论文标题
探索在RBF最小二乘线搭配方法中的过度采样，以进行表面扩散
Exploring Oversampling in RBF Least-Squares Collocation Method of Lines for Surface Diffusion
论文作者
论文摘要
本文研究了radial函数函数的数值行为最小二乘搭配（RBF-LSC）方法（mol）解决了表面扩散问题，这是基于[siam J. Numer所示的理论分析。肛门，61（3），1386-1404}]。具体而言，我们研究了过采样比的影响，被定义为用于准均匀集的RBF中心数量的搭配点数量，对特征值的稳定性，runge-kutta方法所采用的时间步进大小以及该方法的整体准确性。通过提供数值证据和见解，我们证明了使用RBF-LSC-MOL方法实现准确有效的解决方案的过采样比的重要性。我们的结果表明，过采样率在确定特征值的稳定性中起着至关重要的作用，并且我们提供了选择最佳的过采样比，以平衡准确性和计算效率。
This paper investigates the numerical behavior of the radial basis functions least-squares collocation (RBF-LSC) method of lines (MoL) for solving surface diffusion problems, building upon the theoretical analysis presented in [SIAM J. Numer. Anal., 61 (3), 1386-1404}]. Specifically, we examine the impact of the oversampling ratio, defined as the number of collocation points used over the number of RBF centers for quasi-uniform sets, on the stability of the eigenvalues, time stepping sizes taken by Runge-Kutta methods, and overall accuracy of the method. By providing numerical evidence and insights, we demonstrate the importance of the oversampling ratio for achieving accurate and efficient solutions with the RBF-LSC-MoL method. Our results reveal that the oversampling ratio plays a critical role in determining the stability of the eigenvalues, and we provide guidelines for selecting an optimal oversampling ratio that balances accuracy and computational efficiency.
