In this work, a modified multilevel augmented local radial basis function (RBF-FD) meshfree algorithm is developed. The primary goal is the level-by-level calculation and then level-by-level correction from coarsest level to finest level node points. Numerical experiments are presented to verify the accuracy and efficiency of our developed algorithms with 2D convection-diffusion problem and coupled nonlinear equations. Numerical results are presented through the figures and tables to demonstrate accuracy, efficiency, and convergence of the method. The developed scheme saves 56% of the CPU time for the 2D convection-diffusion problem and at least 86% of the CPU time for coupled nonlinear equations than the usual local RBF method available in the literature. The iteration matrix of the modified multilevel RBF-FD method satisfies the necessary and sufficient condition for convergence.

中文翻译：

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稳定对流扩散问题的改进多级无网格算法

在这项工作中，开发了一种改进的多级增强局部径向基函数 (RBF-FD) 无网格算法。主要目标是逐级计算，然后从最粗级到最细级节点逐级校正。数值实验通过二维对流扩散问题和耦合非线性方程来验证我们开发的算法的准确性和效率。数值结果通过图形和表格呈现，以证明该方法的准确性、效率和收敛性。所开发的方案为 2D 对流扩散问题节省了 56 %的 CPU 时间和至少 86 %与文献中可用的常用局部 RBF 方法相比，耦合非线性方程的 CPU 时间更少。改进的多级RBF-FD方法的迭代矩阵满足收敛的充要条件。