technology and multi-grid acceleration algorithm are used to optimize the calculation process, significantly improve the efficiency of numerical simulation, and reduce the consumption of computing resources. The temperature value under the fine-scale model shows fine fluctuations, such as the temperature at positions 1 to 10 slowly rises from 20.35 to 21.8, and then fluctuates between positions 11 and 20, which reflects its keen capture of temperature changes. At the coarse scale, the temperature fluctuation is relatively gentle. The high-precision multi-scale algorithm introduced in this paper can not only effectively improve the accuracy of numerical simulation, but also significantly optimize the computational efficiency and solve complex multi-scale problems in practical engineering problems.