The augmented moving least squares (AMLS) approximation is a meshless scheme to construct continuous functions by using fundamental solutions as basis functions. By incorporating the AMLS approximation into the method of fundamental solutions (MFS), the localized MFS can significantly reduce the computational load and accelerate the solution progress of the MFS. In this paper, error estimates of the AMLS approximation and the localized MFS are established for anisotropic heat conduction problems. Numerical examples are also presented to verify the convergence and accuracy of the methods.

中文翻译：

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关于各向异性导热问题的增广移动最小二乘逼近和基本解的局部化方法

增强移动最小二乘（AMLS）逼近是一种无网格方案，通过使用基本解作为基础函数来构造连续函数。通过将AMLS近似合并到基本解法（MFS）中，本地化MFS可以显着减少计算量并加快MFS的求解进度。在本文中，针对各向异性热传导问题，建立了AMLS近似和局部MFS的误差估计。数值例子也证明了该方法的收敛性和准确性。